diff --git a/.gitattributes b/.gitattributes
index 6825630198..782eb48e2b 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -18,3 +18,5 @@ research/coordinated-frames-and-entrance-banks/** -text -whitespace
 # Frozen PR210 package and round-nine evidence retain their audited bytes.
 research/five-stage-source527-banks/** -text -whitespace
 research/community-round9-audit/** -text -whitespace
+
+research/e8-early-reset-reuse/** -text
diff --git a/.github/workflows/early-reset-reuse.yml b/.github/workflows/early-reset-reuse.yml
new file mode 100644
index 0000000000..ad7aeacfde
--- /dev/null
+++ b/.github/workflows/early-reset-reuse.yml
@@ -0,0 +1,20 @@
+name: Verify early reset and kernel composition
+on: [push, pull_request]
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        python: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python }}
+      - run: python -B research/e8-early-reset-kernel/verify.py "$RUNNER_TEMP/early-reset-reuse"
+      - uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: early-reset-reuse-${{ matrix.python }}
+          path: ${{ runner.temp }}/early-reset-reuse
diff --git a/.github/workflows/eleven-hosting-selected.yml b/.github/workflows/eleven-hosting-selected.yml
new file mode 100644
index 0000000000..05c70a08d3
--- /dev/null
+++ b/.github/workflows/eleven-hosting-selected.yml
@@ -0,0 +1,20 @@
+name: Verify eleven-stage hosting-selected kernel
+on:
+  pull_request:
+  push:
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python-version: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python-version }}
+      - run: python -m pip install sympy
+      - run: python -B research/e8-eleven-hosting-selected/verify.py "$RUNNER_TEMP/eleven-hosting-selected"
+        env:
+          PYTHONINTMAXSTRDIGITS: '0'
+          PYTHONDONTWRITEBYTECODE: '1'
diff --git a/.github/workflows/hosting-selected-kernel.yml b/.github/workflows/hosting-selected-kernel.yml
new file mode 100644
index 0000000000..e84e761482
--- /dev/null
+++ b/.github/workflows/hosting-selected-kernel.yml
@@ -0,0 +1,19 @@
+name: Verify hosting-selected kernel
+on:
+  pull_request:
+  push:
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python-version: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python-version }}
+      - run: python -B research/e8-hosting-selected-kernel/verify.py "$RUNNER_TEMP/hosting-selected-kernel"
+        env:
+          PYTHONINTMAXSTRDIGITS: '0'
+          PYTHONDONTWRITEBYTECODE: '1'
diff --git a/.github/workflows/joint-frame-retiming.yml b/.github/workflows/joint-frame-retiming.yml
new file mode 100644
index 0000000000..eb5bbd2044
--- /dev/null
+++ b/.github/workflows/joint-frame-retiming.yml
@@ -0,0 +1,20 @@
+name: Verify joint B-phase frame retiming
+on: [push, pull_request]
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        python: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python }}
+      - run: python -B research/e8-joint-frame-retiming/verify.py "$RUNNER_TEMP/joint-frame-retiming" --replay-phases
+      - uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: joint-frame-retiming-${{ matrix.python }}
+          path: ${{ runner.temp }}/joint-frame-retiming
diff --git a/.github/workflows/r740-idle-hosting.yml b/.github/workflows/r740-idle-hosting.yml
new file mode 100644
index 0000000000..f70df7106c
--- /dev/null
+++ b/.github/workflows/r740-idle-hosting.yml
@@ -0,0 +1,20 @@
+name: Verify R740 idle-data hosting composition
+on: [push, pull_request]
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        python: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python }}
+      - run: python -B research/e8-r740-idle-hosting/verify.py "$RUNNER_TEMP/r740-idle-hosting"
+      - uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: r740-idle-hosting-${{ matrix.python }}
+          path: ${{ runner.temp }}/r740-idle-hosting
diff --git a/.github/workflows/rank138-idle-hosting.yml b/.github/workflows/rank138-idle-hosting.yml
new file mode 100644
index 0000000000..1aaa2ddfee
--- /dev/null
+++ b/.github/workflows/rank138-idle-hosting.yml
@@ -0,0 +1,19 @@
+name: Verify rank138 idle-data hosting
+on:
+  pull_request:
+  push:
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python-version: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python-version }}
+      - run: python -B research/e8-rank138-idle-hosting/verify.py "$RUNNER_TEMP/rank138-hosting"
+        env:
+          PYTHONINTMAXSTRDIGITS: '0'
+          PYTHONDONTWRITEBYTECODE: '1'
diff --git a/.github/workflows/split-centres-global.yml b/.github/workflows/split-centres-global.yml
new file mode 100644
index 0000000000..1adf7dc2ea
--- /dev/null
+++ b/.github/workflows/split-centres-global.yml
@@ -0,0 +1,23 @@
+name: Split-centres global kappa
+on:
+  pull_request:
+    paths:
+      - 'research/split-centres-global/**'
+      - '.github/workflows/split-centres-global.yml'
+  push:
+    paths:
+      - 'research/split-centres-global/**'
+      - '.github/workflows/split-centres-global.yml'
+  workflow_dispatch:
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python }}
+      - run: python -B research/split-centres-global/verify.py "$RUNNER_TEMP/split-centres-check"
diff --git a/research/e8-early-reset-kernel/EXPECTED.json b/research/e8-early-reset-kernel/EXPECTED.json
new file mode 100644
index 0000000000..d469e00f62
--- /dev/null
+++ b/research/e8-early-reset-kernel/EXPECTED.json
@@ -0,0 +1,10 @@
+{
+  "status": "PASS_CONDITIONAL_EARLY_RESET_KERNEL_ASSEMBLY",
+  "kappa": "226877503533617/200000000000000000",
+  "kappa_decimal": "0.001134387517668085",
+  "bit_lower": "227135162827151674463/200000000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "bit_template_sha256": "1460e30dd4aec672be972a81b00e244ed4ab396c6b2d5058e761edc447896623",
+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f"
+}
diff --git a/research/e8-early-reset-kernel/LICENSE b/research/e8-early-reset-kernel/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-early-reset-kernel/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
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+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
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+      the terms of any separate license agreement you may have executed
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+   6. Trademarks. This License does not grant permission to use the trade
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diff --git a/research/e8-early-reset-kernel/MANIFEST.json b/research/e8-early-reset-kernel/MANIFEST.json
new file mode 100644
index 0000000000..ed5e7bcc7a
--- /dev/null
+++ b/research/e8-early-reset-kernel/MANIFEST.json
@@ -0,0 +1,89 @@
+{
+  "files": {
+    "apply.py": "11eeac4b02521a3286160a87fdac080fefb11c25779d9eaec9f44b18d7b6c1ae",
+    "bit_audit.py": "f5d81ae080ee55d174feef6de2314113864a7e3e3d29c5559071c306edd2f272",
+    "bit_global.py": "50c76ed71ced48af2eacb8d8a91ab43dee035a3c818dcf85d0ad7e1ee032e5d9",
+    "bit_price.py": "36bf15803567a95b139a908461541bf19efe1f5b85fb31c270021833ab1393ee",
+    "combined.py": "83ba7f8deda264c283176c564d9d93dc8948edae0a8e8ed216b48240b5f74c85",
+    "EXPECTED.json": "9a55f73c6a3dd2b06377cbca76299b6672071419ebfe901aff9054ccca4b727a",
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE.md": "268f7fe8538d02bd8cc8f8b895d88035803fee05186ceb469204c7666190fbc7",
+    "PROOF.md": "4d7198ce615099b48013d23df6b8fa421428a78ce4de79e3757e8962e4d82a95",
+    "README.md": "cec5afd2670dcd994fb7c1f2b13cc5a6f8279b1843cd4e98180ec928d7018fe4",
+    "RESET12.json": "a310f1d3a8ec714e6dd12ec5364d16b9fa254527cf684b09dc1846d064e9b41c",
+    "RETIMING.json": "602d826e7bafd7faae4b0a7fd17be7d3edfd45f11a88f57ccd5b78e3f11c36f1",
+    "SELECTION.json": "b4b852b6286f5181fe58c3206a94426fae52acd246c0314eb8fca893f012a6f4",
+    "SOURCE.json": "cadea46917e4c63babc6dc33fe8acf90f8916fbb1599393326e5297fb251bdd3",
+    "source_span.py": "4772d177f37254c6f854af5ee3871aca193cfb24307a53c143c3bf517e56631e",
+    "VALIDATION.json": "3a1277872ee120060e3853b86bd4051369e1ddbc91baea993fdcc70643c8337c",
+    "verify.py": "16c07414bc956744dc93b8e35b642267ea9819be922b0d3e081c543fdbf92a70",
+    "local-evidence/ASSEMBLY-118.json": "3e610791f14777e6024adfe562175d51cd5dbeb2ce585f59d56d58092277bac1",
+    "local-evidence/ASSEMBLY.json": "7c3cc4b503e4cf0fd3e050be46ad0da183c5b1c490f4901245df944fd9d6194e",
+    "local-evidence/AUDIT-118.json": "cd37be4c487f924490c78052a36a8e091b261a7beb60f67f495779078f6ab906",
+    "local-evidence/AUDIT.json": "76a146a9123d8b653e6e46ff93f153653f9cefd0f5c3fdd264a59f1322110262",
+    "local-evidence/BIT-PRICE-118.json": "97e29c84202255a6468bb0444f3438910e7ab4e19bbadb89636ede78376a9306",
+    "local-evidence/BIT-PRICE.json": "9a4a320cab1ce62b0c2329ac1bf3b81f73580fd603a406e4bfaae2962dfdad35",
+    "local-evidence/fill160-35-subsets.json": "98917ba575fd1200d9b57d0ecf9a4d68bdec15ad29929db52c4f127ef7633dd6",
+    "local-evidence/fill160-changed-assembly.json": "9a3f1c219d93dc27744a89018722b2bc82f96a3ba58fb8557804d30ba62b051d",
+    "local-evidence/fill160-initial314-storage-archive.json": "0f55a49b2c3b65865fbc13ff3629096de0c6969e6c230389d90d9d42a9641f43",
+    "local-evidence/fill160-initial314-storage-failure.json": "d3c7133ac8fbd8acec584f7f04caea693aaa9e2dbb4b0cefb37e9eeaf477752b",
+    "local-evidence/fill160-packaging-failure.json": "bb0a5af0c10f33271d0ba6b6a731cab960ea5def6ac7208f59b94677ba6644e4",
+    "local-evidence/fill160-tested-manifest.json": "8fb34d3d7d9819b915a7b734d63b18772c30b1312e89e1e96b8731ce90dd731f",
+    "local-evidence/fill160-verification-provenance.json": "68e74e0dc8ed940a6a6a3f1bc0df1b4277cbcabd222628004a6a9270a30310e8",
+    "local-evidence/FULL-PYTHON311.json": "62b37525bf7b60c0d9101ed571681f3bf46ea75df065939864307e4986018332",
+    "local-evidence/FULL-PYTHON314.json": "85797531db037d06fb597a4c9b6ef6bd71e6a0ab4f220ae70b1b6bf3aeda205f",
+    "local-evidence/full118-python311.json": "368b3d851919f77e6865b51cec731fc5bd0f16e0bd494fbaa2df5b57b9342d1c",
+    "local-evidence/full118-python314.json": "2bb62d9bc89834463959ce755f886e58793ded811dba26b038c20626ef90c814",
+    "local-evidence/GLOBAL-118.json": "a7491dfd2ff51d0574a6e46e3b100531969219dc41d93afbaca38ee3afbfa7e7",
+    "local-evidence/GLOBAL.json": "16c4e829eea1b2d12b70cec7e6a9c0e33ea0eae98a40894a3b779790fd2efbb3",
+    "local-evidence/reset12-reconstruction.json": "178f9fef29a4f7e18c9a3abebf455bb7c0545a85e2bdfdda6d6def5afc8f9239",
+    "local-evidence/reset12-retimed-assembly.json": "a54ca18bca34c7407872dded5402b463be2c76bab271248e519bbd0492b3f575",
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+}
diff --git a/research/e8-early-reset-kernel/NOTICE.md b/research/e8-early-reset-kernel/NOTICE.md
new file mode 100644
index 0000000000..a10bce204c
--- /dev/null
+++ b/research/e8-early-reset-kernel/NOTICE.md
@@ -0,0 +1,3 @@
+Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0.
+
+New contribution: composition of twelve early bit resets, 121 revalidated response-kernel relations and ten exact frame retimings. Earlier revisions combined eleven resets with 110 and then 118 relations. Chafik Boukhalfa/chafreaky #417 supplied the kernel principle and independent replay; #435 supplied the source selection and mixed-width bank implementation. icekylinx #433 supplied split centres and source-basis reuse; ai-nanachi #426 supplied clean-reset reuse; Zhihao Chen #425/#386, Dylan Crow #370 and Jacob Sussman supplied the inherited construction. All vendored notices and parent sources remain preserved.
diff --git a/research/e8-early-reset-kernel/PROOF.md b/research/e8-early-reset-kernel/PROOF.md
new file mode 100644
index 0000000000..0b1bc9e65e
--- /dev/null
+++ b/research/e8-early-reset-kernel/PROOF.md
@@ -0,0 +1,15 @@
+# Composed response cancellation after early helper reuse
+
+First reconstruct the eleven early clean resets using the pinned earlier-reset package, including fresh compensation and cleanup. Apply the twelfth reset at position 1141: helper 460 is cleared using parents 455, 708 and 709 at frame 470 before aliasing logical helper 962 onto it. Recompute compensation and cleanup, with R746. Its exact all-column target response determines which remapped kernel relations remain valid. Retain a pivot p with entrance E and donors D only if response(p) equals the XOR of donor responses, E lies inside each participant's first frame, pivots and donors are disjoint, and each shared donor serves a single entrance. Omit entries invalidated by physical aliases, changed responses, or changed first frames. Choose total entrance rank divisible by eight for exact bank packing.
+
+Remove pivot columns from the initial zero-frame target compensation. Start each pivot at E, emit donor += pivot at E before the main word, and emit the inverse at the full frame after cleanup. The exact response relation cancels the omitted compensation. The entire composed program is replayed on all independent columns; the PR417/435 auditor additionally checks integer source-span legality. All unchanged rational frames and every nested/reflected transition are independently checked by the emitted-template audit.
+
+Residual helper width is 8 minus its entrance rank. With eight replicas, width-seven slots are packed eight at a time with one width-eight slot; width-four slots pack sixteen at a time; remaining width-eight slots pack eight at a time. Every bank is full, every owner disjoint, every helper slot is accounted for, and all 72 emitted local invocations are checked. The emitted histogram, physical stock, coefficient growth, finite cost invoice, two exact moment engines, six bootstrap levels and 47 outer inequalities are recomputed after all transformations.
+
+No separately reported numerical gains are added. The complex supplier is unchanged and all its phases are freshly replayed by the full wrapper. All-size compiler, dirty-bank, compressed-window, restored-work, tape/common-grid, precision and analytic interfaces remain conditional assumptions. No new Lean theorem or unconditional multiplication bound is claimed.
+
+## Frame retiming
+
+After response cancellation, flatten gates into the identical ordered primitive ADD sequence. Apply only the ten source-bound frame substitutions in RETIMING.json. Require the old frame at each unique phase/index, preserve every target/source pair and all other word fields, and bind the resulting byte hash. Independent integer source-span and global rational frame checks prove legality of the final word; the exact scalar replay proves its identity. Recompute transition histograms and all costs after retiming, rather than adding isolated gains.
+
+A remaining half-bank of width-four slots is completed with width-eight slots. Every slot keeps its exact residual width; the independent auditor checks full coverage and disjoint ownership, rather than relying on the packing algorithm.
diff --git a/research/e8-early-reset-kernel/README.md b/research/e8-early-reset-kernel/README.md
new file mode 100644
index 0000000000..2cd902e920
--- /dev/null
+++ b/research/e8-early-reset-kernel/README.md
@@ -0,0 +1,9 @@
+# Twelve early resets, response cancellation and frame retiming
+
+Conditional kappa = 0.001134387517668085. Twelve early resets reduce R758 to R746. Revalidating the response kernel after physical reuse leaves 121 entries with entrance rank 160 and 122 donor slots. Ten exact frame changes preserve the primitive ADD sequence. The 726 complete width-64 helper banks per stage give 14,214 live and 14,223 physical families. The final emitted program is repriced from scratch.
+
+Run `python -B research/e8-early-reset-kernel/verify.py /absolute/new/output` using the Python standard library. This freshly replays every upstream phase and the pinned eleven-reset construction, applies RESET12.json, SELECTION.json and RETIMING.json, and independently audits the complete result.
+
+Before this draft update, all changed scalar/frame/source-span checks, both global programs, independent bank audits, two moments and finite assembly passed. Packaged reconstruction reproduces the exact tested word and rejects eight mutated witnesses. The complete 121-entry construction passed full Python 3.11 and 3.14 replays at code commit f5e0af60ae91e39528d63782ac06f4c6f0e956e3. Both terminal receipts and their eight top-level logs are under local-evidence/fill160-python311 and fill160-python314. The initial 3.14 attempt failed on storage capacity; its failure and verified archive receipt are retained. GitHub CI remains pending. The previous 116-entry version passed both full wrappers at code commit 6a1c6a308429ea11f64b679df6abdf2bf40436b0, with receipts retained under local-evidence/reset12-python311 and reset12-python314. Historical 110-entry and 118-entry full Python 3.11/3.14 receipts remain explicitly bound to earlier source hashes.
+
+All-size interfaces remain conditional assumptions; no unconditional multiplication theorem or new Lean proof is claimed.
diff --git a/research/e8-early-reset-kernel/RESET12.json b/research/e8-early-reset-kernel/RESET12.json
new file mode 100644
index 0000000000..acee5ef6d3
--- /dev/null
+++ b/research/e8-early-reset-kernel/RESET12.json
@@ -0,0 +1,18 @@
+{
+  "source_sha256": "98ffef9246c8bf6c537ab5e134321abea05cf0b7830c9e3fd92cbe4e88d8c308",
+  "word_sha256": "33fba385c1c69d6cbbe6c76e4d2eca9f69453a910f3c9e5e62f3e7b189510ded",
+  "entries": [
+    {
+      "position": 1141,
+      "new_helper": 962,
+      "retired_helper": 460,
+      "parents": [
+        455,
+        708,
+        709
+      ],
+      "frame": 470
+    }
+  ],
+  "R": 746
+}
diff --git a/research/e8-early-reset-kernel/RETIMING.json b/research/e8-early-reset-kernel/RETIMING.json
new file mode 100644
index 0000000000..e1ba4641a4
--- /dev/null
+++ b/research/e8-early-reset-kernel/RETIMING.json
@@ -0,0 +1,139 @@
+{
+  "status": "NOMINATION_NEEDS_EXACT_REPLAY",
+  "source_sha256": "23cb3f6f84283aec61f2c82d9a43884932edc133bdd3fcbb7ee8deee7d7b2d60",
+  "output_sha256": "5391ede2abb1db54715beb12b687572d8c2822dd46f461a4baf240c6c4412aee",
+  "tested_gates": 14163,
+  "candidate_evaluations": 448,
+  "changes": [
+    {
+      "phase": "A",
+      "index": 1471,
+      "old_frame": 472,
+      "new_frame": 470,
+      "delta": {
+        "2": -1,
+        "1": 1,
+        "3": -1,
+        "4": 1
+      },
+      "score": -0.0009710109447872662
+    },
+    {
+      "phase": "A",
+      "index": 1474,
+      "old_frame": 473,
+      "new_frame": 469,
+      "delta": {
+        "2": -1,
+        "1": 1,
+        "3": -1,
+        "4": 1
+      },
+      "score": -0.0009710109447872662
+    },
+    {
+      "phase": "A",
+      "index": 1485,
+      "old_frame": 476,
+      "new_frame": 468,
+      "delta": {
+        "2": -1,
+        "1": 1,
+        "3": -1,
+        "4": 1
+      },
+      "score": -0.0009710109447872662
+    },
+    {
+      "phase": "A",
+      "index": 1488,
+      "old_frame": 477,
+      "new_frame": 467,
+      "delta": {
+        "2": -1,
+        "1": 1,
+        "3": -1,
+        "4": 1
+      },
+      "score": -0.0009710109447872662
+    },
+    {
+      "phase": "A",
+      "index": 1499,
+      "old_frame": 480,
+      "new_frame": 466,
+      "delta": {
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+        "1": 1,
+        "3": -1,
+        "4": 1
+      },
+      "score": -0.0009710109447872662
+    },
+    {
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+      "new_frame": 465,
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+        "3": -1,
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+      },
+      "score": -0.0009710109447872662
+    },
+    {
+      "phase": "A",
+      "index": 1516,
+      "old_frame": 485,
+      "new_frame": 463,
+      "delta": {
+        "2": -1,
+        "1": 1,
+        "3": -1,
+        "4": 1
+      },
+      "score": -0.0009710109447872662
+    },
+    {
+      "phase": "A",
+      "index": 1529,
+      "old_frame": 489,
+      "new_frame": 461,
+      "delta": {
+        "2": -1,
+        "1": 1,
+        "3": -1,
+        "4": 1
+      },
+      "score": -0.0009710109447872662
+    },
+    {
+      "phase": "A",
+      "index": 1542,
+      "old_frame": 493,
+      "new_frame": 459,
+      "delta": {
+        "2": -1,
+        "1": 1,
+        "3": -1,
+        "4": 1
+      },
+      "score": -0.0009710109447872662
+    },
+    {
+      "phase": "A",
+      "index": 1622,
+      "old_frame": 515,
+      "new_frame": 458,
+      "delta": {
+        "2": -1,
+        "1": 1,
+        "3": -1,
+        "4": 1
+      },
+      "score": -0.0009710109447872662
+    }
+  ]
+}
diff --git a/research/e8-early-reset-kernel/SELECTION.json b/research/e8-early-reset-kernel/SELECTION.json
new file mode 100644
index 0000000000..18af4900ce
--- /dev/null
+++ b/research/e8-early-reset-kernel/SELECTION.json
@@ -0,0 +1,1461 @@
+{
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+  "input_sha256": "33fba385c1c69d6cbbe6c76e4d2eca9f69453a910f3c9e5e62f3e7b189510ded",
+  "output_sha256": "23cb3f6f84283aec61f2c82d9a43884932edc133bdd3fcbb7ee8deee7d7b2d60",
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diff --git a/research/e8-early-reset-kernel/SOURCE.json b/research/e8-early-reset-kernel/SOURCE.json
new file mode 100644
index 0000000000..5b994b39a1
--- /dev/null
+++ b/research/e8-early-reset-kernel/SOURCE.json
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+        "path": "research/split-centres-kernel/vendor/kernel417/stages.py",
+        "git_blob": "9ef95d52f4b2ba0389bb2edb15228da698dd75f4",
+        "sha256": "e73ab7836519510ed30dd7e3022dae557fa50fc513d723197929bff741859668"
+      }
+    ]
+  },
+  "scope": "Twelve early resets, 121 revalidated response relations and ten frame retimings, all repriced on the final emitted word.",
+  "composition_update": "The previous 118-entry R747 word is historical. An additional chronological reset gives R746; filter/remap response relations to entrance rank 160, then apply ten frame changes with unchanged primitive ADD order."
+}
diff --git a/research/e8-early-reset-kernel/VALIDATION.json b/research/e8-early-reset-kernel/VALIDATION.json
new file mode 100644
index 0000000000..7c2b61679a
--- /dev/null
+++ b/research/e8-early-reset-kernel/VALIDATION.json
@@ -0,0 +1,10 @@
+{
+  "status": "PASS_FULL_WRAPPER_PYTHON311_AND_314",
+  "kappa": "0.001134387517668085",
+  "entries": 121,
+  "total_entrance_rank": 160,
+  "R": 746,
+  "scope": "Fresh full parent phases and complete 121-entry composed program passed on both Python versions. Initial Python 3.14 attempt failed on SSD capacity; preserved and retried after verified lossless archival. GitHub CI pending.",
+  "tested_code_commit": "f5e0af60ae91e39528d63782ac06f4c6f0e956e3",
+  "tested_manifest_sha256": "8fb34d3d7d9819b915a7b734d63b18772c30b1312e89e1e96b8731ce90dd731f"
+}
diff --git a/research/e8-early-reset-kernel/apply.py b/research/e8-early-reset-kernel/apply.py
new file mode 100644
index 0000000000..68e7669351
--- /dev/null
+++ b/research/e8-early-reset-kernel/apply.py
@@ -0,0 +1,77 @@
+"""Apply a source-bound subset of PR435/417 response relations after PR434 resets."""
+from pathlib import Path
+import copy,hashlib,json,sys
+from collections import defaultdict,Counter
+ROOT=Path(__file__).resolve().parent
+
+def reconstruct(raw,s):
+ assert hashlib.sha256(raw).hexdigest()==s['input_sha256'];c=json.loads(raw);w=copy.deepcopy(c);v=c['v'];n=2*v+c['R'];frames=[sum(1<<x for x in f) for f in c['frames']];fids={m:i for i,m in enumerate(frames)};response=Counter();first={}
+ for f,d,ss in c['D']:
+  assert not frames[f]
+  for x in ss:response[x]^=1<<(d-v)
+ for phase in ('A','B','C'):
+  for f,d,ss in c[phase]:
+   for x in [d]+ss:
+    if x>=2*v and f:first.setdefault(x,frames[f])
+ pivots={};donors={};by=defaultdict(list)
+ for lines,p,ds in s['entries']:
+  E=sum(1<<x for x in lines);assert E in fids and E and 2*v<=p<n and p not in c['ret'] and p not in pivots and p not in donors and c['start'][p]==0
+  z=response[p]
+  for d in ds:
+   assert 2*v<=d<n and d not in c['ret'] and d not in pivots and d!=p and c['start'][d]==0
+   assert donors.setdefault(d,E)==E;z^=response[d];by[d,E].append(p)
+  assert not z and all(E&first[x]==E for x in [p]+ds)
+  pivots[p]=E
+ assert not set(pivots)&set(donors)
+ for p,E in pivots.items():w['start'][p]=fids[E]
+ w['D']=[[f,d,[x for x in ss if x not in pivots]] for f,d,ss in w['D']]
+ w['A']=[[fids[E],d,sorted(ps)] for (d,E),ps in sorted(by.items())]+w['A'];w['C']+=[[c['final'][0],d,sorted(ps)] for (d,E),ps in sorted(by.items())]
+ data=json.dumps(w,sort_keys=True,separators=(',',':')).encode();assert hashlib.sha256(data).hexdigest()==s['output_sha256'];return data
+
+def retime(raw,s):
+ assert hashlib.sha256(raw).hexdigest()==s['source_sha256']
+ original=json.loads(raw);w=copy.deepcopy(original)
+ for phase in ('D','A','B','C'):
+  w[phase]=[[f,d,[x]] for f,d,ss in w[phase] for x in ss]
+ seen=set()
+ for z in s['changes']:
+  phase,i=z['phase'],z['index'];assert phase in ('D','A','B','C') and (phase,i) not in seen;seen.add((phase,i))
+  assert 0<=i<len(w[phase]) and w[phase][i][0]==z['old_frame'] and 0<=z['new_frame']<len(w['frames'])
+  w[phase][i][0]=z['new_frame']
+ for phase in ('D','A','B','C'):
+  assert [(d,x) for _,d,ss in original[phase] for x in ss]==[(d,x) for _,d,ss in w[phase] for x in ss]
+ data=json.dumps(w,sort_keys=True,separators=(',',':')).encode()
+ assert hashlib.sha256(data).hexdigest()==s['output_sha256'];return data
+
+if __name__=='__main__':
+ import importlib.util
+ spec=importlib.util.spec_from_file_location('early_reset',ROOT.parent/'e8-early-reset-reuse/replay.py');reset=importlib.util.module_from_spec(spec);spec.loader.exec_module(reset)
+ raw=Path(sys.argv[1]).read_bytes();out=Path(sys.argv[2]);s=json.loads((ROOT/'SELECTION.json').read_text());rs=json.loads((ROOT/'RESET12.json').read_text());ts=json.loads((ROOT/'RETIMING.json').read_text())
+ reset_raw=reset.reconstruct(raw,rs);kernel_raw=reconstruct(reset_raw,s);data=retime(kernel_raw,ts)
+ controls=[]
+ for name in ('wrong reset source','missing reset parent','wrong insertion time'):
+  bad=copy.deepcopy(rs);rr=raw
+  if name=='wrong reset source':rr+=b' '
+  elif name=='missing reset parent':bad['entries'][0]['parents'].pop()
+  else:bad['entries'][0]['position']=0
+  try:reset.reconstruct(rr,bad)
+  except AssertionError:controls.append(name)
+  else:raise AssertionError(name)
+ for name in ('wrong kernel source','missing donor','duplicate pivot'):
+  bad=copy.deepcopy(s);rr=reset_raw
+  if name=='wrong kernel source':rr+=b' '
+  elif name=='missing donor':bad['entries'][0][2].pop()
+  else:bad['entries'][1][1]=bad['entries'][0][1]
+  try:reconstruct(rr,bad)
+  except AssertionError:controls.append(name)
+  else:raise AssertionError(name)
+ for name in ('wrong old frame','duplicate frame change'):
+  bad=copy.deepcopy(ts)
+  if name=='wrong old frame':bad['changes'][0]['old_frame']=-1
+  else:bad['changes'].append(copy.deepcopy(bad['changes'][0]))
+  try:retime(kernel_raw,bad)
+  except AssertionError:controls.append(name)
+  else:raise AssertionError(name)
+ out.write_bytes(data)
+ result=dict(status='PASS_FROZEN_RESET_KERNEL_RETIMING',input_sha256=rs['source_sha256'],reset_sha256=rs['word_sha256'],kernel_sha256=s['output_sha256'],output_sha256=ts['output_sha256'],entries=len(s['entries']),total_entrance_rank=s['total_entrance_rank'],donor_slots=s['donor_slots'],new_frames=0,frame_changes=len(ts['changes']),additional_resets=len(rs['entries']),controls=controls)
+ (out.parent/'bit-kernel-receipt.json').write_text(json.dumps(result,indent=2)+'\n');print(json.dumps(result))
diff --git a/research/e8-early-reset-kernel/bit_audit.py b/research/e8-early-reset-kernel/bit_audit.py
new file mode 100644
index 0000000000..083ee8192f
--- /dev/null
+++ b/research/e8-early-reset-kernel/bit_audit.py
@@ -0,0 +1,129 @@
+# Adapted with exact rational span checks by icekylinx; Codex assistance.
+"""Independent audit of the emitted bit template, including mutation controls.
+Prepared by Zhihao Chen with OpenAI Codex assistance; Apache-2.0.
+"""
+import argparse, copy, gzip, hashlib, json, struct, time
+from collections import Counter, defaultdict
+from pathlib import Path
+from fractions import Fraction as Q
+
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out
+    blob=gzip.decompress((out/'GLOBAL-TEMPLATE.json.gz').read_bytes()); t=json.loads(blob)
+    g=json.loads((out/'GLOBAL.json').read_text()); geo=json.loads((out/'GEOMETRY.json').read_text())
+    assert hashlib.sha256(blob).hexdigest()==g['template_sha256']
+    assert t['geometry_sha256']==sha(out/'GEOMETRY.json') and t['source_record_sha256']==sha(a.local_check/'records/249-records.bin')
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    records=list(struct.iter_unpack('<6i',(a.local_check/'records/249-records.bin').read_bytes()))
+    word=json.loads((a.local_check/'bit-source-centres.json').read_text())
+    assert g['word_sha256']==sha(a.local_check/'bit-source-centres.json')
+    def rank(rows):
+        piv={}
+        for rr in rows:
+            row=list(map(Q,rr))
+            for k,b in sorted(piv.items()):
+                q=row[k]
+                if q:row=[x-q*y for x,y in zip(row,b)]
+            k=next((j for j,x in enumerate(row) if x),None)
+            if k is not None:
+                q=row[k];piv[k]=[x/q for x in row]
+        return len(piv)
+    dimensions={};proj={}
+    for key,f in fs.items():
+        k=int(key);B=f['B'];roots=[word['lines'][j] for j in word['frames'][k]]
+        assert rank(B)==f['dim']==rank(B+roots)==rank(roots)
+        dimensions[k]=f['dim'];proj[k]=B
+    sets=[set(f) for f in word['frames']];pairs={}
+    for op,x,y,c,r,z in records:
+        if op==0:
+            assert sets[y]<=sets[c] and dimensions[c]-dimensions[y]==r
+            pairs[y,c]=r
+    # Positive definite rational form: exact inclusion implies commuting
+    # orthogonal projectors and rank(P_V-P_U)=dim(V)-dim(U), also in reflection.
+    assert len(proj)==len(word['frames'])
+    expected={}
+    for rev in (False,True):
+        es=[]
+        for op,x,y,c,f,z in (reversed(records) if rev else records):
+            if op==0: es.append([0,x,c if rev else y,y if rev else c,f,int(rev)])
+            elif op==1: es.append([1,x,y,-c if rev else c,f,int(rev)])
+            elif op==(3 if rev else 2): es.append([2,x,y,c,f,abs(dimensions[c]-dimensions[f]),int(rev)])
+            else: es.append([3,x,y,c,f,z,int(rev)])
+        expected['reverse' if rev else 'forward']=es
+    assert t['local_programs']==expected
+
+    st=json.loads((a.local_check/'records/249-states.json').read_text())
+    width=[8-dimensions[st['initial'][str(i)]] for i in range(240,986)]; ENT=sum(8-x for x in width); assert ENT%8==0
+    NB=(8*746-ENT)//8; LIVE=7680+9*NB; assert g['live']==LIVE
+    def validate(q,check_profile=True):
+        assert (q['m'],q['live'],q['replicas'],q['stages'])==(64,LIVE,8,9)
+        assert q['bank_padding'] is None and q['local_programs']==expected
+        hist=Counter(); occupation=defaultdict(set); calls=set()
+        for c in q['calls']:
+            st,rep,p=c['stage'],c['replica'],c['pair']; rev=c['orientation']=='reverse'
+            assert 0<=st<9 and 0<=rep<8 and p==max(0,(st-1)//2)
+            assert rev==(st in (1,3,5,7)) and (st,rep) not in calls; calls.add((st,rep))
+            own=c['owners']; assert len(own)==986
+            assert len({(f,tuple(r)) for f,r in own})==986
+            for i,(family,route) in enumerate(own):
+                assert 0<=family<LIVE
+                if i<240:
+                    side=i//120; side=1-side if rev else side
+                    assert family==rep*960+(2*p+side)*120+i%120 and route==['data',st,i%120]
+                else:
+                    j=i-240; assert route[0]=='bank' and route[2]==width[j] and 7680+st*NB<=family<7680+(st+1)*NB
+                    cells=set(range(route[1],route[1]+route[2])); assert cells<=set(range(64)) and not (cells & occupation[family])
+                    occupation[family]|=cells
+            for e in q['local_programs'][c['orientation']]:
+                if e[0]==0 and e[4]: hist[e[4]]+=1
+                if e[0]==2: hist[e[5]]+=1
+        assert calls=={(s,r) for s in range(9) for r in range(8)}
+        assert set(occupation)==set(range(7680,LIVE)) and all(s==set(range(64)) for s in occupation.values())
+        levels=[-1]*4; scalar=[1<<i for i in range(8)]; seen=[]; br=0; exchanged=False
+        for e in q['schedule']:
+            if e['kind']=='local_cover_sweep':
+                s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1 and not exchanged
+                src,dst=(2*p+1,2*p) if rev else (2*p,2*p+1)
+                scalar[dst]^=scalar[src]; levels[p]=s; seen.append(s)
+            elif e['kind']=='idle':
+                p,src,dst,r=e['pair'],e['source_level'],e['target_level'],e['rank']
+                assert levels[p]==src and src<=dst<=8
+                assert r==7*(dst-src); levels[p]=dst
+                if r: hist[r]+=1920
+            elif e['kind']=='bridge':
+                d,s=e['dst'],e['src']; assert levels[d]==levels[s] and e['coefficient'] in (-1,1)
+                scalar[2*d]^=scalar[2*s]; scalar[2*s+1]^=scalar[2*d+1]; br+=1
+            else:
+                assert e['kind']=='exchange' and levels==[8]*4 and not exchanged
+                for p in range(4): scalar[2*p],scalar[2*p+1]=scalar[2*p+1],scalar[2*p]
+                exchanged=True
+        assert exchanged and scalar==[1<<i for i in range(8)] and seen==list(range(9)) and br==9
+        assert 64*LIVE-sum(r*n for r,n in hist.items())==2496
+        if check_profile: assert hist==Counter({int(k):v for k,v in g['profile'].items()})
+        return hist
+    hist=validate(t)
+    controls=[]
+    def rejects(name,mutator):
+        q=copy.deepcopy(t); mutator(q)
+        try: validate(q)
+        except (AssertionError,KeyError,IndexError): controls.append(name)
+        else: raise AssertionError('mutation accepted: '+name)
+    rejects('omit an idle child',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='idle')))
+    rejects('omit a bridge',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='bridge')))
+    rejects('omit terminal exchange',lambda q:q['schedule'].pop())
+    rejects('remove a local invocation',lambda q:q['calls'].pop())
+    rejects('re-use a helper bank slot',lambda q:q['calls'][0]['owners'].__setitem__(241,q['calls'][0]['owners'][240]))
+    rejects('understate live stock',lambda q:q.__setitem__('live',LIVE-1))
+    rejects('omit a local paid move',lambda q:q['local_programs']['forward'].pop(next(i for i,e in enumerate(q['local_programs']['forward']) if e[0]==0)))
+    rejects('wrong reflected copy charge',lambda q:q['local_programs']['reverse'][next(i for i,e in enumerate(q['local_programs']['reverse']) if e[0]==2)].__setitem__(5,0))
+    result=dict(status='PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT',template_sha256=g['template_sha256'],
+                source_frames=len(proj),exact_nested_frame_pairs=len(pairs),exact_reflected_pairs=len(pairs),
+                orthogonal_lift_argument='Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.',
+                exact_bank_families=LIVE-7680,mixed_width_slots=True,entrance_rank_total=ENT,mutations_rejected=controls,
+                profile=dict(sorted(hist.items())),seconds=time.monotonic()-start)
+    (out/'AUDIT.json').write_text(json.dumps(result,indent=2)+'\n'); print(json.dumps(result),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-early-reset-kernel/bit_global.py b/research/e8-early-reset-kernel/bit_global.py
new file mode 100644
index 0000000000..fb15e79c6b
--- /dev/null
+++ b/research/e8-early-reset-kernel/bit_global.py
@@ -0,0 +1,262 @@
+# Adapted for the PR426/source-centre composition by icekylinx with Codex assistance.
+"""Source-bound compressed nine-stage bit template and exact scalar audits.
+
+Prepared by Zhihao Chen with OpenAI Codex assistance, Apache-2.0.
+The local E8 bit word is Dylan Crow's pinned PR #370 contribution.
+"""
+import argparse, gzip, hashlib, json, struct, time
+from collections import Counter
+from pathlib import Path
+
+H,V,R,L,K,T,M=8,120,746,9,4,8,64
+LOCAL=2*V+R; DATA=2*K*V*T
+
+def tile_banks(width):
+    """exact width-64 bank tiling of the per-stage helper slots (8 replicas x R helpers, slot width = 8 - entrance rank);
+    returns {(replica, helper): (bank, offset)} and the bank count; every bank is filled exactly (no padding)."""
+    slots=sorted(((width[h],rep,h) for rep in range(T) for h in range(R)),key=lambda x:(-x[0],x[1],x[2]))
+    bins=[]; place={}
+    by={}
+    for w_,rep,h in slots: by.setdefault(w_,[]).append((rep,h))
+    def take(w_):
+        return by[w_].pop(0) if by.get(w_) else None
+    # deterministic exact packing: width-7 slots go eight to a bank with one width-8 slot; other widths fill banks alone
+    for w_ in sorted(by,reverse=True):
+        if w_==8: continue
+        while by.get(w_):
+            b=len(bins); off=0; cont=[]
+            if w_==7:
+                for _ in range(8): rep,h=take(7); cont.append((rep,h,off,7)); off+=7
+                rep,h=take(8); cont.append((rep,h,off,8)); off+=8
+            else:
+                assert 64%w_==0
+                for _ in range(min(64//w_,len(by[w_]))): rep,h=take(w_); cont.append((rep,h,off,w_)); off+=w_
+                assert (64-off)%8==0
+                while off<64:
+                    rep,h=take(8); cont.append((rep,h,off,8)); off+=8
+            assert off==64; bins.append(cont)
+    while by.get(8):
+        cont=[]; off=0
+        for _ in range(8): rep,h=take(8); cont.append((rep,h,off,8)); off+=8
+        bins.append(cont)
+    for b,cont in enumerate(bins):
+        for rep,h,off,w_ in cont: place[rep,h]=(b,off,w_)
+    assert len(place)==T*R
+    return place,len(bins)
+
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+def write(p,x): p.write_text(json.dumps(x,indent=2)+'\n')
+
+def recipe():
+    out=[dict(kind='local',stage=0,pair=0,reverse=False)]; stage=1
+    for j in range(K):
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=True)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=1))
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=False)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=-1))
+    for j in reversed(range(K-1)): out.append(dict(kind='bridge',dst=j+1,src=j,coefficient=1))
+    out.append(dict(kind='exchange'))
+    return out
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--source',type=Path,required=True)
+    ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out; out.mkdir(parents=True,exist_ok=True)
+    wp=a.source/'bit-source-centres.json'; w=json.loads(wp.read_bytes())
+    inherited=Path('inherited/bit-geometry.json.gz')
+    geo=json.loads(gzip.decompress(inherited.read_bytes()))
+    base=Path('work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz')
+    original=json.loads(gzip.decompress(base.read_bytes()))
+    assert geo['word_sha256']==sha(base)
+    assert w['lines']==original['lines'] and w['frames'][:len(original['frames'])]==original['frames'] and w['form']==original['form']
+    kr=json.loads((a.source/'bit-kernel-receipt.json').read_text()); assert kr['output_sha256'] and len(w['frames'])==len(original['frames'])+kr['new_frames']
+    geo['inherited_geometry_sha256']=sha(inherited);geo['word_sha256']=sha(wp)
+    geo['reuse_scope']='Unchanged ports, rational frames, compressed windows and whole rank-eight bank slots; changed owners are replayed separately.'
+    write(out/'GEOMETRY.json',geo)
+    rp=a.local_check/'records/249-records.bin';raw=rp.read_bytes();rec=list(struct.iter_unpack('<6i',raw))
+    state=json.loads((a.local_check/'records/249-states.json').read_text())
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    dims={int(f):z['dim'] for f,z in fs.items()}
+    assert (state['v'],state['n'])==(V,LOCAL)
+    expected_adds=sum(e[0]==1 for e in rec)
+    initial=[state['initial'][str(i)] for i in range(LOCAL)]
+    final=[state['final'][str(i)] for i in range(LOCAL)]
+    assert all(dims[final[i]]==H for i in range(2*V,LOCAL))
+    width={i-2*V:H-dims[initial[i]] for i in range(2*V,LOCAL)}; ENT=sum(H-x for x in width.values()); assert ENT%8==0
+    place,NB=tile_banks(width); assert NB==(8*R-ENT)//8
+    LIVE=DATA+L*NB
+    streams={}; checks={}; localH=None
+    for reverse in (False,True):
+        cur=(final if reverse else initial)[:]+[-1]; val=[1<<i for i in range(LOCAL)]+[0]
+        norm=[1]*LOCAL+[0]; maxnorm=1; center=None; hist=Counter(); events=[]; copies=0; adds=0
+        dim=lambda f:H-dims[f] if reverse else dims[f]
+        for op,x,y,c,f,z in (reversed(rec) if reverse else rec):
+            if op==0:
+                oldf,newf=(c,y) if reverse else (y,c)
+                assert cur[x]==oldf and dim(newf)-dim(oldf)==f>=0
+                cur[x]=newf
+                if f: hist[f]+=1
+                events.append([0,x,oldf,newf,f,int(reverse)])
+            elif op==1:
+                assert cur[x]==cur[y]==f and x!=y and x<LOCAL
+                if center is not None: assert x!=center
+                if y==LOCAL: assert center is not None
+                if c&1: val[x]^=val[y]
+                norm[x]+=abs(c)*norm[y]; maxnorm=max(maxnorm,norm[x]); adds+=1
+                events.append([1,x,y,-c if reverse else c,f,int(reverse)])
+            elif op==(3 if reverse else 2):
+                assert center is None and y==LOCAL and cur[x]==c and val[LOCAL]==0
+                copy_rank=abs(dim(c)-dim(f)); assert copy_rank==8
+                assert z==(0 if reverse else copy_rank)
+                center=x; cur[LOCAL]=f; val[LOCAL]=val[x]; norm[LOCAL]=norm[x]
+                hist[copy_rank]+=1; copies+=1; events.append([2,x,LOCAL,c,f,copy_rank,int(reverse)])
+            else:
+                assert op==(2 if reverse else 3)
+                assert center==x and y==LOCAL and cur[x]==c and cur[LOCAL]==f
+                assert val[LOCAL]==val[x]
+                val[LOCAL]=0; norm[LOCAL]=0; cur[LOCAL]=-1; center=None
+                events.append([3,x,LOCAL,c,f,z,int(reverse)])
+        assert center is None and copies==9 and adds==expected_adds
+        assert cur[:LOCAL]==(initial if reverse else final)
+        for i in range(LOCAL):
+            want=(1<<i) ^ ((1<<(i-V)) if V<=i<2*V else 0)
+            assert val[i]==want
+        assert val[LOCAL]==0
+        if localH is None: localH=hist
+        else: assert localH==hist
+        key='reverse' if reverse else 'forward'; streams[key]=events
+        checks[key]=dict(copies=copies,adds=adds,records=len(events),all_columns=LOCAL,
+                         cancellation_free_row_l1=maxnorm,profile=dict(sorted(hist.items())),
+                         sha256=hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest())
+    assert sum(r*n for r,n in localH.items())==H*R-ENT+72+2*V*(H-1)
+
+    events=recipe(); levels=[-1]*K; schedule=[]; bridge_controls=[]
+    # Full scalar replay on separate dirty helpers for all nine stages.
+    # Physical banking then uses the separately checked injective cover owners.
+    n=2*K*V+L*R; vals=[1<<i for i in range(n)]+[0]; temp=n
+    stages=[]
+    for e in events:
+        if e['kind']=='local':
+            s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1
+            def mapper(i):
+                if i==LOCAL: return temp
+                if i<2*V:
+                    side=i//V; side=1-side if rev else side
+                    return (2*p+side)*V+i%V
+                return 2*K*V+s*R+i-2*V
+            before=vals[:]; opened=False
+            for z in streams['reverse' if rev else 'forward']:
+                if z[0]==0: continue
+                x,y=mapper(z[1]),mapper(z[2])
+                if z[0]==1:
+                    if z[3]&1: vals[x]^=vals[y]
+                elif z[0]==2:
+                    assert not opened; vals[temp]=vals[x]; opened=True
+                else:
+                    assert opened and vals[temp]==vals[x]; vals[temp]=0; opened=False
+            assert not opened
+            d=(2*p+(0 if rev else 1))*V; src=(2*p+(1 if rev else 0))*V
+            for t in range(V): before[d+t]^=before[src+t]
+            assert vals==before
+            levels[p]=s; schedule.append(dict(kind='local_cover_sweep',**{k:v for k,v in e.items() if k!='kind'}))
+            if s in (1,3,5):
+                j=(s+1)//2; assert levels[j]==-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7*(s+1),source_level=-1,target_level=s))
+            elif s in (2,4,6):
+                j=s//2; assert levels[j]==s-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7,source_level=s-1,target_level=s))
+            elif s==8:
+                for j in range(4):
+                    oldlevel=levels[j]; assert oldlevel==2*j+2
+                    schedule.append(dict(kind='idle',pair=j,rank=7*(8-oldlevel),source_level=oldlevel,target_level=8))
+                    levels[j]=8
+            stages.append(dict(stage=s,all_columns=n,helper_columns=L*R,reverse=rev))
+        elif e['kind']=='bridge':
+            d,s=e['dst'],e['src']; assert levels[d]==levels[s]
+            for t in range(V): vals[2*d*V+t]^=vals[2*s*V+t]; vals[(2*s+1)*V+t]^=vals[(2*d+1)*V+t]
+            schedule.append(e)
+        else:
+            assert levels==[8]*4
+            for j in range(K):
+                for t in range(V):
+                    x=2*j*V+t; y=(2*j+1)*V+t; vals[x],vals[y]=vals[y],vals[x]
+            schedule.append(e)
+    assert vals==[1<<i for i in range(n)]+[0]
+    # Integer scalar eight-bank matrix, with each individual bridge shear omitted.
+    def small(skip=-1):
+        z=[[int(i==j) for j in range(8)] for i in range(8)]; count=0
+        def add(d,s,c): z[d]=[x+c*y for x,y in zip(z[d],z[s])]
+        for e in events:
+            if e['kind']=='local':
+                p=e['pair']; add(2*p,2*p+1,-1) if e['reverse'] else add(2*p+1,2*p,1)
+            elif e['kind']=='bridge':
+                d,s,c=e['dst'],e['src'],e['coefficient']
+                for x,y,sgn in [(2*d,2*s,c),(2*s+1,2*d+1,-c)]:
+                    if count!=skip: add(x,y,sgn)
+                    count+=1
+            else:
+                for j in range(4): z[2*j],z[2*j+1]=z[2*j+1],[-x for x in z[2*j]]
+        return z,count
+    ident=[[int(i==j) for j in range(8)] for i in range(8)]
+    z,nb=small(); assert z==ident and nb==18
+    for skip in range(nb): assert small(skip)[0]!=ident; bridge_controls.append(skip)
+
+    paid=Counter(); calls=[]; assignment=set(); expanded=hashlib.sha256(); full_event_count=0
+    for e in events:
+        if e['kind']!='local': continue
+        s,p,rev=e['stage'],e['pair'],e['reverse']; ori='reverse' if rev else 'forward'
+        for rep in range(T):
+            owners=[]
+            for i in range(2*V):
+                side=i//V; side=1-side if rev else side
+                owners.append([rep*(2*K*V)+(2*p+side)*V+i%V, ['data',s,i%V]])
+            for r in range(R):
+                bank,off,w_=place[rep,r]
+                owners.append([DATA+s*NB+bank,['bank',off,w_]])
+                assignment.add((s,rep,r,bank,off))
+            assert len({(f,tuple(route)) for f,route in owners})==LOCAL
+            assert all(0<=f<LIVE for f,route in owners)
+            # Stream one full renamed instruction program into a source-bound
+            # digest, including exact owner route descriptors and reflection.
+            for z in streams[ori]:
+                op=z[0]
+                if op==0: paid[z[4]]+=bool(z[4]); mapped=[op,owners[z[1]],*z[2:]]
+                else:
+                    ox=owners[z[1]]; oy=owners[z[2]] if z[2]<LOCAL else [LIVE,['private',0]]
+                    mapped=[op,ox,oy,*z[3:]]
+                    if op==2: paid[z[5]]+=1
+                expanded.update((json.dumps(mapped,separators=(',',':'))+'\n').encode()); full_event_count+=1
+            calls.append(dict(stage=s,replica=rep,pair=p,orientation=ori,owners=owners,local_hash=checks[ori]['sha256']))
+    paid.pop(0,None)
+    assert len(assignment)==L*T*R==53712 and len(calls)==72
+    for e in schedule:
+        if e['kind']=='idle' and e['rank']: paid[e['rank']]+=2*V*T
+    mass=sum(r*c for r,c in paid.items()); assert M*LIVE-mass==2496
+    cf=checks['forward']['cancellation_free_row_l1']; cb=checks['reverse']['cancellation_free_row_l1']
+    prefix=(1<<nb)*cf**5*cb**4; charged_prefix=64*((prefix.bit_length()+63)//64);assert prefix<1<<charged_prefix
+    print('Fresh prefix bits',prefix.bit_length(),'charged',charged_prefix,flush=True)
+    template=dict(version='compressed-nine-e8-bit-v1',m=M,h=H,stages=L,replicas=T,live=LIVE,private_centre_reserve=9,
+                  cover='O(I_64/2,F_q) for admitted odd address primes q',loop_order='Each recipe phase: replicas then all cover classes; finish every local invocation before the next.',
+                  schedule=schedule,local_programs=streams,calls=calls,bank_padding=None,
+                  helper_route='owner (DATA + stage*NB + bank(replica,helper), isometry onto coordinates [offset, offset+width) of the bank, width = 8 - entrance rank; exact width-64 tiling, no padding)',banks_per_stage=NB,entrance_rank_total=ENT,
+                  data_route='owner (replica*960 + (2*pair+side)*120+port, d*rho_stage,port)',
+                  bit_operator='D_U exchanges the two address halves on projector U; D_I D_P = D_(I-P) exactly.',
+                  geometry_sha256=sha(out/'GEOMETRY.json'),source_record_sha256=sha(rp))
+    blob=json.dumps(template,separators=(',',':'),sort_keys=True).encode(); (out/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+    result=dict(status='PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE',h=H,m=M,v=V,R=R,replicas=T,live=LIVE,physical=LIVE+9,
+                word_sha256=sha(wp),source_records_sha256=sha(rp),local_checks=checks,scalar_stages=stages,
+                independent_unbanked_scalar_columns=n,all_scalar_columns_restored=True,
+                geometry_sha256=sha(out/'GEOMETRY.json'),template_sha256=hashlib.sha256(blob).hexdigest(),
+                emitted_program_sha256=expanded.hexdigest(),emitted_events=full_event_count,local_invocations=len(calls),
+                bank_assignments=len(assignment),banks_per_stage=NB,entrance_rank_total=ENT,mixed_width_slots=True,padding_calls=0,
+                profile=dict(sorted(paid.items())),paid_calls=sum(paid.values()),rank_mass=mass,deficit=2496,
+                maxchild=max(paid),halving_depth=2,halving_integer_inequality=[64**2,2*42**2],
+                local_additions=expected_adds,bridge_additions=18*V*T,copy_erase_episodes=9*72,
+                global_prefix_bound=str(prefix),global_prefix_bits=prefix.bit_length(),charged_prefix_bits=charged_prefix,
+                omitted_bridge_shears_rejected=bridge_controls,
+                scope='Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.',
+                seconds=time.monotonic()-start)
+    write(out/'GLOBAL.json',result)
+    print(json.dumps({k:v for k,v in result.items() if k not in ('local_checks','scalar_stages','global_prefix_bound')}),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-early-reset-kernel/bit_price.py b/research/e8-early-reset-kernel/bit_price.py
new file mode 100644
index 0000000000..005da012a3
--- /dev/null
+++ b/research/e8-early-reset-kernel/bit_price.py
@@ -0,0 +1,18 @@
+"""Exact price of the emitted bit program; no histogram supplied by discovery."""
+import json,importlib.util
+from fractions import Fraction as Q
+from pathlib import Path
+
+def load(name):
+ p=Path('work/pr361/code/engines')/(name+'.py');sp=importlib.util.spec_from_file_location('price_'+name,p);m=importlib.util.module_from_spec(sp);sp.loader.exec_module(m);return m
+p=Path('bit426-source-centres/global');g=json.loads((p/'GLOBAL.json').read_text());a=json.loads((p/'AUDIT.json').read_text())
+assert a['template_sha256']==g['template_sha256']
+H={int(r):n for r,n in a['profile'].items()};m,W=g['m'],g['live']
+M,B=load('moment'),load('base_two_moment');root=M.certify(H,m,W,True);lo,hi=Q(root['lower']),Q(root['upper'])
+fb=32*m*m*sum(H.values())
+def other(x):
+ l,u=B.moment(m,W,list(H.items()),x);a,b=B.moment(m,W,[(1,fb)],x);return l+a/10**16,u+b/10**16
+assert other(lo)[1]<1<other(hi)[0]
+root.update(source_template_sha256=g['template_sha256'],two_exact_engines=True)
+Path('BIT-PRICE.json').write_text(json.dumps(root,indent=2)+'\n')
+print('PASS two rational bit moments',root['lower'])
diff --git a/research/e8-early-reset-kernel/combined.py b/research/e8-early-reset-kernel/combined.py
new file mode 100644
index 0000000000..1007ea9d2b
--- /dev/null
+++ b/research/e8-early-reset-kernel/combined.py
@@ -0,0 +1,55 @@
+"""Fresh bit finite invoice and joint strict arithmetic for two changed suppliers.
+icekylinx, with Codex assistance. Inherited all-size interfaces remain conditional.
+"""
+import json,hashlib,importlib.util
+from pathlib import Path
+from fractions import Fraction as Q
+import os
+ROOT=Path(os.environ['E8_OUTPUT']);D=ROOT/'bit426-source-centres/global';C=ROOT/'split-centres'
+read=lambda p:json.loads(p.read_text())
+g=read(D/'GLOBAL.json');geo=read(D/'GEOMETRY.json');audit=read(D/'AUDIT.json')
+cx=read(C/'INTEGRATION.json');ca=read(C/'INDEPENDENT-REPLAY.json')
+assert audit['template_sha256']==g['template_sha256'] and ca['template_sha256']==cx['global_template_sha256']
+assert len(audit['mutations_rejected'])==8 and len(ca['mutation_controls_rejected'])==7
+P={int(r):z for r,z in audit['profile'].items()};m,W=64,g['live'];E=sum(P.values());T,L,R,V,K=8,9,746,120,4
+mass=sum(r*z for r,z in P.items());assert m*W-mass==2496 and g['live']==W
+physical=g['physical'];d=m*m;N=2*m
+unit=L*T*g['local_additions']+g['bridge_additions']
+J=8*T*L*(2*V+R)+8*(2*K*V*T)+2*g['bank_assignments']+2*g['copy_erase_episodes']
+high=16*(d+1)**2;good=8*m*m+8;compiler=128*N**3
+selectors=2*L*T*((W-1)+R*m*(geo['max_route_factors']+(m-1)+m))
+prefix=int(g['global_prefix_bound']);charged_prefix=64*((prefix.bit_length()+63)//64);assert prefix<1<<charged_prefix
+coefficient=unit+J*high+J*physical+E*(good+compiler)+16*m**3+g['copy_erase_episodes']+selectors+prefix+1
+two=(coefficient+1)**2*(E+1)**2
+charged_two=64*((two.bit_length()+63)//64);assert two<1<<charged_two and 2*max(P)**2<m*m
+row=2*(m*m+1)+9909+252;assert row==18355<20161
+assert geo['bad_prime_factors']==[2] and geo['route_denominators']==[1,2,4]
+def load(name):
+ p=ROOT/'work/pr361/code/engines'/(name+'.py');sp=importlib.util.spec_from_file_location('joint_'+name,p);mod=importlib.util.module_from_spec(sp);sp.loader.exec_module(mod);return mod
+M,Other,Outer=load('moment'),load('base_two_moment'),load('outer')
+root=M.certify(P,m,W,True);c=Q(root['lower']);grid=Q(1,10**18);b=Q(ca['complex_b'])
+fb=32*m*m*E
+lo,hi=Other.moment(m,W,list(P.items()),c);bl,bh=Other.moment(m,W,[(1,fb)],c)
+assert hi+bh/10**16<1
+eta=beta=Q(1,10**18);s=min(c,(1-beta)*b)-Q(1,10**24)
+assert 0<s<c and s<(1-beta)*b
+chain=[Q(384599,10**10)];cutoffs=[]
+def ceil(x):return -((-x.numerator)//x.denominator)
+for j in range(6):
+ old=chain[-1];a=(1-s)*s+s*old
+ gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+ cutoff=max(ceil(36/gap**2),ceil(2*(4+charged_two)/gap))
+ assert cutoff*gap**2>=36 and cutoff*gap>=2*(4+charged_two)
+ cutoffs.append(dict(gap=str(gap),cutoff_log2=str(cutoff)));chain.append(a)
+q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin/grid;k=grid*((ticks.numerator-1)//ticks.denominator)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}
+a=Outer.assembly(chain[-1],b,bridge,k,eta=eta,beta=beta)
+assert len(a['strict_constraints'])==47 and all(x>0 for x in a['strict_constraints'].values())
+controls=[]
+for name,kk,ee,bb in [('next_grid',k+grid,eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]:
+ try:Outer.assembly(chain[-1],b,bridge,kk,eta=ee,beta=bb)
+ except AssertionError:controls.append(name)
+ else:raise AssertionError(name)
+result=dict(status='PASS_CONDITIONAL_EARLY_RESET_KERNEL_ASSEMBLY',kappa=str(k),kappa_decimal=format(float(k),'.18f'),bit_lower=str(c),complex_lower=str(b),binding_component='bit',gain_over_pr425_percent=float(100*(k/Q(1048005508028206,10**18)-1)),bit_invoice=dict(prefix_bits=prefix.bit_length(),charged_prefix_bits=charged_prefix,coefficient_bits=coefficient.bit_length(),two_level_coefficient_bits=two.bit_length(),charged_two_level_coefficient_bits=charged_two,row_coefficient=row,live=W,physical=physical),strict_outer_constraints={n:str(x) for n,x in a['strict_constraints'].items()},outer_controls=controls,bootstrap=cutoffs,bit_template_sha256=g['template_sha256'],complex_template_sha256=cx['global_template_sha256'],scope='Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim.')
+(ROOT/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n')
+print(result['status'],result['kappa_decimal'],result['gain_over_pr425_percent'],result['bit_invoice'])
diff --git a/research/e8-early-reset-kernel/local-evidence/ASSEMBLY-118.json b/research/e8-early-reset-kernel/local-evidence/ASSEMBLY-118.json
new file mode 100644
index 0000000000..83bb28f6ee
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/ASSEMBLY-118.json
@@ -0,0 +1,103 @@
+{
+  "status": "PASS_CONDITIONAL_EARLY_RESET_KERNEL_ASSEMBLY",
+  "kappa": "45340333148791/40000000000000000",
+  "kappa_decimal": "0.001133508328719775",
+  "bit_lower": "1134794627881866057683/1000000000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr425_percent": 8.158623216822614,
+  "bit_invoice": {
+    "prefix_bits": 226,
+    "charged_prefix_bits": 256,
+    "coefficient_bits": 226,
+    "two_level_coefficient_bits": 488,
+    "charged_two_level_coefficient_bits": 512,
+    "row_coefficient": 18355,
+    "live": 14223,
+    "physical": 14232
+  },
+  "strict_outer_constraints": {
+    "bit_positive": "8865583030327078557349651159791103195758253628551574089325712854609428298691641374628468365814082531330986606348062624284395896648229682097440238805152128233500519/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "384311885347366755150348840208896804241746371448425910674287145390571701308358625371531634185917468669013393651937375715604103351770317902559761194847871766499481/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "30066013450793671/1000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "384311885347366745900453924534451491741746371448425910674287145390571701308358625371531634185917468669013393651937375715604103351770317902559761194847871766499481/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_positive": "4432791515163539269809242549568473040529475654484683848904602798753140060020107832704805884215399891037024937359948780811211341976052216764324222754346382019310020694847871766499481/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_internal": "8865583030327078557349651159791103195758253628551574089325712854609428298691641374628468365814082531330986606348062624284395896648229682097440238805152128233500519/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_leaf": "192155942673683381815809992594304303220524345515316151095397201246859939979892167295194115784600108962975062640051219188788658023947783235675777245653617980689979305152128233500519/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_positive": "4432791515163540246371742549568473040529475654484683848904602798753140060020107832704805884215399891037024937359948780811211341976052216764324222754346382019310020694847871766499481/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_below_one": "3901817208484836459753628257450431526959470524345515316151095397201246859939979892167295194115784600108962975062640051219188788658023947783235675777245653617980689979305152128233500519/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_reservations": "1/4000000000000000000",
+    "lambda_above_tau": "8865583030327078557349651159791103195758253628551574089325712854609428298691641374628468365814082531330986606348062624284395896648229682097440238805152128233500519/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_sigma": "384311885347366764015931870535975361591397531239529106432540773942145790634071479980959932877558843297481759466019907046590709699832942186955657843077553863939719805152128233500519/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_internal": "8865583030327078557349651159791103195758253628551574089325712854609428298691641374628468365814082531330986606348062624284395896648229682097440238805152128233500519/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_prime_above_lambda": "8865583030327078557349651159791103195758253628551574089325712854609428298691641374628468365814082531330986606348062624284395896648229682097440238805152128233500519/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_leaf": "192155942673683381815809992594304303220524345515316151095397201246859939979892167295194115784600108962975062640051219188788658023947783235675777245653617980689979305152128233500519/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_reservations": "1/4000000000000000000",
+    "lambda_prime_below_one": "4432791515163539269809242549568473040529475654484683848904602798753140060020107832704805884215399891037024937359948780811211341976052216764324222754346382019310020694847871766499481/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim."
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/ASSEMBLY.json b/research/e8-early-reset-kernel/local-evidence/ASSEMBLY.json
new file mode 100644
index 0000000000..2d9275b4b3
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/ASSEMBLY.json
@@ -0,0 +1,103 @@
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+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f",
+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim."
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/AUDIT-118.json b/research/e8-early-reset-kernel/local-evidence/AUDIT-118.json
new file mode 100644
index 0000000000..908c0f3d62
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/AUDIT-118.json
@@ -0,0 +1,34 @@
+{
+  "status": "PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT",
+  "template_sha256": "344198ec3d0838ce37c081ecce0a876739d2a6e7d3625ce0e3d1b93b621bc9f7",
+  "source_frames": 944,
+  "exact_nested_frame_pairs": 3357,
+  "exact_reflected_pairs": 3357,
+  "orthogonal_lift_argument": "Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.",
+  "exact_bank_families": 6543,
+  "mixed_width_slots": true,
+  "entrance_rank_total": 160,
+  "mutations_rejected": [
+    "omit an idle child",
+    "omit a bridge",
+    "omit terminal exchange",
+    "remove a local invocation",
+    "re-use a helper bank slot",
+    "understate live stock",
+    "omit a local paid move",
+    "wrong reflected copy charge"
+  ],
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diff --git a/research/e8-early-reset-kernel/local-evidence/AUDIT.json b/research/e8-early-reset-kernel/local-evidence/AUDIT.json
new file mode 100644
index 0000000000..643c814b0b
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/AUDIT.json
@@ -0,0 +1,34 @@
+{
+  "status": "PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT",
+  "template_sha256": "f9ce9ac945d9e8ea737dc5e456e366a7e2a21d8b989d24b742d7f124d26fb32f",
+  "source_frames": 944,
+  "exact_nested_frame_pairs": 3357,
+  "exact_reflected_pairs": 3357,
+  "orthogonal_lift_argument": "Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.",
+  "exact_bank_families": 6579,
+  "mixed_width_slots": true,
+  "entrance_rank_total": 128,
+  "mutations_rejected": [
+    "omit an idle child",
+    "omit a bridge",
+    "omit terminal exchange",
+    "remove a local invocation",
+    "re-use a helper bank slot",
+    "understate live stock",
+    "omit a local paid move",
+    "wrong reflected copy charge"
+  ],
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+}
diff --git a/research/e8-early-reset-kernel/local-evidence/BIT-PRICE-118.json b/research/e8-early-reset-kernel/local-evidence/BIT-PRICE-118.json
new file mode 100644
index 0000000000..e4a325dd65
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/BIT-PRICE-118.json
@@ -0,0 +1,17 @@
+{
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+  "upper": "0.001134794627881866057684",
+  "lower_endpoint_residual_upper": "-1.343918196056376078771778731691543898160655071315154189250671754099554E-24",
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+  "strict_rational_signs": true,
+  "moment_minus_one_at_current_k_required_rate": [
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+    "0.001133508328719775504132064628782242703940278922458884422182968591698260"
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+  "two_exact_engines": true
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/BIT-PRICE.json b/research/e8-early-reset-kernel/local-evidence/BIT-PRICE.json
new file mode 100644
index 0000000000..0339fa04e3
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/BIT-PRICE.json
@@ -0,0 +1,17 @@
+{
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+  "strict_rational_signs": true,
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+}
diff --git a/research/e8-early-reset-kernel/local-evidence/FULL-PYTHON311.json b/research/e8-early-reset-kernel/local-evidence/FULL-PYTHON311.json
new file mode 100644
index 0000000000..e78af127aa
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/FULL-PYTHON311.json
@@ -0,0 +1,49 @@
+{
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+}
diff --git a/research/e8-early-reset-kernel/local-evidence/FULL-PYTHON314.json b/research/e8-early-reset-kernel/local-evidence/FULL-PYTHON314.json
new file mode 100644
index 0000000000..37155858c0
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/FULL-PYTHON314.json
@@ -0,0 +1,49 @@
+{
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+  "kappa": "566550276142217/500000000000000000",
+  "kappa_decimal": "0.001133100552284434",
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+  "parent_phase_mode": "full replay"
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/GLOBAL-118.json b/research/e8-early-reset-kernel/local-evidence/GLOBAL-118.json
new file mode 100644
index 0000000000..cc2c83ad04
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/GLOBAL-118.json
@@ -0,0 +1,165 @@
+{
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diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-changed-assembly.json b/research/e8-early-reset-kernel/local-evidence/fill160-changed-assembly.json
new file mode 100644
index 0000000000..49bc743d6b
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-changed-assembly.json
@@ -0,0 +1,103 @@
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+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim."
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-initial314-storage-archive.json b/research/e8-early-reset-kernel/local-evidence/fill160-initial314-storage-archive.json
new file mode 100644
index 0000000000..99399a7df8
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-initial314-storage-archive.json
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+    "early-kernel121-full314/baseline/changed/work": "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/early-kernel121-full314/baseline/baseline/work"
+  }
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-initial314-storage-failure.json b/research/e8-early-reset-kernel/local-evidence/fill160-initial314-storage-failure.json
new file mode 100644
index 0000000000..127417968c
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-initial314-storage-failure.json
@@ -0,0 +1,25 @@
+{
+  "error": "RuntimeError(('global-program', 1, 'Traceback (most recent call last):\\n  File \"/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/early-reuse-publication/research/e8-early-reset-kernel/bit_global.py\", line 262, in <module>\\n    if __name__==\\'__main__\\': main()\\n                             ~~~~^^\\n  File \"/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/early-reuse-publication/research/e8-early-reset-kernel/bit_global.py\", line 75, in main\\n    write(out/\\'GEOMETRY.json\\',geo)\\n    ~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^\\n  File \"/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/early-reuse-publication/research/e8-early-reset-kernel/bit_global.py\", line 48, in write\\n    def write(p,x): p.write_text(json.dumps(x,indent=2)+\\'\\\\n\\')\\n                    ~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\\n  File \"/opt/homebrew/Cellar/python@3.14/3.14.8/Frameworks/Python.framework/Versions/3.14/lib/python3.14/pathlib/__init__.py\", line 810, in write_text\\n    return f.write(data)\\n           ~~~~~~~^^^^^^\\nOSError: [Errno 28] No space left on device\\n'))",
+  "completed": [
+    {
+      "name": "full-early-reuse434",
+      "seconds": 110.17919108294882,
+      "log_sha256": "c0edbb5dd9975ae1879cf20f98ed89b925ff3f9b695f027aca13f4930a6f81a6"
+    },
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+    }
+  ]
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-packaging-failure.json b/research/e8-early-reset-kernel/local-evidence/fill160-packaging-failure.json
new file mode 100644
index 0000000000..4d279fd711
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-packaging-failure.json
@@ -0,0 +1,78 @@
+{
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+  "first_published_incomplete_manifest_commit": "c615725c52751a28dbf11d2036e092655b5e8776",
+  "metadata_commit": "6ce33cf6ba40527d3864c4d70e313c4a79242c4b",
+  "error": "Broad prose replacement altered numeric substrings inside source-reference metadata. Assertion against the prior pinned SOURCE.json detected the mismatch. Pinned fields restored from exact prior GitHub commit. No numerical witness changed.",
+  "affected_fields": [
+    "kernel_provenance"
+  ],
+  "bad_source": {
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+    "parent_code_head": "50585107b561a170ccd2c6be09dbe90041ea7f6f",
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+    "kernel_source_head": "2c9c833ac8709402c37fc88a6a23393fb0d397fb",
+    "kernel_provenance": {
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+      "files": [
+        {
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+          "git_blob": "ce13906fe7473999b0ffc721f60fbf853645e371",
+          "sha256": "c94a1dd1c078deddbde088dc6291190977266009073c4cb4108f9e2faf898381"
+        },
+        {
+          "path": "research/split-centres-kernel/code/bit_global.py",
+          "git_blob": "c8f37eb96eb13847fa157c574d7ab445edaae61c",
+          "sha256": "6d0eea0aaafbe90f1cdb43d7719ceb7b472fbbb6e6a7cb58bcfe82c31ac801c0"
+        },
+        {
+          "path": "research/split-centres-kernel/code/bit_kernel.py",
+          "git_blob": "c0b7445f769713d0cd647c1e01f8befc39fffbd1",
+          "sha256": "14f164fcc0674f73163808a9d9762eb439ea130895f593cb78a6cafaed2dfb11"
+        },
+        {
+          "path": "research/split-centres-kernel/code/combined.py",
+          "git_blob": "cead756a2c8fb52d6ba4cc7fe27200950d9a6b2c",
+          "sha256": "4f1f280b050e9aca659f10ad8996164e47f4e42fe4fd8631c822227413c427ae"
+        },
+        {
+          "path": "research/split-centres-kernel/stages/kernel-selection.json",
+          "git_blob": "6426b40cde286df8894a4c7740e8cd5b520130d1",
+          "sha256": "87994a173608a930c83bfb35a05994f9681031f1b79df148cc2e2579fec9ef1f"
+        },
+        {
+          "path": "research/split-centres-kernel/vendor/kernel417/LICENSE",
+          "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64",
+          "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4"
+        },
+        {
+          "path": "research/split-centres-kernel/vendor/kernel417/e8core.py",
+          "git_blob": "f2874bae8ef044240211fd892afb457d13759c74",
+          "sha256": "3f4e25f700b7eb5821ab9cdfc65541f3f921baffeb8704beb21c6d7072052d29"
+        },
+        {
+          "path": "research/split-centres-kernel/vendor/kernel417/engines/base_two_moment.py",
+          "git_blob": "14a90fa0e788217856f070382c9e61bd7c603c61",
+          "sha256": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098"
+        },
+        {
+          "path": "research/split-centres-kernel/vendor/kernel417/engines/moment.py",
+          "git_blob": "7d697cb45203fe72d97037403d6da41f71f3b7fd",
+          "sha256": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482"
+        },
+        {
+          "path": "research/split-centres-kernel/vendor/kernel417/engines/outer.py",
+          "git_blob": "43007488ad2c43187c77cc6798beff8b1cd76ad2",
+          "sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+        },
+        {
+          "path": "research/split-centres-kernel/vendor/kernel417/stages.py",
+          "git_blob": "9ef95d52f4b2ba0389bb2edb16028da698dd75f4",
+          "sha256": "e73ab7836519510ed30dd7e3022dae557fa50fc513d723197929bff741859668"
+        }
+      ]
+    },
+    "scope": "Twelve early resets, 121 revalidated response relations and ten frame retimings, all repriced on the final emitted word.",
+    "composition_update": "The previous 118-entry R747 word is historical. An additional chronological reset gives R746; filter/remap response relations to entrance rank 160, then apply ten frame changes with unchanged primitive ADD order."
+  }
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python311/RESULT.json b/research/e8-early-reset-kernel/local-evidence/fill160-python311/RESULT.json
new file mode 100644
index 0000000000..0d39673021
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python311/RESULT.json
@@ -0,0 +1,49 @@
+{
+  "status": "PASS_FULL_EARLY_RESET_KERNEL_COMPOSITION",
+  "kappa": "226877503533617/200000000000000000",
+  "kappa_decimal": "0.001134387517668085",
+  "source_manifest_sha256": "8fb34d3d7d9819b915a7b734d63b18772c30b1312e89e1e96b8731ce90dd731f",
+  "checks": [
+    {
+      "name": "full-early-reuse434",
+      "seconds": 116.33714474993758,
+      "log_sha256": "c0edbb5dd9975ae1879cf20f98ed89b925ff3f9b695f027aca13f4930a6f81a6"
+    },
+    {
+      "name": "kernel-reconstruction",
+      "seconds": 0.1418250419665128,
+      "log_sha256": "cd88170488b9ccf42b83160b2c4f906e1168ab0b75a75a6fd5a297d61a7e7f2c"
+    },
+    {
+      "name": "export",
+      "seconds": 0.5549206249415874,
+      "log_sha256": "9e4b041b2e8a963dc2add4c83531030c5984a7fde15384aa773fd88e285fa0a3"
+    },
+    {
+      "name": "integer-source-spans",
+      "seconds": 0.06492312496993691,
+      "log_sha256": "9cf4d31f2941a5bbecaca75562bb7d45b2770228d605fbda9f9291d97955bd49"
+    },
+    {
+      "name": "global-program",
+      "seconds": 2.6963896669913083,
+      "log_sha256": "f19c51b1dcbd8c59ba973d0bb4e11453a069f8f15ad7247f99ce0d2dbf88581d"
+    },
+    {
+      "name": "independent-audit",
+      "seconds": 2.9941658749012277,
+      "log_sha256": "3a92a656a9fbddb0af95935f9b80b16969e92613335a946ddad70fa1d0c64a55"
+    },
+    {
+      "name": "two-moments",
+      "seconds": 0.13234495802316815,
+      "log_sha256": "0bb045a48dfe657d47aec493e632f4c3134b47f5598dd525cb102d21b7b43c2d"
+    },
+    {
+      "name": "finite-assembly",
+      "seconds": 0.14394558395724744,
+      "log_sha256": "282740a9cfd2570265b59855b5e1f4c5136969f18d075653316d50e8e0a8d6ae"
+    }
+  ],
+  "parent_phase_mode": "full replay"
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python311/export.log b/research/e8-early-reset-kernel/local-evidence/fill160-python311/export.log
new file mode 100644
index 0000000000..3a694a081a
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python311/export.log
@@ -0,0 +1 @@
+exported 19064 records, 944 frames, n 986 ZERO 0
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python311/finite-assembly.log b/research/e8-early-reset-kernel/local-evidence/fill160-python311/finite-assembly.log
new file mode 100644
index 0000000000..5d845b9e87
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python311/finite-assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_EARLY_RESET_KERNEL_ASSEMBLY 0.001134387517668085 8.2425148511294 {'prefix_bits': 226, 'charged_prefix_bits': 256, 'coefficient_bits': 226, 'two_level_coefficient_bits': 488, 'charged_two_level_coefficient_bits': 512, 'row_coefficient': 18355, 'live': 14214, 'physical': 14223}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python311/full-early-reuse434.log b/research/e8-early-reset-kernel/local-evidence/fill160-python311/full-early-reuse434.log
new file mode 100644
index 0000000000..d8e9693dc9
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python311/full-early-reuse434.log
@@ -0,0 +1,14 @@
+RUN full-parent433
+PASS full-parent433
+RUN reconstruct
+PASS reconstruct
+RUN export
+PASS export
+RUN global-program
+PASS global-program
+RUN independent-audit
+PASS independent-audit
+RUN two-moments
+PASS two-moments
+RUN finite-assembly
+PASS finite-assembly
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python311/global-program.log b/research/e8-early-reset-kernel/local-evidence/fill160-python311/global-program.log
new file mode 100644
index 0000000000..053a0f47c5
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python311/global-program.log
@@ -0,0 +1,2 @@
+Fresh prefix bits 226 charged 256
+{"status": "PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE", "h": 8, "m": 64, "v": 120, "R": 746, "replicas": 8, "live": 14214, "physical": 14223, "word_sha256": "5391ede2abb1db54715beb12b687572d8c2822dd46f461a4baf240c6c4412aee", "source_records_sha256": "55eb30cb382849836181bd13e66cf6c642f92cd8b35a59e8d0fe26bdedb23c68", "independent_unbanked_scalar_columns": 7674, "all_scalar_columns_restored": true, "geometry_sha256": "74b85155a0bfd55f0c4630a83e934ff45a56b23848b024774d1dad78a4933ec3", "template_sha256": "1460e30dd4aec672be972a81b00e244ed4ab396c6b2d5058e761edc447896623", "emitted_program_sha256": "9205d8567ceb5ac01d77a8248d9a84bc2b34b0f5c309d167b242f22f88df1032", "emitted_events": 1372608, "local_invocations": 72, "bank_assignments": 53712, "banks_per_stage": 726, "entrance_rank_total": 160, "mixed_width_slots": true, "padding_calls": 0, "profile": {"1": 181656, "2": 73800, "3": 21240, "4": 25776, "5": 7200, "7": 6768, "8": 648, "14": 3840, "28": 3840, "42": 3840}, "paid_calls": 328608, "rank_mass": 907200, "deficit": 2496, "maxchild": 42, "halving_depth": 2, "halving_integer_inequality": [4096, 3528], "local_additions": 14731, "bridge_additions": 17280, "copy_erase_episodes": 648, "global_prefix_bits": 226, "charged_prefix_bits": 256, "omitted_bridge_shears_rejected": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], "scope": "Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.", "seconds": 2.6608524170005694}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python311/independent-audit.log b/research/e8-early-reset-kernel/local-evidence/fill160-python311/independent-audit.log
new file mode 100644
index 0000000000..1c42179ca2
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python311/independent-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT", "template_sha256": "1460e30dd4aec672be972a81b00e244ed4ab396c6b2d5058e761edc447896623", "source_frames": 944, "exact_nested_frame_pairs": 3355, "exact_reflected_pairs": 3355, "orthogonal_lift_argument": "Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.", "exact_bank_families": 6534, "mixed_width_slots": true, "entrance_rank_total": 160, "mutations_rejected": ["omit an idle child", "omit a bridge", "omit terminal exchange", "remove a local invocation", "re-use a helper bank slot", "understate live stock", "omit a local paid move", "wrong reflected copy charge"], "profile": {"1": 181656, "2": 73800, "3": 21240, "4": 25776, "5": 7200, "7": 6768, "8": 648, "14": 3840, "28": 3840, "42": 3840}, "seconds": 2.9549905830062926}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python311/integer-source-spans.log b/research/e8-early-reset-kernel/local-evidence/fill160-python311/integer-source-spans.log
new file mode 100644
index 0000000000..24037de73c
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python311/integer-source-spans.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_F2_AND_INTEGER_SOURCE_SPANS", "columns": 986, "profile": {"1": 2523, "4": 358, "2": 1025, "3": 295, "5": 100, "8": 9, "7": 14}, "word_sha256": "5391ede2abb1db54715beb12b687572d8c2822dd46f461a4baf240c6c4412aee"}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python311/kernel-reconstruction.log b/research/e8-early-reset-kernel/local-evidence/fill160-python311/kernel-reconstruction.log
new file mode 100644
index 0000000000..e1705ab105
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python311/kernel-reconstruction.log
@@ -0,0 +1 @@
+{"status": "PASS_FROZEN_RESET_KERNEL_RETIMING", "input_sha256": "98ffef9246c8bf6c537ab5e134321abea05cf0b7830c9e3fd92cbe4e88d8c308", "reset_sha256": "33fba385c1c69d6cbbe6c76e4d2eca9f69453a910f3c9e5e62f3e7b189510ded", "kernel_sha256": "23cb3f6f84283aec61f2c82d9a43884932edc133bdd3fcbb7ee8deee7d7b2d60", "output_sha256": "5391ede2abb1db54715beb12b687572d8c2822dd46f461a4baf240c6c4412aee", "entries": 121, "total_entrance_rank": 160, "donor_slots": 122, "new_frames": 0, "frame_changes": 10, "additional_resets": 1, "controls": ["wrong reset source", "missing reset parent", "wrong insertion time", "wrong kernel source", "missing donor", "duplicate pivot", "wrong old frame", "duplicate frame change"]}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python311/two-moments.log b/research/e8-early-reset-kernel/local-evidence/fill160-python311/two-moments.log
new file mode 100644
index 0000000000..b9d06b96f3
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python311/two-moments.log
@@ -0,0 +1 @@
+PASS two rational bit moments 0.001135675814135758372315
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python314/RESULT.json b/research/e8-early-reset-kernel/local-evidence/fill160-python314/RESULT.json
new file mode 100644
index 0000000000..c968b1f5ea
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python314/RESULT.json
@@ -0,0 +1,49 @@
+{
+  "status": "PASS_FULL_EARLY_RESET_KERNEL_COMPOSITION",
+  "kappa": "226877503533617/200000000000000000",
+  "kappa_decimal": "0.001134387517668085",
+  "source_manifest_sha256": "8fb34d3d7d9819b915a7b734d63b18772c30b1312e89e1e96b8731ce90dd731f",
+  "checks": [
+    {
+      "name": "full-early-reuse434",
+      "seconds": 110.97235024999827,
+      "log_sha256": "c0edbb5dd9975ae1879cf20f98ed89b925ff3f9b695f027aca13f4930a6f81a6"
+    },
+    {
+      "name": "kernel-reconstruction",
+      "seconds": 0.12091325002256781,
+      "log_sha256": "cd88170488b9ccf42b83160b2c4f906e1168ab0b75a75a6fd5a297d61a7e7f2c"
+    },
+    {
+      "name": "export",
+      "seconds": 0.38167262508068234,
+      "log_sha256": "9e4b041b2e8a963dc2add4c83531030c5984a7fde15384aa773fd88e285fa0a3"
+    },
+    {
+      "name": "integer-source-spans",
+      "seconds": 0.08635591703932732,
+      "log_sha256": "9cf4d31f2941a5bbecaca75562bb7d45b2770228d605fbda9f9291d97955bd49"
+    },
+    {
+      "name": "global-program",
+      "seconds": 2.7085493330378085,
+      "log_sha256": "eb30fd19c5707570c1cb33586e513f6a0b03ed2aece03a97ea1b4fcbce9be729"
+    },
+    {
+      "name": "independent-audit",
+      "seconds": 1.90598908404354,
+      "log_sha256": "8d5f85d6ddc0c4f662bc4c7aa010eba3f96cd544a5f2f3b2b55c22cf116f0596"
+    },
+    {
+      "name": "two-moments",
+      "seconds": 0.1436035829829052,
+      "log_sha256": "0bb045a48dfe657d47aec493e632f4c3134b47f5598dd525cb102d21b7b43c2d"
+    },
+    {
+      "name": "finite-assembly",
+      "seconds": 0.15973495796788484,
+      "log_sha256": "282740a9cfd2570265b59855b5e1f4c5136969f18d075653316d50e8e0a8d6ae"
+    }
+  ],
+  "parent_phase_mode": "full replay"
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python314/export.log b/research/e8-early-reset-kernel/local-evidence/fill160-python314/export.log
new file mode 100644
index 0000000000..3a694a081a
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python314/export.log
@@ -0,0 +1 @@
+exported 19064 records, 944 frames, n 986 ZERO 0
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python314/finite-assembly.log b/research/e8-early-reset-kernel/local-evidence/fill160-python314/finite-assembly.log
new file mode 100644
index 0000000000..5d845b9e87
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python314/finite-assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_EARLY_RESET_KERNEL_ASSEMBLY 0.001134387517668085 8.2425148511294 {'prefix_bits': 226, 'charged_prefix_bits': 256, 'coefficient_bits': 226, 'two_level_coefficient_bits': 488, 'charged_two_level_coefficient_bits': 512, 'row_coefficient': 18355, 'live': 14214, 'physical': 14223}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python314/full-early-reuse434.log b/research/e8-early-reset-kernel/local-evidence/fill160-python314/full-early-reuse434.log
new file mode 100644
index 0000000000..d8e9693dc9
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python314/full-early-reuse434.log
@@ -0,0 +1,14 @@
+RUN full-parent433
+PASS full-parent433
+RUN reconstruct
+PASS reconstruct
+RUN export
+PASS export
+RUN global-program
+PASS global-program
+RUN independent-audit
+PASS independent-audit
+RUN two-moments
+PASS two-moments
+RUN finite-assembly
+PASS finite-assembly
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python314/global-program.log b/research/e8-early-reset-kernel/local-evidence/fill160-python314/global-program.log
new file mode 100644
index 0000000000..708c7bcd5a
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python314/global-program.log
@@ -0,0 +1,2 @@
+Fresh prefix bits 226 charged 256
+{"status": "PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE", "h": 8, "m": 64, "v": 120, "R": 746, "replicas": 8, "live": 14214, "physical": 14223, "word_sha256": "5391ede2abb1db54715beb12b687572d8c2822dd46f461a4baf240c6c4412aee", "source_records_sha256": "55eb30cb382849836181bd13e66cf6c642f92cd8b35a59e8d0fe26bdedb23c68", "independent_unbanked_scalar_columns": 7674, "all_scalar_columns_restored": true, "geometry_sha256": "74b85155a0bfd55f0c4630a83e934ff45a56b23848b024774d1dad78a4933ec3", "template_sha256": "1460e30dd4aec672be972a81b00e244ed4ab396c6b2d5058e761edc447896623", "emitted_program_sha256": "9205d8567ceb5ac01d77a8248d9a84bc2b34b0f5c309d167b242f22f88df1032", "emitted_events": 1372608, "local_invocations": 72, "bank_assignments": 53712, "banks_per_stage": 726, "entrance_rank_total": 160, "mixed_width_slots": true, "padding_calls": 0, "profile": {"1": 181656, "2": 73800, "3": 21240, "4": 25776, "5": 7200, "7": 6768, "8": 648, "14": 3840, "28": 3840, "42": 3840}, "paid_calls": 328608, "rank_mass": 907200, "deficit": 2496, "maxchild": 42, "halving_depth": 2, "halving_integer_inequality": [4096, 3528], "local_additions": 14731, "bridge_additions": 17280, "copy_erase_episodes": 648, "global_prefix_bits": 226, "charged_prefix_bits": 256, "omitted_bridge_shears_rejected": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], "scope": "Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.", "seconds": 2.6492195419268683}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python314/independent-audit.log b/research/e8-early-reset-kernel/local-evidence/fill160-python314/independent-audit.log
new file mode 100644
index 0000000000..6be917fed4
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python314/independent-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT", "template_sha256": "1460e30dd4aec672be972a81b00e244ed4ab396c6b2d5058e761edc447896623", "source_frames": 944, "exact_nested_frame_pairs": 3355, "exact_reflected_pairs": 3355, "orthogonal_lift_argument": "Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.", "exact_bank_families": 6534, "mixed_width_slots": true, "entrance_rank_total": 160, "mutations_rejected": ["omit an idle child", "omit a bridge", "omit terminal exchange", "remove a local invocation", "re-use a helper bank slot", "understate live stock", "omit a local paid move", "wrong reflected copy charge"], "profile": {"1": 181656, "2": 73800, "3": 21240, "4": 25776, "5": 7200, "7": 6768, "8": 648, "14": 3840, "28": 3840, "42": 3840}, "seconds": 1.8504693750292063}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python314/integer-source-spans.log b/research/e8-early-reset-kernel/local-evidence/fill160-python314/integer-source-spans.log
new file mode 100644
index 0000000000..24037de73c
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python314/integer-source-spans.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_F2_AND_INTEGER_SOURCE_SPANS", "columns": 986, "profile": {"1": 2523, "4": 358, "2": 1025, "3": 295, "5": 100, "8": 9, "7": 14}, "word_sha256": "5391ede2abb1db54715beb12b687572d8c2822dd46f461a4baf240c6c4412aee"}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python314/kernel-reconstruction.log b/research/e8-early-reset-kernel/local-evidence/fill160-python314/kernel-reconstruction.log
new file mode 100644
index 0000000000..e1705ab105
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python314/kernel-reconstruction.log
@@ -0,0 +1 @@
+{"status": "PASS_FROZEN_RESET_KERNEL_RETIMING", "input_sha256": "98ffef9246c8bf6c537ab5e134321abea05cf0b7830c9e3fd92cbe4e88d8c308", "reset_sha256": "33fba385c1c69d6cbbe6c76e4d2eca9f69453a910f3c9e5e62f3e7b189510ded", "kernel_sha256": "23cb3f6f84283aec61f2c82d9a43884932edc133bdd3fcbb7ee8deee7d7b2d60", "output_sha256": "5391ede2abb1db54715beb12b687572d8c2822dd46f461a4baf240c6c4412aee", "entries": 121, "total_entrance_rank": 160, "donor_slots": 122, "new_frames": 0, "frame_changes": 10, "additional_resets": 1, "controls": ["wrong reset source", "missing reset parent", "wrong insertion time", "wrong kernel source", "missing donor", "duplicate pivot", "wrong old frame", "duplicate frame change"]}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-python314/two-moments.log b/research/e8-early-reset-kernel/local-evidence/fill160-python314/two-moments.log
new file mode 100644
index 0000000000..b9d06b96f3
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-python314/two-moments.log
@@ -0,0 +1 @@
+PASS two rational bit moments 0.001135675814135758372315
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-tested-manifest.json b/research/e8-early-reset-kernel/local-evidence/fill160-tested-manifest.json
new file mode 100644
index 0000000000..4cb7004bb6
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-tested-manifest.json
@@ -0,0 +1,66 @@
+{
+  "files": {
+    "apply.py": "11eeac4b02521a3286160a87fdac080fefb11c25779d9eaec9f44b18d7b6c1ae",
+    "bit_audit.py": "f5d81ae080ee55d174feef6de2314113864a7e3e3d29c5559071c306edd2f272",
+    "bit_global.py": "50c76ed71ced48af2eacb8d8a91ab43dee035a3c818dcf85d0ad7e1ee032e5d9",
+    "bit_price.py": "36bf15803567a95b139a908461541bf19efe1f5b85fb31c270021833ab1393ee",
+    "combined.py": "83ba7f8deda264c283176c564d9d93dc8948edae0a8e8ed216b48240b5f74c85",
+    "EXPECTED.json": "9a55f73c6a3dd2b06377cbca76299b6672071419ebfe901aff9054ccca4b727a",
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE.md": "268f7fe8538d02bd8cc8f8b895d88035803fee05186ceb469204c7666190fbc7",
+    "PROOF.md": "4d7198ce615099b48013d23df6b8fa421428a78ce4de79e3757e8962e4d82a95",
+    "README.md": "a4ec63243ba9abab6a5a5b19e2e47edace8af6a3c519c5580e03a3ab99c76f3c",
+    "RESET12.json": "a310f1d3a8ec714e6dd12ec5364d16b9fa254527cf684b09dc1846d064e9b41c",
+    "RETIMING.json": "602d826e7bafd7faae4b0a7fd17be7d3edfd45f11a88f57ccd5b78e3f11c36f1",
+    "SELECTION.json": "b4b852b6286f5181fe58c3206a94426fae52acd246c0314eb8fca893f012a6f4",
+    "SOURCE.json": "cadea46917e4c63babc6dc33fe8acf90f8916fbb1599393326e5297fb251bdd3",
+    "source_span.py": "4772d177f37254c6f854af5ee3871aca193cfb24307a53c143c3bf517e56631e",
+    "VALIDATION.json": "c69b8e37d53aaddb03e10f15ed9a66cf3372126fec70ae6ddd0955165febc0bc",
+    "verify.py": "16c07414bc956744dc93b8e35b642267ea9819be922b0d3e081c543fdbf92a70",
+    "local-evidence/ASSEMBLY-118.json": "3e610791f14777e6024adfe562175d51cd5dbeb2ce585f59d56d58092277bac1",
+    "local-evidence/ASSEMBLY.json": "7c3cc4b503e4cf0fd3e050be46ad0da183c5b1c490f4901245df944fd9d6194e",
+    "local-evidence/AUDIT-118.json": "cd37be4c487f924490c78052a36a8e091b261a7beb60f67f495779078f6ab906",
+    "local-evidence/AUDIT.json": "76a146a9123d8b653e6e46ff93f153653f9cefd0f5c3fdd264a59f1322110262",
+    "local-evidence/BIT-PRICE-118.json": "97e29c84202255a6468bb0444f3438910e7ab4e19bbadb89636ede78376a9306",
+    "local-evidence/BIT-PRICE.json": "9a4a320cab1ce62b0c2329ac1bf3b81f73580fd603a406e4bfaae2962dfdad35",
+    "local-evidence/fill160-changed-assembly.json": "9a3f1c219d93dc27744a89018722b2bc82f96a3ba58fb8557804d30ba62b051d",
+    "local-evidence/fill160-packaging-failure.json": "bb0a5af0c10f33271d0ba6b6a731cab960ea5def6ac7208f59b94677ba6644e4",
+    "local-evidence/FULL-PYTHON311.json": "62b37525bf7b60c0d9101ed571681f3bf46ea75df065939864307e4986018332",
+    "local-evidence/FULL-PYTHON314.json": "85797531db037d06fb597a4c9b6ef6bd71e6a0ab4f220ae70b1b6bf3aeda205f",
+    "local-evidence/full118-python311.json": "368b3d851919f77e6865b51cec731fc5bd0f16e0bd494fbaa2df5b57b9342d1c",
+    "local-evidence/full118-python314.json": "2bb62d9bc89834463959ce755f886e58793ded811dba26b038c20626ef90c814",
+    "local-evidence/GLOBAL-118.json": "a7491dfd2ff51d0574a6e46e3b100531969219dc41d93afbaca38ee3afbfa7e7",
+    "local-evidence/GLOBAL.json": "16c4e829eea1b2d12b70cec7e6a9c0e33ea0eae98a40894a3b779790fd2efbb3",
+    "local-evidence/reset12-reconstruction.json": "178f9fef29a4f7e18c9a3abebf455bb7c0545a85e2bdfdda6d6def5afc8f9239",
+    "local-evidence/reset12-retimed-assembly.json": "a54ca18bca34c7407872dded5402b463be2c76bab271248e519bbd0492b3f575",
+    "local-evidence/reset12-tested-manifest.json": "ad6b66aba41895ac66bd8e988717ab2e16ca974f93a6fa309c50de0b09f1a28e",
+    "local-evidence/reset12-verification-provenance.json": "7c56f467e0e6de0549c37f2b37023f10b46209a0c71f03d1da818368882971f2",
+    "local-evidence/SOURCE-SPANS-118.log": "115ea64de78aaa3ea6edc9684f66f9ec6f88c806608caf85ae32853059c14f37",
+    "local-evidence/SOURCE-SPANS.log": "bdf95dbce8337be57aab8a3d3b42a711ee276496c40cbb4c5356fc9cc9b2e811",
+    "local-evidence/VALIDATION-110-ENTRIES.json": "77ad775cf69f5d913568b6276b0dfeb2eaef0306f57b71c0a467bff793807267",
+    "vendor/kernel417/e8core.py": "3f4e25f700b7eb5821ab9cdfc65541f3f921baffeb8704beb21c6d7072052d29",
+    "vendor/kernel417/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "vendor/kernel417/stages.py": "e73ab7836519510ed30dd7e3022dae557fa50fc513d723197929bff741859668",
+    "vendor/kernel417/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "vendor/kernel417/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "vendor/kernel417/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "local-evidence/reset12-python311/export.log": "d4ea7999a985f7287ace0551ca025d99c304cb78cbc30eee6223585ed9af109f",
+    "local-evidence/reset12-python311/finite-assembly.log": "8b5598ec4d2b0dfadde4ae6f3dbe913b6e213937db89b485234c4d323fa38db8",
+    "local-evidence/reset12-python311/full-early-reuse434.log": "c0edbb5dd9975ae1879cf20f98ed89b925ff3f9b695f027aca13f4930a6f81a6",
+    "local-evidence/reset12-python311/global-program.log": "bea6486730cae31b0e9de7b4c20de1786a4aa2ff54831f3e6f3c4b5347a0e608",
+    "local-evidence/reset12-python311/independent-audit.log": "a1443ac2d80c54dc2f3fb6e500a05e4e2598624314a665581d1ca059e4d14e53",
+    "local-evidence/reset12-python311/integer-source-spans.log": "7e45fe477c18d80a06f9cbd2655394950953ad8c9cc12e7d512bd1d39c890126",
+    "local-evidence/reset12-python311/kernel-reconstruction.log": "14e8624214481449cc954f2490f8873de6e033f990b1e945acf466ff92077616",
+    "local-evidence/reset12-python311/RESULT.json": "8cb22e90ae44fcb3977187f132ffcc08a1c426a6bb43a97ecfa37cedfc931e7d",
+    "local-evidence/reset12-python311/two-moments.log": "c866854ad55093f6feb992efced66f2cd2a1076cb7c9374fdb22565f3d2eaf82",
+    "local-evidence/reset12-python314/export.log": "d4ea7999a985f7287ace0551ca025d99c304cb78cbc30eee6223585ed9af109f",
+    "local-evidence/reset12-python314/finite-assembly.log": "8b5598ec4d2b0dfadde4ae6f3dbe913b6e213937db89b485234c4d323fa38db8",
+    "local-evidence/reset12-python314/full-early-reuse434.log": "c0edbb5dd9975ae1879cf20f98ed89b925ff3f9b695f027aca13f4930a6f81a6",
+    "local-evidence/reset12-python314/global-program.log": "52fd486807379dc18d48e24cc0ebdc21a03c57847a4f1be478463caa41d05ecf",
+    "local-evidence/reset12-python314/independent-audit.log": "9851de62a8b18ef2e34ef94aa1d31d1c69748b59c44e5909cc7ae26b83091d43",
+    "local-evidence/reset12-python314/integer-source-spans.log": "7e45fe477c18d80a06f9cbd2655394950953ad8c9cc12e7d512bd1d39c890126",
+    "local-evidence/reset12-python314/kernel-reconstruction.log": "14e8624214481449cc954f2490f8873de6e033f990b1e945acf466ff92077616",
+    "local-evidence/reset12-python314/RESULT.json": "db6f8600d45da3dc50780c3e8ac1d86be4ae047ef32b03fc8619eddb0d660e5d",
+    "local-evidence/reset12-python314/two-moments.log": "c866854ad55093f6feb992efced66f2cd2a1076cb7c9374fdb22565f3d2eaf82"
+  }
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/fill160-verification-provenance.json b/research/e8-early-reset-kernel/local-evidence/fill160-verification-provenance.json
new file mode 100644
index 0000000000..41ef788e5c
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/fill160-verification-provenance.json
@@ -0,0 +1,5 @@
+{
+  "tested_code_commit": "f5e0af60ae91e39528d63782ac06f4c6f0e956e3",
+  "tested_manifest_sha256": "8fb34d3d7d9819b915a7b734d63b18772c30b1312e89e1e96b8731ce90dd731f",
+  "publication_changes": "Documentation and evidence only; executable code, witnesses and expected outputs unchanged from both successful runs."
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/full118-python311.json b/research/e8-early-reset-kernel/local-evidence/full118-python311.json
new file mode 100644
index 0000000000..b21cc704d5
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/full118-python311.json
@@ -0,0 +1,49 @@
+{
+  "status": "PASS_FULL_EARLY_RESET_KERNEL_COMPOSITION",
+  "kappa": "45340333148791/40000000000000000",
+  "kappa_decimal": "0.001133508328719775",
+  "source_manifest_sha256": "df718aaeeb1fc73421109d91663c6a5829219ccfc48b88687fc875cfc6955012",
+  "checks": [
+    {
+      "name": "full-early-reuse434",
+      "seconds": 121.56365308398381,
+      "log_sha256": "c0edbb5dd9975ae1879cf20f98ed89b925ff3f9b695f027aca13f4930a6f81a6"
+    },
+    {
+      "name": "kernel-reconstruction",
+      "seconds": 0.07501316606067121,
+      "log_sha256": "fdee05569fd6c1227d3fdac42f3054ca5f909e83c6a27da1b4218331da785102"
+    },
+    {
+      "name": "export",
+      "seconds": 0.5756898750551045,
+      "log_sha256": "b12ba3c1d79793c1dc63a96a2275b9180d27536ec3f3355aa4a93947177efeb0"
+    },
+    {
+      "name": "integer-source-spans",
+      "seconds": 0.06597908306866884,
+      "log_sha256": "115ea64de78aaa3ea6edc9684f66f9ec6f88c806608caf85ae32853059c14f37"
+    },
+    {
+      "name": "global-program",
+      "seconds": 2.9918768339557573,
+      "log_sha256": "fad57b028db849255b61c1e29af13c1032e3a1bef9c073590c94de8f5033c4d3"
+    },
+    {
+      "name": "independent-audit",
+      "seconds": 3.200223374995403,
+      "log_sha256": "ef941de8a12fd910aeaa1095bc18bc805cd7dee045794f0b944464391ea36bec"
+    },
+    {
+      "name": "two-moments",
+      "seconds": 0.14873512496706098,
+      "log_sha256": "98d0243f63083c3904760bb64b266759447a118ec4fbf35bd7ce27ce2811f244"
+    },
+    {
+      "name": "finite-assembly",
+      "seconds": 0.15828608407173306,
+      "log_sha256": "68a90258d62698774d5aea32775020dd38cdc4859410d5ce58e5b8cfc1dc2547"
+    }
+  ],
+  "parent_phase_mode": "full replay"
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/full118-python314.json b/research/e8-early-reset-kernel/local-evidence/full118-python314.json
new file mode 100644
index 0000000000..1acf7198a7
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/full118-python314.json
@@ -0,0 +1,49 @@
+{
+  "status": "PASS_FULL_EARLY_RESET_KERNEL_COMPOSITION",
+  "kappa": "45340333148791/40000000000000000",
+  "kappa_decimal": "0.001133508328719775",
+  "source_manifest_sha256": "df718aaeeb1fc73421109d91663c6a5829219ccfc48b88687fc875cfc6955012",
+  "checks": [
+    {
+      "name": "full-early-reuse434",
+      "seconds": 112.24914187507238,
+      "log_sha256": "c0edbb5dd9975ae1879cf20f98ed89b925ff3f9b695f027aca13f4930a6f81a6"
+    },
+    {
+      "name": "kernel-reconstruction",
+      "seconds": 0.06330962502397597,
+      "log_sha256": "fdee05569fd6c1227d3fdac42f3054ca5f909e83c6a27da1b4218331da785102"
+    },
+    {
+      "name": "export",
+      "seconds": 0.38195537496358156,
+      "log_sha256": "b12ba3c1d79793c1dc63a96a2275b9180d27536ec3f3355aa4a93947177efeb0"
+    },
+    {
+      "name": "integer-source-spans",
+      "seconds": 0.0829408330610022,
+      "log_sha256": "115ea64de78aaa3ea6edc9684f66f9ec6f88c806608caf85ae32853059c14f37"
+    },
+    {
+      "name": "global-program",
+      "seconds": 2.733515041996725,
+      "log_sha256": "024192f433a71220e27a4b1090d1c1a1647150e5abd0e6d220721bd75bf79e1e"
+    },
+    {
+      "name": "independent-audit",
+      "seconds": 1.9839933750918135,
+      "log_sha256": "8d750a03e66a01fd09034f5d81a0e256f46bc44bc0d955bdf96d2e6bac9c876b"
+    },
+    {
+      "name": "two-moments",
+      "seconds": 0.15150654094759375,
+      "log_sha256": "98d0243f63083c3904760bb64b266759447a118ec4fbf35bd7ce27ce2811f244"
+    },
+    {
+      "name": "finite-assembly",
+      "seconds": 0.17155462503433228,
+      "log_sha256": "68a90258d62698774d5aea32775020dd38cdc4859410d5ce58e5b8cfc1dc2547"
+    }
+  ],
+  "parent_phase_mode": "full replay"
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python311/RESULT.json b/research/e8-early-reset-kernel/local-evidence/reset12-python311/RESULT.json
new file mode 100644
index 0000000000..3d329a0c6d
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python311/RESULT.json
@@ -0,0 +1,49 @@
+{
+  "status": "PASS_FULL_EARLY_RESET_KERNEL_COMPOSITION",
+  "kappa": "1134386495022041/1000000000000000000",
+  "kappa_decimal": "0.001134386495022041",
+  "source_manifest_sha256": "ad6b66aba41895ac66bd8e988717ab2e16ca974f93a6fa309c50de0b09f1a28e",
+  "checks": [
+    {
+      "name": "full-early-reuse434",
+      "seconds": 118.25037250004243,
+      "log_sha256": "c0edbb5dd9975ae1879cf20f98ed89b925ff3f9b695f027aca13f4930a6f81a6"
+    },
+    {
+      "name": "kernel-reconstruction",
+      "seconds": 0.14224062499124557,
+      "log_sha256": "14e8624214481449cc954f2490f8873de6e033f990b1e945acf466ff92077616"
+    },
+    {
+      "name": "export",
+      "seconds": 0.5562727079959586,
+      "log_sha256": "d4ea7999a985f7287ace0551ca025d99c304cb78cbc30eee6223585ed9af109f"
+    },
+    {
+      "name": "integer-source-spans",
+      "seconds": 0.06550845806486905,
+      "log_sha256": "7e45fe477c18d80a06f9cbd2655394950953ad8c9cc12e7d512bd1d39c890126"
+    },
+    {
+      "name": "global-program",
+      "seconds": 2.6464757920475677,
+      "log_sha256": "bea6486730cae31b0e9de7b4c20de1786a4aa2ff54831f3e6f3c4b5347a0e608"
+    },
+    {
+      "name": "independent-audit",
+      "seconds": 3.00883733399678,
+      "log_sha256": "a1443ac2d80c54dc2f3fb6e500a05e4e2598624314a665581d1ca059e4d14e53"
+    },
+    {
+      "name": "two-moments",
+      "seconds": 0.13161599996965379,
+      "log_sha256": "c866854ad55093f6feb992efced66f2cd2a1076cb7c9374fdb22565f3d2eaf82"
+    },
+    {
+      "name": "finite-assembly",
+      "seconds": 0.14666924998164177,
+      "log_sha256": "8b5598ec4d2b0dfadde4ae6f3dbe913b6e213937db89b485234c4d323fa38db8"
+    }
+  ],
+  "parent_phase_mode": "full replay"
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python311/export.log b/research/e8-early-reset-kernel/local-evidence/reset12-python311/export.log
new file mode 100644
index 0000000000..faa64f2c75
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python311/export.log
@@ -0,0 +1 @@
+exported 19041 records, 944 frames, n 986 ZERO 0
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python311/finite-assembly.log b/research/e8-early-reset-kernel/local-evidence/reset12-python311/finite-assembly.log
new file mode 100644
index 0000000000..d8d183fe0a
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python311/finite-assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_EARLY_RESET_KERNEL_ASSEMBLY 0.001134386495022041 8.242417270912869 {'prefix_bits': 226, 'charged_prefix_bits': 256, 'coefficient_bits': 226, 'two_level_coefficient_bits': 488, 'charged_two_level_coefficient_bits': 512, 'row_coefficient': 18355, 'live': 14223, 'physical': 14232}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python311/full-early-reuse434.log b/research/e8-early-reset-kernel/local-evidence/reset12-python311/full-early-reuse434.log
new file mode 100644
index 0000000000..d8e9693dc9
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python311/full-early-reuse434.log
@@ -0,0 +1,14 @@
+RUN full-parent433
+PASS full-parent433
+RUN reconstruct
+PASS reconstruct
+RUN export
+PASS export
+RUN global-program
+PASS global-program
+RUN independent-audit
+PASS independent-audit
+RUN two-moments
+PASS two-moments
+RUN finite-assembly
+PASS finite-assembly
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python311/global-program.log b/research/e8-early-reset-kernel/local-evidence/reset12-python311/global-program.log
new file mode 100644
index 0000000000..f1f539d110
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python311/global-program.log
@@ -0,0 +1,2 @@
+Fresh prefix bits 226 charged 256
+{"status": "PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE", "h": 8, "m": 64, "v": 120, "R": 746, "replicas": 8, "live": 14223, "physical": 14232, "word_sha256": "a64ccdd734888efe0cf36962b614b405583d68da478205e37ed0b82fa307081d", "source_records_sha256": "5b83af9e7996b8e388dee898de3eaa6bf7b7c099e41589745ab48ecbdb14feee", "independent_unbanked_scalar_columns": 7674, "all_scalar_columns_restored": true, "geometry_sha256": "4ec791160bf348c5445f92869ff688bfb41d215f5c614b73e2540763d63a72f0", "template_sha256": "f4104a1c51bed199e02f7d9edd7436cd5ad26ceca49b3c34106efc1a2bd59b64", "emitted_program_sha256": "3c616050a58352f755bf9442c609253dc4e2aedd26cdc1ff266f352807b564da", "emitted_events": 1370952, "local_invocations": 72, "bank_assignments": 53712, "banks_per_stage": 727, "entrance_rank_total": 152, "mixed_width_slots": true, "padding_calls": 0, "profile": {"1": 181080, "2": 73512, "3": 21528, "4": 25272, "5": 7776, "7": 6768, "8": 648, "14": 3840, "28": 3840, "42": 3840}, "paid_calls": 328104, "rank_mass": 907776, "deficit": 2496, "maxchild": 42, "halving_depth": 2, "halving_integer_inequality": [4096, 3528], "local_additions": 14715, "bridge_additions": 17280, "copy_erase_episodes": 648, "global_prefix_bits": 226, "charged_prefix_bits": 256, "omitted_bridge_shears_rejected": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], "scope": "Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.", "seconds": 2.610876874998212}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python311/independent-audit.log b/research/e8-early-reset-kernel/local-evidence/reset12-python311/independent-audit.log
new file mode 100644
index 0000000000..02a33c2016
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python311/independent-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT", "template_sha256": "f4104a1c51bed199e02f7d9edd7436cd5ad26ceca49b3c34106efc1a2bd59b64", "source_frames": 944, "exact_nested_frame_pairs": 3357, "exact_reflected_pairs": 3357, "orthogonal_lift_argument": "Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.", "exact_bank_families": 6543, "mixed_width_slots": true, "entrance_rank_total": 152, "mutations_rejected": ["omit an idle child", "omit a bridge", "omit terminal exchange", "remove a local invocation", "re-use a helper bank slot", "understate live stock", "omit a local paid move", "wrong reflected copy charge"], "profile": {"1": 181080, "2": 73512, "3": 21528, "4": 25272, "5": 7776, "7": 6768, "8": 648, "14": 3840, "28": 3840, "42": 3840}, "seconds": 2.973931625019759}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python311/integer-source-spans.log b/research/e8-early-reset-kernel/local-evidence/reset12-python311/integer-source-spans.log
new file mode 100644
index 0000000000..3095912ab1
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python311/integer-source-spans.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_F2_AND_INTEGER_SOURCE_SPANS", "columns": 986, "profile": {"1": 2515, "4": 351, "2": 1021, "3": 299, "5": 108, "8": 9, "7": 14}, "word_sha256": "a64ccdd734888efe0cf36962b614b405583d68da478205e37ed0b82fa307081d"}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python311/kernel-reconstruction.log b/research/e8-early-reset-kernel/local-evidence/reset12-python311/kernel-reconstruction.log
new file mode 100644
index 0000000000..36899d0eec
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python311/kernel-reconstruction.log
@@ -0,0 +1 @@
+{"status": "PASS_FROZEN_RESET_KERNEL_RETIMING", "input_sha256": "98ffef9246c8bf6c537ab5e134321abea05cf0b7830c9e3fd92cbe4e88d8c308", "reset_sha256": "33fba385c1c69d6cbbe6c76e4d2eca9f69453a910f3c9e5e62f3e7b189510ded", "kernel_sha256": "ad81e6d6c6bfde1c2db9d9f0b4767af4db1affdfa2912038426360cb0895ef65", "output_sha256": "a64ccdd734888efe0cf36962b614b405583d68da478205e37ed0b82fa307081d", "entries": 116, "total_entrance_rank": 152, "donor_slots": 115, "new_frames": 0, "frame_changes": 10, "additional_resets": 1, "controls": ["wrong reset source", "missing reset parent", "wrong insertion time", "wrong kernel source", "missing donor", "duplicate pivot", "wrong old frame", "duplicate frame change"]}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python311/two-moments.log b/research/e8-early-reset-kernel/local-evidence/reset12-python311/two-moments.log
new file mode 100644
index 0000000000..3523e1d748
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python311/two-moments.log
@@ -0,0 +1 @@
+PASS two rational bit moments 0.001135674789165607479118
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python314/RESULT.json b/research/e8-early-reset-kernel/local-evidence/reset12-python314/RESULT.json
new file mode 100644
index 0000000000..e14f143ee3
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python314/RESULT.json
@@ -0,0 +1,49 @@
+{
+  "status": "PASS_FULL_EARLY_RESET_KERNEL_COMPOSITION",
+  "kappa": "1134386495022041/1000000000000000000",
+  "kappa_decimal": "0.001134386495022041",
+  "source_manifest_sha256": "ad6b66aba41895ac66bd8e988717ab2e16ca974f93a6fa309c50de0b09f1a28e",
+  "checks": [
+    {
+      "name": "full-early-reuse434",
+      "seconds": 108.24978258297779,
+      "log_sha256": "c0edbb5dd9975ae1879cf20f98ed89b925ff3f9b695f027aca13f4930a6f81a6"
+    },
+    {
+      "name": "kernel-reconstruction",
+      "seconds": 0.1143968750257045,
+      "log_sha256": "14e8624214481449cc954f2490f8873de6e033f990b1e945acf466ff92077616"
+    },
+    {
+      "name": "export",
+      "seconds": 0.36100183392409235,
+      "log_sha256": "d4ea7999a985f7287ace0551ca025d99c304cb78cbc30eee6223585ed9af109f"
+    },
+    {
+      "name": "integer-source-spans",
+      "seconds": 0.07987483299802989,
+      "log_sha256": "7e45fe477c18d80a06f9cbd2655394950953ad8c9cc12e7d512bd1d39c890126"
+    },
+    {
+      "name": "global-program",
+      "seconds": 2.5945157079258934,
+      "log_sha256": "52fd486807379dc18d48e24cc0ebdc21a03c57847a4f1be478463caa41d05ecf"
+    },
+    {
+      "name": "independent-audit",
+      "seconds": 1.8685832909541205,
+      "log_sha256": "9851de62a8b18ef2e34ef94aa1d31d1c69748b59c44e5909cc7ae26b83091d43"
+    },
+    {
+      "name": "two-moments",
+      "seconds": 0.1405484579736367,
+      "log_sha256": "c866854ad55093f6feb992efced66f2cd2a1076cb7c9374fdb22565f3d2eaf82"
+    },
+    {
+      "name": "finite-assembly",
+      "seconds": 0.15280125010758638,
+      "log_sha256": "8b5598ec4d2b0dfadde4ae6f3dbe913b6e213937db89b485234c4d323fa38db8"
+    }
+  ],
+  "parent_phase_mode": "full replay"
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python314/export.log b/research/e8-early-reset-kernel/local-evidence/reset12-python314/export.log
new file mode 100644
index 0000000000..faa64f2c75
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python314/export.log
@@ -0,0 +1 @@
+exported 19041 records, 944 frames, n 986 ZERO 0
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python314/finite-assembly.log b/research/e8-early-reset-kernel/local-evidence/reset12-python314/finite-assembly.log
new file mode 100644
index 0000000000..d8d183fe0a
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python314/finite-assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_EARLY_RESET_KERNEL_ASSEMBLY 0.001134386495022041 8.242417270912869 {'prefix_bits': 226, 'charged_prefix_bits': 256, 'coefficient_bits': 226, 'two_level_coefficient_bits': 488, 'charged_two_level_coefficient_bits': 512, 'row_coefficient': 18355, 'live': 14223, 'physical': 14232}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python314/full-early-reuse434.log b/research/e8-early-reset-kernel/local-evidence/reset12-python314/full-early-reuse434.log
new file mode 100644
index 0000000000..d8e9693dc9
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python314/full-early-reuse434.log
@@ -0,0 +1,14 @@
+RUN full-parent433
+PASS full-parent433
+RUN reconstruct
+PASS reconstruct
+RUN export
+PASS export
+RUN global-program
+PASS global-program
+RUN independent-audit
+PASS independent-audit
+RUN two-moments
+PASS two-moments
+RUN finite-assembly
+PASS finite-assembly
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python314/global-program.log b/research/e8-early-reset-kernel/local-evidence/reset12-python314/global-program.log
new file mode 100644
index 0000000000..fc602bcb67
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python314/global-program.log
@@ -0,0 +1,2 @@
+Fresh prefix bits 226 charged 256
+{"status": "PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE", "h": 8, "m": 64, "v": 120, "R": 746, "replicas": 8, "live": 14223, "physical": 14232, "word_sha256": "a64ccdd734888efe0cf36962b614b405583d68da478205e37ed0b82fa307081d", "source_records_sha256": "5b83af9e7996b8e388dee898de3eaa6bf7b7c099e41589745ab48ecbdb14feee", "independent_unbanked_scalar_columns": 7674, "all_scalar_columns_restored": true, "geometry_sha256": "4ec791160bf348c5445f92869ff688bfb41d215f5c614b73e2540763d63a72f0", "template_sha256": "f4104a1c51bed199e02f7d9edd7436cd5ad26ceca49b3c34106efc1a2bd59b64", "emitted_program_sha256": "3c616050a58352f755bf9442c609253dc4e2aedd26cdc1ff266f352807b564da", "emitted_events": 1370952, "local_invocations": 72, "bank_assignments": 53712, "banks_per_stage": 727, "entrance_rank_total": 152, "mixed_width_slots": true, "padding_calls": 0, "profile": {"1": 181080, "2": 73512, "3": 21528, "4": 25272, "5": 7776, "7": 6768, "8": 648, "14": 3840, "28": 3840, "42": 3840}, "paid_calls": 328104, "rank_mass": 907776, "deficit": 2496, "maxchild": 42, "halving_depth": 2, "halving_integer_inequality": [4096, 3528], "local_additions": 14715, "bridge_additions": 17280, "copy_erase_episodes": 648, "global_prefix_bits": 226, "charged_prefix_bits": 256, "omitted_bridge_shears_rejected": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], "scope": "Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.", "seconds": 2.5404236250324175}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python314/independent-audit.log b/research/e8-early-reset-kernel/local-evidence/reset12-python314/independent-audit.log
new file mode 100644
index 0000000000..e84a34e62e
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python314/independent-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT", "template_sha256": "f4104a1c51bed199e02f7d9edd7436cd5ad26ceca49b3c34106efc1a2bd59b64", "source_frames": 944, "exact_nested_frame_pairs": 3357, "exact_reflected_pairs": 3357, "orthogonal_lift_argument": "Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.", "exact_bank_families": 6543, "mixed_width_slots": true, "entrance_rank_total": 152, "mutations_rejected": ["omit an idle child", "omit a bridge", "omit terminal exchange", "remove a local invocation", "re-use a helper bank slot", "understate live stock", "omit a local paid move", "wrong reflected copy charge"], "profile": {"1": 181080, "2": 73512, "3": 21528, "4": 25272, "5": 7776, "7": 6768, "8": 648, "14": 3840, "28": 3840, "42": 3840}, "seconds": 1.814236250007525}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python314/integer-source-spans.log b/research/e8-early-reset-kernel/local-evidence/reset12-python314/integer-source-spans.log
new file mode 100644
index 0000000000..3095912ab1
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python314/integer-source-spans.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_F2_AND_INTEGER_SOURCE_SPANS", "columns": 986, "profile": {"1": 2515, "4": 351, "2": 1021, "3": 299, "5": 108, "8": 9, "7": 14}, "word_sha256": "a64ccdd734888efe0cf36962b614b405583d68da478205e37ed0b82fa307081d"}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python314/kernel-reconstruction.log b/research/e8-early-reset-kernel/local-evidence/reset12-python314/kernel-reconstruction.log
new file mode 100644
index 0000000000..36899d0eec
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python314/kernel-reconstruction.log
@@ -0,0 +1 @@
+{"status": "PASS_FROZEN_RESET_KERNEL_RETIMING", "input_sha256": "98ffef9246c8bf6c537ab5e134321abea05cf0b7830c9e3fd92cbe4e88d8c308", "reset_sha256": "33fba385c1c69d6cbbe6c76e4d2eca9f69453a910f3c9e5e62f3e7b189510ded", "kernel_sha256": "ad81e6d6c6bfde1c2db9d9f0b4767af4db1affdfa2912038426360cb0895ef65", "output_sha256": "a64ccdd734888efe0cf36962b614b405583d68da478205e37ed0b82fa307081d", "entries": 116, "total_entrance_rank": 152, "donor_slots": 115, "new_frames": 0, "frame_changes": 10, "additional_resets": 1, "controls": ["wrong reset source", "missing reset parent", "wrong insertion time", "wrong kernel source", "missing donor", "duplicate pivot", "wrong old frame", "duplicate frame change"]}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-python314/two-moments.log b/research/e8-early-reset-kernel/local-evidence/reset12-python314/two-moments.log
new file mode 100644
index 0000000000..3523e1d748
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-python314/two-moments.log
@@ -0,0 +1 @@
+PASS two rational bit moments 0.001135674789165607479118
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-reconstruction.json b/research/e8-early-reset-kernel/local-evidence/reset12-reconstruction.json
new file mode 100644
index 0000000000..8974e56828
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-reconstruction.json
@@ -0,0 +1,23 @@
+{
+  "status": "PASS_FROZEN_RESET_KERNEL_RETIMING",
+  "input_sha256": "98ffef9246c8bf6c537ab5e134321abea05cf0b7830c9e3fd92cbe4e88d8c308",
+  "reset_sha256": "33fba385c1c69d6cbbe6c76e4d2eca9f69453a910f3c9e5e62f3e7b189510ded",
+  "kernel_sha256": "ad81e6d6c6bfde1c2db9d9f0b4767af4db1affdfa2912038426360cb0895ef65",
+  "output_sha256": "a64ccdd734888efe0cf36962b614b405583d68da478205e37ed0b82fa307081d",
+  "entries": 116,
+  "total_entrance_rank": 152,
+  "donor_slots": 115,
+  "new_frames": 0,
+  "frame_changes": 10,
+  "additional_resets": 1,
+  "controls": [
+    "wrong reset source",
+    "missing reset parent",
+    "wrong insertion time",
+    "wrong kernel source",
+    "missing donor",
+    "duplicate pivot",
+    "wrong old frame",
+    "duplicate frame change"
+  ]
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-retimed-assembly.json b/research/e8-early-reset-kernel/local-evidence/reset12-retimed-assembly.json
new file mode 100644
index 0000000000..3a55a898fa
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-retimed-assembly.json
@@ -0,0 +1,103 @@
+{
+  "status": "PASS_CONDITIONAL_EARLY_RESET_KERNEL_ASSEMBLY",
+  "kappa": "1134386495022041/1000000000000000000",
+  "kappa_decimal": "0.001134386495022041",
+  "bit_lower": "567837394582803739559/500000000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr425_percent": 8.242417270912869,
+  "bit_invoice": {
+    "prefix_bits": 226,
+    "charged_prefix_bits": 256,
+    "coefficient_bits": 226,
+    "two_level_coefficient_bits": 488,
+    "charged_two_level_coefficient_bits": 512,
+    "row_coefficient": 18355,
+    "live": 14223,
+    "physical": 14232
+  },
+  "strict_outer_constraints": {
+    "bit_positive": "1135674789165607476762950437600136482894435608351465471751006476460052468033709894322509001124352104286361612170721636984672041266974479004307242564495446749598936027/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "48311760040721523237049562399863517105564391648534528248993523539947531966290105677490998875647895713638387829278363015327958733025520995692757435504553250401063973/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "30066013450793671/1000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "48311760040721522053063013193534517105564391648534528248993523539947531966290105677490998875647895713638387829278363015327958733025520995692757435504553250401063973/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_positive": "567837394582803737245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_internal": "1135674789165607476762950437600136482894435608351465471751006476460052468033709894322509001124352104286361612170721636984672041266974479004307242564495446749598936027/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_leaf": "24155880020360762162206295762374735315732633424403747018932370121439237734151529298797967471533842179328195038991285794025591537234397482518419984726755629507774550995446749598936027/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_positive": "567837394582803862245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_below_one": "499432162605417196137754199570365539235315732633424403747018932370121439237734151529298797967471533842179328195038991285794025591537234397482518419984726755629507774550995446749598936027/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_reservations": "1/4000000000000000000",
+    "lambda_above_tau": "1135674789165607476762950437600136482894435608351465471751006476460052468033709894322509001124352104286361612170721636984672041266974479004307242564495446749598936027/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_sigma": "48311760040721524372724351565470993868514829248671011143429131891413003717296582137543466909357790036147388953630467301689570903747157980364798702479032254708306537495446749598936027/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_internal": "1135674789165607476762950437600136482894435608351465471751006476460052468033709894322509001124352104286361612170721636984672041266974479004307242564495446749598936027/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_prime_above_lambda": "1135674789165607476762950437600136482894435608351465471751006476460052468033709894322509001124352104286361612170721636984672041266974479004307242564495446749598936027/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_leaf": "24155880020360762162206295762374735315732633424403747018932370121439237734151529298797967471533842179328195038991285794025591537234397482518419984726755629507774550995446749598936027/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_reservations": "1/4000000000000000000",
+    "lambda_prime_below_one": "567837394582803737245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "epsilon_positive": "499999999999999999500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/500567837394582803737245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973",
+    "epsilon_below_one": "567837394582804237245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973/500567837394582803737245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973",
+    "guard_width": "567837394582804237245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973/500567837394582803737245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973",
+    "K_geometry": "375567837394582803862245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973/500567837394582803737245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973000000000000000000",
+    "K_dominates_log": "567837394582803861677963035051656902438466936941135488296800263302964509284780840822641270262617687119469772432542556385302603501756888311507171552507641853010645433731308879908838523995446749598936027/500567837394582803737245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973000000000000000000",
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+    "gamma_sublinear": "1/2000000000000000000",
+    "cell_above_band": "999999999999999998499432162605417196262754199570365539235315732633424403747018932370121439237734151529298797967471533842179328195038991285794025591537234397482518419984726755629507774550995446749598936027/2002271349578331214948983201718537843058737069466302385011924270519514243049063393882804808130113864631282687219844034856823897633851062410069926320061092977481968901796018213001604255892000000000000000000",
+    "prime_interval_packing": "567837394582804237245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973/500567837394582803737245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973",
+    "alpha_positive": "1135674789165607973923763464686117792122734303516731741277867893181525271550629311523843302791083844940141577393551270591277011964522490828988751567780886223502870882735862130309902496995446749598936027/1001135674789165607474491600859268921529368534733151192505962135259757121524531696941402404065056932315641343609922017428411948816925531205034963160030546488740984450898009106500802127946000000000000000000",
+    "alpha_below_one": "999999999999999999500567837394582803737245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973/1001135674789165607474491600859268921529368534733151192505962135259757121524531696941402404065056932315641343609922017428411948816925531205034963160030546488740984450898009106500802127946000000000000000000",
+    "alpha_below_one_fourth": "249148243908125793894699136750131112590219399379771066385212665921757755109582294923826757713473149233970194325086953086511710192266860310429752038439855735961743241841766414494890629489504553250401063973/1001135674789165607474491600859268921529368534733151192505962135259757121524531696941402404065056932315641343609922017428411948816925531205034963160030546488740984450898009106500802127946000000000000000000",
+    "delta_positive": "1/8000000000000000000",
+    "delta_below_one_eighth": "999999999999999999/8000000000000000000",
+    "short_record_fallback": "499431517726803822588123071239367259217295111352889011618907232388848480809352679820082014863775504375216932247026723180551239757309681437743761312668307922101361140764794047837440085905136967017675486515058236875623939289902132168035898710949869064026676730957943098436917196037833162021151275336091659154545830807641575819445683784907730976810438544729/500567837394582803737245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "small_field_exposure": "1/1000000000000000000",
+    "artificial_boundary": "28036341593253299444685434739680353900151530512749741542484841130411954677543957505014512612368619379512626601615089956182644377556500024703736744346365784447263947168782111141137144770619013659751203191919/4004542699156662429897966403437075686117474138932604770023848541039028486098126787765609616260227729262565374439688069713647795267702124820139852640122185954963937803592036426003208511784000000000000000000",
+    "literal_scalar_guard": "1",
+    "row_product_gap": "23971789/25",
+    "balanced_prefix_above_kappa": "502823019265554445599918932587586269276258086610551532908735467033238561084196356589914176536311049146491748690852420013625698283092847568696838387654373537154859179143337205665513971107/500567837394582803737245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973000000000000000000",
+    "coordinate_movement_above_kappa": "1288294143566476762950437600136482894435608351465471751006476460052468033709894322509001124352104286361612170721636984672041266974479004307242564495446749598936027/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_phase_layer_above_kappa": "1127590935485820931336566078975904255786909621987968327877199701680000160965254059606487251891291494335538442945705649709861937315040983089678403819550146392183476847166326207556453567/250283918697291401868622900214817230382342133683287798126490533814939280381132924235350601016264233078910335902480504357102987204231382801258740790007636622185246112724502276625200531986500000000000000000",
+    "bulk_exposure_above_kappa": "1288294143566476762950437600136482894435608351465471751006476460052468033709894322509001124352104286361612170721636984672041266974479004307242564495446749598936027/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "Gaussian_arithmetic_above_kappa": "1519744967151521546113122458552517850386643356051534282004978398116515684862241610365807402127846062382830630502014316537975714222428952536987299201158622075386412305901674879072106448991/4004542699156662429897966403437075686117474138932604770023848541039028486098126787765609616260227729262565374439688069713647795267702124820139852640122185954963937803592036426003208511784000000000000000000",
+    "scalar_work_above_kappa": "3522016316729852761062105660271055693445380425517836667016902668636029927911305004248612210257959927014113317721858351394799611856280014947057225521219715052868381207697693092073710704883/4004542699156662429897966403437075686117474138932604770023848541039028486098126787765609616260227729262565374439688069713647795267702124820139852640122185954963937803592036426003208511784000000000000000000",
+    "dimension_above_kappa": "499432162605417195765577218835919984835234665221010673023277018980672972146469618562537359051667890432093504731350040432285774282389654411108216703077574324326346162205368983904458115170337205665513971107/500567837394582803737245800429634460764684267366575596252981067629878560762265848470701202032528466157820671804961008714205974408462765602517481580015273244370492225449004553250401063973000000000000000000"
+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "1246079287922516651747375691465487591099689/1000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "23185215992417"
+    },
+    {
+      "gap": "1415140832595034396474941776427135002188181754409885381132694613/1000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "17976418748903226163"
+    },
+    {
+      "gap": "1607139766697007916546017997463292336138025494980115458929693051534507965928335896721/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "13937831381067034658715072"
+    },
+    {
+      "gap": "1825188115703288057906103588665105413373277523419207384605150381331166473627703091402094501403784476275357/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "10806554204179814659704240499139"
+    },
+    {
+      "gap": "2072820128488904054524662831687306918802149932299369615044187873014231653127961511325271757981851846286779331714212966319219769/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "8378750651734173154233973391771573239"
+    },
+    {
+      "gap": "2354049562399863517105564391648534528248993523539947531966290105677490998875647895713638387829278363015327958733025520995692757435504553250401063973/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "6496378138443258334045184443573088118162369"
+    }
+  ],
+  "bit_template_sha256": "f4104a1c51bed199e02f7d9edd7436cd5ad26ceca49b3c34106efc1a2bd59b64",
+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f",
+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim."
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-tested-manifest.json b/research/e8-early-reset-kernel/local-evidence/reset12-tested-manifest.json
new file mode 100644
index 0000000000..fdf55597d0
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-tested-manifest.json
@@ -0,0 +1,44 @@
+{
+  "files": {
+    "apply.py": "11eeac4b02521a3286160a87fdac080fefb11c25779d9eaec9f44b18d7b6c1ae",
+    "bit_audit.py": "f5d81ae080ee55d174feef6de2314113864a7e3e3d29c5559071c306edd2f272",
+    "bit_global.py": "7e3d651b759b3d6ed09be1c30390321eb20b08b92710980603252428628c5e8d",
+    "bit_price.py": "36bf15803567a95b139a908461541bf19efe1f5b85fb31c270021833ab1393ee",
+    "combined.py": "83ba7f8deda264c283176c564d9d93dc8948edae0a8e8ed216b48240b5f74c85",
+    "EXPECTED.json": "2fb27286985893cd81468b3d41eaf80c9d3fc41cb5390d46d60cfef29b2f1813",
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE.md": "4cd95f5fecad72bd29dd2f42d1429c3ec153b63551fcc9623d2fbf8a6702c75f",
+    "PROOF.md": "7ddea4da1a0f2440d9992bc3acd85189e3d44c3fa0e9f26482b0733494348b50",
+    "README.md": "b36ab0ccde09283e0798920fd163742431bb59c57268f48ef9955891e22b2829",
+    "RESET12.json": "a310f1d3a8ec714e6dd12ec5364d16b9fa254527cf684b09dc1846d064e9b41c",
+    "RETIMING.json": "0a6d2ae3f046d1d18e29ce068b3cd09b026dde97801b0a0f0bfca8d17ccd9926",
+    "SELECTION.json": "48a5602482c9e8b102765ee29dd61f82c4dc82dd44849ca2fba464237927121f",
+    "SOURCE.json": "92d4ab60b5689b395f1aa2e909c1fa3f4e4622ada47f680014fb85068c9d71ba",
+    "source_span.py": "4772d177f37254c6f854af5ee3871aca193cfb24307a53c143c3bf517e56631e",
+    "VALIDATION.json": "fa3c3b56669b2cd08533fc1250a1d6d4979b2c19fe2740f2a153500fba1babb7",
+    "verify.py": "16c07414bc956744dc93b8e35b642267ea9819be922b0d3e081c543fdbf92a70",
+    "local-evidence/ASSEMBLY-118.json": "3e610791f14777e6024adfe562175d51cd5dbeb2ce585f59d56d58092277bac1",
+    "local-evidence/ASSEMBLY.json": "7c3cc4b503e4cf0fd3e050be46ad0da183c5b1c490f4901245df944fd9d6194e",
+    "local-evidence/AUDIT-118.json": "cd37be4c487f924490c78052a36a8e091b261a7beb60f67f495779078f6ab906",
+    "local-evidence/AUDIT.json": "76a146a9123d8b653e6e46ff93f153653f9cefd0f5c3fdd264a59f1322110262",
+    "local-evidence/BIT-PRICE-118.json": "97e29c84202255a6468bb0444f3438910e7ab4e19bbadb89636ede78376a9306",
+    "local-evidence/BIT-PRICE.json": "9a4a320cab1ce62b0c2329ac1bf3b81f73580fd603a406e4bfaae2962dfdad35",
+    "local-evidence/FULL-PYTHON311.json": "62b37525bf7b60c0d9101ed571681f3bf46ea75df065939864307e4986018332",
+    "local-evidence/FULL-PYTHON314.json": "85797531db037d06fb597a4c9b6ef6bd71e6a0ab4f220ae70b1b6bf3aeda205f",
+    "local-evidence/full118-python311.json": "368b3d851919f77e6865b51cec731fc5bd0f16e0bd494fbaa2df5b57b9342d1c",
+    "local-evidence/full118-python314.json": "2bb62d9bc89834463959ce755f886e58793ded811dba26b038c20626ef90c814",
+    "local-evidence/GLOBAL-118.json": "a7491dfd2ff51d0574a6e46e3b100531969219dc41d93afbaca38ee3afbfa7e7",
+    "local-evidence/GLOBAL.json": "16c4e829eea1b2d12b70cec7e6a9c0e33ea0eae98a40894a3b779790fd2efbb3",
+    "local-evidence/reset12-reconstruction.json": "178f9fef29a4f7e18c9a3abebf455bb7c0545a85e2bdfdda6d6def5afc8f9239",
+    "local-evidence/reset12-retimed-assembly.json": "a54ca18bca34c7407872dded5402b463be2c76bab271248e519bbd0492b3f575",
+    "local-evidence/SOURCE-SPANS-118.log": "115ea64de78aaa3ea6edc9684f66f9ec6f88c806608caf85ae32853059c14f37",
+    "local-evidence/SOURCE-SPANS.log": "bdf95dbce8337be57aab8a3d3b42a711ee276496c40cbb4c5356fc9cc9b2e811",
+    "local-evidence/VALIDATION-110-ENTRIES.json": "77ad775cf69f5d913568b6276b0dfeb2eaef0306f57b71c0a467bff793807267",
+    "vendor/kernel417/e8core.py": "3f4e25f700b7eb5821ab9cdfc65541f3f921baffeb8704beb21c6d7072052d29",
+    "vendor/kernel417/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "vendor/kernel417/stages.py": "e73ab7836519510ed30dd7e3022dae557fa50fc513d723197929bff741859668",
+    "vendor/kernel417/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "vendor/kernel417/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "vendor/kernel417/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+  }
+}
diff --git a/research/e8-early-reset-kernel/local-evidence/reset12-verification-provenance.json b/research/e8-early-reset-kernel/local-evidence/reset12-verification-provenance.json
new file mode 100644
index 0000000000..59e034f989
--- /dev/null
+++ b/research/e8-early-reset-kernel/local-evidence/reset12-verification-provenance.json
@@ -0,0 +1,5 @@
+{
+  "tested_code_commit": "6a1c6a308429ea11f64b679df6abdf2bf40436b0",
+  "tested_manifest_sha256": "ad6b66aba41895ac66bd8e988717ab2e16ca974f93a6fa309c50de0b09f1a28e",
+  "publication_changes": "Documentation and verification receipts only; all executable code, frozen witnesses and expected outputs retain their tested hashes."
+}
diff --git a/research/e8-early-reset-kernel/source_span.py b/research/e8-early-reset-kernel/source_span.py
new file mode 100644
index 0000000000..a8722a7e4f
--- /dev/null
+++ b/research/e8-early-reset-kernel/source_span.py
@@ -0,0 +1,10 @@
+"""PR417/435 independent all-column replay, including integer source-span legality."""
+from pathlib import Path
+import sys,json,hashlib
+ROOT=Path(__file__).resolve().parent;sys.path.insert(0,str(ROOT/'vendor/kernel417'))
+from e8core import Lat,replay
+w=json.loads(Path(sys.argv[1]).read_text());frames=json.loads(Path(sys.argv[2]).read_text())['frames'];L=Lat(w['lines']);masks=[sum(1<<x for x in f) for f in w['frames']]
+# These ranks/bases are independently checked over Q by bit_audit.py in the wrapper.
+for i,m in enumerate(masks):L._close[m]=m;L._dim[m]=frames[str(i)]['dim']
+r=replay(w,L=L,masks=masks,span_mode='z');assert not r['viol'],r['viol'][:10]
+print(json.dumps(dict(status='PASS_INDEPENDENT_F2_AND_INTEGER_SOURCE_SPANS',columns=r['n'],profile=dict(r['H']),word_sha256=hashlib.sha256(Path(sys.argv[1]).read_bytes()).hexdigest())))
diff --git a/research/e8-early-reset-kernel/vendor/kernel417/LICENSE b/research/e8-early-reset-kernel/vendor/kernel417/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-early-reset-kernel/vendor/kernel417/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
+      other entities that control, are controlled by, or are under common
+      control with that entity. For the purposes of this definition,
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diff --git a/research/e8-early-reset-kernel/vendor/kernel417/e8core.py b/research/e8-early-reset-kernel/vendor/kernel417/e8core.py
new file mode 100644
index 0000000000..f2874bae8e
--- /dev/null
+++ b/research/e8-early-reset-kernel/vendor/kernel417/e8core.py
@@ -0,0 +1,203 @@
+"""Our own engine for bitE8/1 words (E8 root-line labels, h = 8): frame algebra over Q via root-line masks,
+legality/F2 replay, five-stage histogram, exact bit coarse saving and PR #315 outer assembly (our engine copies).
+Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0."""
+import gzip, json, os, importlib.util
+from fractions import Fraction as Q
+from collections import Counter
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+def _load(n):
+    s = importlib.util.spec_from_file_location('e8_' + n, os.path.join(HERE, "engines", n + ".py"))
+    m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+moment = _load('moment'); other = _load('base_two_moment'); outer = _load('outer')
+
+B2 = Q(876248285600677, 10**18)   # Sussman E8 five-stage (PR #352)
+B3 = Q(932783231884153, 10**18)   # DaysSky seven-stage B_3 (PR #363; no Lean proof)
+
+
+def load_word(p):
+    with (gzip.open(p, 'rt') if p.endswith('.gz') else open(p)) as f:
+        return json.load(f)
+
+
+def save_word(c, p):
+    with gzip.open(p, 'wt') as f:
+        json.dump(c, f, separators=(',', ':'))
+
+
+def rank(vecs):
+    rows = [[Q(x) for x in r] for r in vecs]; rk = 0
+    n = len(rows[0]) if rows else 0
+    for col in range(n):
+        p = next((i for i in range(rk, len(rows)) if rows[i][col] != 0), None)
+        if p is None: continue
+        rows[rk], rows[p] = rows[p], rows[rk]
+        for i in range(len(rows)):
+            if i != rk and rows[i][col] != 0:
+                f = rows[i][col] / rows[rk][col]; rows[i] = [a - f * b for a, b in zip(rows[i], rows[rk])]
+        rk += 1
+    return rk
+
+
+class Lat:
+    """Root-spanned subspaces of Q^8 represented by the mask of root lines they contain."""
+    def __init__(self, lines):
+        self.lines = [tuple(x) for x in lines]; self.v = len(lines)
+        self._dim = {0: 0}; self._close = {}
+        # Gram (form <x,y>/2) for orthogonality
+        self.ip = [[sum(a * b for a, b in zip(x, y)) // 2 for y in self.lines] for x in self.lines]
+
+    def close(self, mask):
+        """mask of all root lines in span(roots of mask)"""
+        if mask in self._close: return self._close[mask]
+        idx = [i for i in range(self.v) if mask >> i & 1]
+        basis = []
+        for i in idx:
+            if rank([self.lines[j] for j in basis] + [self.lines[i]]) > len(basis): basis.append(i)
+        d = len(basis); out = 0
+        if d == 8: out = (1 << self.v) - 1
+        elif d:
+            B = [self.lines[j] for j in basis]
+            for i in range(self.v):
+                if rank(B + [self.lines[i]]) == d: out |= 1 << i
+        self._close[mask] = out; self._close[out] = out; self._dim[out] = d
+        return out
+
+    def dim(self, mask):
+        if mask not in self._dim: self.close(mask)
+        return self._dim[mask]
+
+    def basis(self, mask):
+        b = []
+        for i in range(self.v):
+            if mask >> i & 1 and rank([self.lines[j] for j in b] + [self.lines[i]]) > len(b): b.append(i)
+        return b
+
+    def perp(self, t):
+        return self.close(sum(1 << j for j in range(self.v) if self.ip[t][j] == 0))
+
+
+def to_masks(c, L):
+    return [L.close(sum(1 << i for i in fr)) for fr in c['frames']]
+
+
+PHASES = ('D', 'A', 'B', 'C')
+
+
+def replay(c, L=None, masks=None, check_f2=True, span=True, span_mode='z'):
+    """Exact legality + F2 replay + histogram of a bitE8/1 word. Returns dict(H_local, steps, ...).
+    Legality: each register's frames nested (mask inclusion = exact Q-subspace inclusion for root-spanned frames) and
+    strictly increasing at each move; every gate at one common frame; D compensation at frame 0; y at frame 0 at the
+    scatter; COPY of retained totals; final frames (x, helpers FULL; y_t at its cap t-perp).
+    Source-span: every non-target operand's x-support lies in the gate frame."""
+    L = L or Lat(c['lines']); masks = masks or to_masks(c, L)
+    v, R, h = c['v'], c['R'], c['h']; n = 2 * v + R; FULL = (1 << v) - 1
+    cur = [masks[f] for f in c['start']]
+    for r in range(v): assert cur[r] == L.close(1 << r), 'x start'
+    for r in range(v, 2 * v): assert cur[r] == 0, 'y start at 0'
+    sig = [L.dim(cur[r]) for r in range(n)]
+    H = Counter(); steps = 0; viol = []
+    val = [1 << i for i in range(n)]
+    zsupp = [{i: 1} if i < v else {} for i in range(n)]  # integer support of each register over the x columns (all ADDs are +1)
+    def climb(r, m):
+        nonlocal steps
+        if cur[r] == m: return
+        assert cur[r] & ~m == 0 and cur[r] != m, ('not nested', r)
+        H[L.dim(m) - L.dim(cur[r])] += 1; steps += 1; cur[r] = m
+    def run(gates, ph):
+        for k, (f, d, srcs) in enumerate(gates):
+            m = masks[f]
+            assert d not in srcs and len(set(srcs)) == len(srcs), (ph, k)   # rohanarun: source destinations allowed (#433 source-basis gates); spans checked below
+            for x in [d] + srcs: climb(x, m)
+            for s in srcs:
+                val[d] ^= val[s]
+                if span:
+                    if s < v or s >= 2 * v:
+                        ms = sum(1 << i for i in zsupp[s])
+                        if ms & ~m: viol.append((ph, k, s))
+                    zd = zsupp[d]
+                    for i, a in zsupp[s].items():
+                        w = zd.get(i, 0) + a
+                        if w: zd[i] = w
+                        else: zd.pop(i, None)
+                    if span_mode == 'f2':
+                        zsupp[d] = {i: 1 for i in range(v) if val[d] >> i & 1}
+            if span and (d >= 2 * v or d < v):
+                md = sum(1 << i for i in zsupp[d])
+                if md & ~m: viol.append((ph, k, d))
+    run(c['D'], 'D')
+    for r in range(v, n): assert cur[r] == masks[c['start'][r]], 'D compensation at frame 0 (helpers untouched otherwise)'
+    run(c['A'], 'A')
+    for t in range(v): assert cur[v + t] == 0, 'y at frame 0 at the scatter'
+    copies = [val[q] for q in c['ret']]
+    for q in c['ret']:
+        assert q >= 2 * v or q < v; H[L.dim(cur[q])] += 1   # rohanarun: #433 retains totals in source rows
+    for t, row in enumerate(c['scatter']):
+        for k in row: val[v + t] ^= copies[k]
+    run(c['B'], 'B'); run(c['C'], 'C')
+    for r in range(n): climb(r, masks[c['final'][r]])
+    for r in range(v): assert cur[r] == FULL
+    for r in range(2 * v, n): assert cur[r] == FULL
+    for t in range(v): assert cur[v + t] == L.perp(t), 'y final at cap'
+    if check_f2:
+        for s in range(v): assert val[s] == 1 << s
+        for t in range(v): assert val[v + t] == (1 << (v + t)) | (1 << t), ('target', t)
+        for r in range(2 * v, n): assert val[r] == 1 << r, ('helper', r)
+    return dict(sig=sig, viol=viol, H=H, steps=steps, n=n, v=v, R=R, h=h, L=L, masks=masks, ncopy=len(c['ret']))
+
+
+def profile(H_local, v, h=8):
+    prof = Counter({j: 5 * c for j, c in H_local.items()})
+    for j in (2 * h - 2, h - 1, 2 * h + 2, 4): prof[j] += 2 * v
+    return prof
+
+
+def coarse(H, m, W):
+    grid = Q(1, 10**18)
+    root = moment.certify(dict(H), m, W, True); c = Q(int(Q(root['lower']) * 10**18), 10**18)
+    assert moment.moment(H, m, W, c, True)[1] < 1 < moment.moment(H, m, W, c + grid, True)[0]
+    fb = 32 * m * m * sum(H.values())
+    _, up = other.moment(m, W, list(H.items()), c); _, bad = other.moment(m, W, [(1, fb)], c)
+    lo, _ = other.moment(m, W, list(H.items()), c + grid); blo, _ = other.moment(m, W, [(1, fb)], c + grid)
+    assert up + Q(1, 10**16) * bad < 1 < lo + Q(1, 10**16) * blo
+    return c
+
+
+def kappa(c, b):
+    grid = Q(1, 10**18); eta = Q(1, 10**12); beta = Q(1, 10**9); cap = (1 - beta) * b
+    sv = min(c, Q(((cap - grid) * 10**18).__floor__(), 10**18)); binding = 'bit' if sv == c else 'complex'
+    chain = [Q(384599, 10**10)]
+    for _ in range(3):
+        a = (1 - sv) * sv + sv * chain[-1]; assert chain[-1] < a < sv < 1 - a; chain.append(a)
+    bit = chain[-1]
+    bridge = dict(proof='PROOF.md', representation='Exact powers with source-bound finite overcharges',
+                  semantic=dict(G=dict(base=2, exponent=30000), E=dict(base=2, exponent=100000), B_upper=dict(base=2, exponent=100001),
+                                C0=dict(base=2, exponent=210000), C1=1, strict_literal_gap=1, induction_gap_lower=1),
+                  rows=dict(coefficient=20161, degree=10**6, suffix_slope=4 * 10**6, degree_gap=Q(10**6) - Q(51 * 20161, 25)))
+    q = bit * (1 - 2 * eta); mn = (1 - eta) * q / (1 + q); t = mn * 10**18; k = Q((t.numerator - 1) // t.denominator, 10**18)
+    asm = outer.assembly(bit, b, bridge, k, eta=eta, beta=beta)
+    assert len(asm['strict_constraints']) == 47 and min(asm['strict_constraints'].values()) > 0
+    try:
+        outer.assembly(bit, b, bridge, k + grid, eta=eta, beta=beta); raise SystemExit('ADJACENT ADMITTED')
+    except AssertionError: pass
+    return k, binding
+
+
+def price_word(c, **kw):
+    r = replay(c, **kw)
+    v, h, R = r['v'], r['h'], r['R']; m = 5 * h
+    resid = sum(h - r['sig'][x] for x in range(2 * v, 2 * v + R))
+    T = 1 if resid % h == 0 else h
+    W = (4 * v * h + resid) * T // h; assert (4 * v * h + resid) * T % h == 0
+    prof = Counter({j: T * k for j, k in profile(r['H'], v, h).items()}); mass = sum(a * b for a, b in prof.items())
+    L_copy = h * r['ncopy']
+    assert m * W - mass == T * (4 * v - 5 * L_copy), ('deficit', m * W - mass)
+    assert 2 * max(prof) < m
+    cc = coarse(prof, m, W)
+    return dict(c=cc, H=r['H'], prof=prof, W=W, T=T, resid=resid, m=m, deficit=m * W - mass, replay=r)
+
+
+def phi_fn(m, W, a):
+    """linearized moment term per child of rank r (float), for search scoring"""
+    import math
+    return lambda r: r / (m * W) * math.exp(a * math.log(m / r))
diff --git a/research/e8-early-reset-kernel/vendor/kernel417/engines/base_two_moment.py b/research/e8-early-reset-kernel/vendor/kernel417/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/e8-early-reset-kernel/vendor/kernel417/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/e8-early-reset-kernel/vendor/kernel417/engines/moment.py b/research/e8-early-reset-kernel/vendor/kernel417/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/e8-early-reset-kernel/vendor/kernel417/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/e8-early-reset-kernel/vendor/kernel417/engines/outer.py b/research/e8-early-reset-kernel/vendor/kernel417/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/e8-early-reset-kernel/vendor/kernel417/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/e8-early-reset-kernel/vendor/kernel417/stages.py b/research/e8-early-reset-kernel/vendor/kernel417/stages.py
new file mode 100644
index 0000000000..9ef95d52f4
--- /dev/null
+++ b/research/e8-early-reset-kernel/vendor/kernel417/stages.py
@@ -0,0 +1,143 @@
+"""Transcript stages on the E8 bit word (bitE8/1), applied from frozen selections, each bound to the exact input word.
+
+retime  (our #329 descent2 / #287 concave retiming, ported to E8 frames): every selected gate g gets a new frame F with
+        close(LB_g + prev frames of its participants) <= F <= rootspan(AND of their next frames), where LB_g is the
+        x-support of the non-target operands (source-span rule); pinned: D gates (frame 0), y at frame 0 at the scatter,
+        retained totals at FULL at COPY, start and final frames. Checked on the joint retimed configuration.
+kernel  (our #320/#329 shared-donor response kernel; #272/#299/#319 lineage): entry = pivot p, entrance E, donors D with
+        resp(p) = XOR resp(D) over F2, where resp(h) = the targets whose frame-0 completion (D) gates read h; E inside the
+        first frame of p and of every donor. p starts at E and leaves the D gates; each donor climbs to E at the start of
+        A and pays d += (its pivots) at E; after C it pays d += (its pivots) again at FULL (F2: d -= p).
+        Exclusivity: pivots are never donors, a donor serves one entrance. Total entrance rank = 0 mod 8 (integral
+        B_4 width W; the residuals then tile width-72 banks with 9 replicas, checked separately).
+
+usage: stages.py retime|kernel IN.json.gz OUT.json.gz SELECTION.json
+After applying, the full exact replay of e8core (legality, F2 on all columns, source spans) must pass and the output
+must equal the frozen output content hash. (This package uses the kernel stage only: on PR #376's word our retiming
+descent finds no move, before or after the kernel.)
+Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0."""
+import sys, os, json, hashlib
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+from e8core import *
+
+
+def content_sha(c):
+    return hashlib.sha256(json.dumps(c, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+
+
+class Framer:
+    def __init__(self, c):
+        self.fl = c['frames']; self.key = {}; self.v = c['v']
+        for k, fr in enumerate(self.fl): self.key.setdefault(sum(1 << i for i in fr), k)
+    def fid(self, m):
+        if m not in self.key: self.key[m] = len(self.fl); self.fl.append([i for i in range(self.v) if m >> i & 1])
+        return self.key[m]
+
+
+def mask_of(lines): return sum(1 << i for i in lines)
+
+
+def occurrences(c, masks):
+    """per register: list of (kind, ref) with pins ('p', mask) and gates ('g', (phase, k)) in time order"""
+    v = c['v']; n = 2 * v + c['R']; FULL = (1 << v) - 1
+    occ = [[('p', masks[c['start'][r]])] for r in range(n)]
+    for ph in ('D', 'A'):
+        for k, (f, d, s) in enumerate(c[ph]):
+            for x in [d] + s: occ[x].append(('g', (ph, k)))
+    for t in range(v): occ[v + t].append(('p', 0))
+    for q in c['ret']: occ[q].append(('p', FULL))
+    for ph in ('B', 'C'):
+        for k, (f, d, s) in enumerate(c[ph]):
+            for x in [d] + s: occ[x].append(('g', (ph, k)))
+    for r in range(n): occ[r].append(('p', masks[c['final'][r]]))
+    return occ
+
+
+def lower_bounds(c, L):
+    v = c['v']; n = 2 * v + c['R']; sup = [1 << i if i < v else 0 for i in range(n)]; lb = {}
+    for ph in ('D', 'A', 'B', 'C'):
+        for k, (f, d, srcs) in enumerate(c[ph]):
+            need = 0
+            for s in srcs:
+                sup[d] |= sup[s]
+                if s < v or s >= 2 * v: need |= sup[s]
+            if d >= 2 * v: need |= sup[d]
+            lb[(ph, k)] = L.close(need) if need else 0
+    return lb
+
+
+def retime(c, sel):
+    L = Lat(c['lines']); masks = to_masks(c, L); occ = occurrences(c, masks); lb = lower_bounds(c, L)
+    gm = {(ph, k): masks[g[0]] for ph in ('D', 'A', 'B', 'C') for k, g in enumerate(c[ph])}
+    pos = {}
+    for r, o in enumerate(occ):
+        for i, (kind, x) in enumerate(o):
+            if kind == 'g': pos.setdefault(x, []).append((r, i))
+    def fr(r, i):
+        kind, x = occ[r][i]; return x if kind == 'p' else gm[x]
+    seen = set()
+    for ph, k, old_lines, new_lines in sel:
+        g = (ph, k); assert ph != 'D' and g not in seen; seen.add(g)
+        assert gm[g] == L.close(mask_of(old_lines)), ('selection not bound to this word', g)
+        F = L.close(mask_of(new_lines)); assert F == mask_of(new_lines), 'frame given as all its root lines'
+        gm[g] = F
+    for g in seen:  # the joint retimed configuration: every moved gate inside its feasible interval
+        F = gm[g]; lo = lb[g]; hi = (1 << c['v']) - 1
+        for r, i in pos[g]: lo |= fr(r, i - 1); hi &= fr(r, i + 1)
+        assert lo & ~F == 0 and F & ~hi == 0, ('outside the feasible interval', g)
+    out = json.loads(json.dumps(c)); fm = Framer(out)
+    for ph in ('D', 'A', 'B', 'C'):
+        out[ph] = [[fm.fid(gm[(ph, k)]), d, list(s)] for k, (f, d, s) in enumerate(c[ph])]
+    return out
+
+
+def kernel(c, sel):
+    L = Lat(c['lines']); masks = to_masks(c, L); v = c['v']; n = 2 * v + c['R']; FULL = (1 << v) - 1
+    occ = occurrences(c, masks)
+    gm = {(ph, k): masks[g[0]] for ph in ('D', 'A', 'B', 'C') for k, g in enumerate(c[ph])}
+    first = {}
+    for h in range(2 * v, n):
+        assert masks[c['start'][h]] == 0
+        first[h] = next(x if kind == 'p' else gm[x] for kind, x in occ[h][1:] if (x if kind == 'p' else gm[x]) != 0)
+    resp = {}
+    for f, t, srcs in c['D']:
+        assert masks[f] == 0
+        for s in srcs: resp[s] = resp.get(s, 0) ^ (1 << (t - v))
+    ret = set(c['ret']); pivots = {}; donor_at = {}; tot = 0
+    for E_lines, p, D in sel:
+        E = L.close(mask_of(E_lines)); assert E == mask_of(E_lines) and E != 0
+        assert p not in ret and p not in pivots and p not in donor_at and 2 * v <= p < n
+        x = resp.get(p, 0)
+        for d in D:
+            assert d not in ret and d not in pivots and 2 * v <= d < n
+            assert donor_at.setdefault(d, E) == E, 'donor serves one entrance'
+            x ^= resp.get(d, 0)
+        assert x == 0, ('response relation fails', p)
+        for h in [p] + D: assert E & ~first[h] == 0, ('entrance not inside first frame', h)
+        pivots[p] = E; tot += L.dim(E)
+    assert not set(pivots) & set(donor_at)
+    assert tot % 8 == 0, 'total entrance rank 0 mod 8'
+    out = json.loads(json.dumps(c)); fm = Framer(out)
+    for p, E in pivots.items(): out['start'][p] = fm.fid(E)
+    out['D'] = [[f, t, [s for s in srcs if s not in pivots]] for f, t, srcs in c['D']]
+    byd = {}
+    for E_lines, p, D in sel:
+        for d in D: byd.setdefault((d, mask_of(E_lines)), []).append(p)
+    out['A'] = [[fm.fid(E), d, sorted(ps)] for (d, E), ps in sorted(byd.items())] + out['A']
+    out['C'] = out['C'] + [[fm.fid(FULL), d, sorted(ps)] for (d, E), ps in sorted(byd.items())]
+    return out, len(sel), tot, len(byd)
+
+
+if __name__ == '__main__':
+    st, inp, outp, selp = sys.argv[1:5]
+    c = load_word(inp); sel = json.load(open(selp))
+    assert sel['input_sha256'] == content_sha(c), 'selection bound to a different input word'
+    if st == 'retime':
+        w = retime(c, sel['gates']); info = '%d gates retimed' % len(sel['gates'])
+    else:
+        w, ne, tot, nd = kernel(c, sel['entries']); info = '%d entries, total entrance rank %d, %d donor slots' % (ne, tot, nd)
+    r = replay(w, span_mode='z'); assert not r['viol'], r['viol'][:5]
+    assert content_sha(w) == sel['output_sha256'], 'output differs from the frozen stage output'
+    save_word(w, outp)
+    print('   stage %s: %s | exact replay PASS (legality, F2 on %d columns, source spans) | local histogram %s | output sha %s'
+          % (st, info, r['n'], dict(sorted(r['H'].items())), sel['output_sha256'][:16]))
diff --git a/research/e8-early-reset-kernel/verify.py b/research/e8-early-reset-kernel/verify.py
new file mode 100644
index 0000000000..2cb303ae52
--- /dev/null
+++ b/research/e8-early-reset-kernel/verify.py
@@ -0,0 +1,32 @@
+"""Fresh parent replay, chronological reset reconstruction, banks and exact assembly."""
+from pathlib import Path
+import hashlib,json,os,subprocess,sys,time
+assert __debug__
+ROOT=Path(__file__).resolve().parent;PARENT=ROOT.parent/'e8-early-reset-reuse';UPSTREAM=ROOT.parent/'split-centres-global';out=Path(sys.argv[1]).resolve();assert not out.exists() and not out.is_relative_to(ROOT.parent)
+read=lambda p:json.loads(p.read_text());sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+def integrity():
+ assert {p.relative_to(ROOT).as_posix():sha(p) for p in ROOT.rglob('*') if p.is_file() and p.name!='MANIFEST.json'}==read(ROOT/'MANIFEST.json')['files']
+ assert sha(PARENT/'MANIFEST.json')==read(ROOT/'SOURCE.json')['parent_manifest_sha256']
+integrity();out.mkdir(parents=True);env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONINTMAXSTRDIGITS='0');env.pop('PYTHONOPTIMIZE',None);steps=[]
+def run(name,file,*args,cwd=None):
+ t=time.monotonic();log=out/(name+'.log');print('RUN',name,flush=True)
+ with log.open('w') as f:q=subprocess.run([sys.executable,'-B',str(file),*map(str,args)],cwd=cwd,env=env,stdout=f,stderr=subprocess.STDOUT)
+ if q.returncode:raise RuntimeError((name,q.returncode,log.read_text()[-2000:]))
+ steps.append(dict(name=name,seconds=time.monotonic()-t,log_sha256=sha(log)));print('PASS',name,flush=True)
+try:
+ base=out/'baseline';run('full-early-reuse434',PARENT/'verify.py',base)
+ changed=out/'changed';changed.mkdir()
+ for name in ('work','inherited','split-centres'):(changed/name).symlink_to(base/'baseline'/name,target_is_directory=True)
+ bit=changed/'bit426-source-centres';bit.mkdir()
+ run('kernel-reconstruction',ROOT/'apply.py',base/'changed/bit426-source-centres/bit-source-centres.json',bit/'bit-source-centres.json')
+ run('export',UPSTREAM/'vendor/export_records.py',bit/'bit-source-centres.json',bit/'records')
+ run('integer-source-spans',ROOT/'source_span.py',bit/'bit-source-centres.json',bit/'records/frames.json')
+ run('global-program',ROOT/'bit_global.py','--source',bit,'--local-check',bit,'--out',bit/'global',cwd=changed)
+ run('independent-audit',ROOT/'bit_audit.py','--local-check',bit,'--out',bit/'global',cwd=changed)
+ run('two-moments',ROOT/'bit_price.py',cwd=changed)
+ env['E8_OUTPUT']=str(changed);run('finite-assembly',ROOT/'combined.py',cwd=changed)
+ actual=read(changed/'RESULT.json');expected=read(ROOT/'EXPECTED.json')
+ for k,v in expected.items():assert actual[k]==v,(k,actual[k],v)
+ integrity();result=dict(status='PASS_FULL_EARLY_RESET_KERNEL_COMPOSITION',kappa=actual['kappa'],kappa_decimal=actual['kappa_decimal'],source_manifest_sha256=sha(ROOT/'MANIFEST.json'),checks=steps,parent_phase_mode=read(base/'RESULT.json')['parent_phase_mode']);(out/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n')
+except BaseException as e:
+ (out/'FAILURE.json').write_text(json.dumps(dict(error=repr(e),completed=steps),indent=2)+'\n');raise
diff --git a/research/e8-early-reset-reuse/EXPECTED.json b/research/e8-early-reset-reuse/EXPECTED.json
new file mode 100644
index 0000000000..5cb40a0157
--- /dev/null
+++ b/research/e8-early-reset-reuse/EXPECTED.json
@@ -0,0 +1,10 @@
+{
+  "status": "PASS_CONDITIONAL_EARLY_RESET_REUSE_ASSEMBLY",
+  "kappa": "1128250848293019/1000000000000000000",
+  "kappa_decimal": "0.001128250848293019",
+  "bit_lower": "1129525236098815991751/1000000000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "bit_template_sha256": "10dfc644197ef152062bf69960ecdc2405c847ce47147b520c3172c51cd82bd9",
+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f"
+}
diff --git a/research/e8-early-reset-reuse/LICENSE b/research/e8-early-reset-reuse/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-early-reset-reuse/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/e8-early-reset-reuse/MANIFEST.json b/research/e8-early-reset-reuse/MANIFEST.json
new file mode 100644
index 0000000000..1980f550b0
--- /dev/null
+++ b/research/e8-early-reset-reuse/MANIFEST.json
@@ -0,0 +1,30 @@
+{
+  "files": {
+    "EXPECTED.json": "5521c7e995fec77941243b28e090f95f2188f193d5f61275275cfa11215eecc0",
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE.md": "c4085541471fe63d8f735beacd397d356446376ad3e56b2673940a2df3b8437e",
+    "PROOF.md": "09388e2f9e6b8fcc626a5172d55c45a957835075c51c68d1e86fd42ff4655ae8",
+    "README.md": "442bf686c0b24b9d7781b7b138f32fddea5d4efffeddc6e41d04719d2545e0cd",
+    "SELECTION.json": "9d47ade3fb69b3ef62a1a3ae75cebdddd57d144923977c5f2a07848ab596ea32",
+    "SOURCE.json": "c52287239c43aece2b3533ef48ee204d845d652066bca716c288b0c47e779521",
+    "VALIDATION.json": "bcb864a6b73d4ff4a24ab70ad51287653723c2115ce1c81db7817b81df2d9e92",
+    "bit_audit.py": "219eb4dd8e5380fb0432daa6a30c265755a78834616b2c5fc7aa161feb0231ee",
+    "bit_global.py": "9c2178df133dc663416aac13d8c8da80a9e4f5f7174bb36413180fcbad994ffb",
+    "bit_price.py": "36bf15803567a95b139a908461541bf19efe1f5b85fb31c270021833ab1393ee",
+    "combined.py": "dc621dce9ac1634a2701318311b30dffee7cce7e0c6be7ae808f44b27eb17f0f",
+    "local-evidence/ASSEMBLY.json": "c9ce28f59a5e460d39a888bbbc464e3fd6dd1c0b2c54ae86baeeea99febc8176",
+    "local-evidence/BIT-AUDIT.json": "2e458c3936e42539095610a50c730266dddd96e94d1ead171a99dd5f1fe9ef47",
+    "local-evidence/BIT-GLOBAL.json": "39f89d1e5bf51e9b1f1155e123dc3226627e465a246d37bb00f55d44d20bcaa0",
+    "local-evidence/BIT-PRICE.json": "96ec606146b5157871048e28f6649c31c1b6117d43be732e6a96bcc269c0e1b6",
+    "local-evidence/FAILED-INLINING.json": "95cbb0e6df953d25a888198c1072edf03db85b7c967a234680db3e095abd2dc7",
+    "local-evidence/FAILED-LATE-RESET.json": "f6ed36b59de745d50f37fcb4c80d129d9a2de0dfe1fe3de2d18e678135f7d9b6",
+    "local-evidence/FULL-PORTABLE-PYTHON311.json": "1dcca855b20cbac311a435f23f60001c342083edbef3194ba42a30e1f24c1982",
+    "local-evidence/FULL-PORTABLE-PYTHON314.json": "5687ed9209e11e64304d008a4a10678dc07cdc3522f5112c9a80557d45125c4a",
+    "local-evidence/FULL-PYTHON314-INITIAL.json": "0966528d4b30459d8b35296f31dbadfa34cdc7792419b34ab2505b7098923325",
+    "local-evidence/PARENT-FULL-REPLAY.json": "0ba447d6de6edd9fbe2371c36e3605dffa0c6526a874cfcb9bd19285c056bf1e",
+    "local-evidence/PYTHON311-GZIP-FAILURE.log": "ec1937c575536aeebe8f9c22d673fd66d1355ff870e2fdc80346205b29e42784",
+    "local-evidence/PYTHON311-INITIAL-FAILURE.json": "7902e8ca1e167b98d1c29170f8d57c9896b38ccab89065e4ed4e2c3feea79076",
+    "replay.py": "e0782ba05dda36323500390349d1180f6117a9c6112b09b9e21e29f67c4e5f5f",
+    "verify.py": "4e2082878acc1298f4354325b28f3cf047006170a9883148e7cf23002f6f02f1"
+  }
+}
diff --git a/research/e8-early-reset-reuse/NOTICE.md b/research/e8-early-reset-reuse/NOTICE.md
new file mode 100644
index 0000000000..ba47405801
--- /dev/null
+++ b/research/e8-early-reset-reuse/NOTICE.md
@@ -0,0 +1,3 @@
+Rohan Arun, with substantial OpenAI Codex assistance. Apache-2.0.
+
+New contribution: eleven earlier clean resets selected and composed on PR433's R758 bit word. The clean-reset reuse principle and base bit lineage are from ai-nanachi #426; the split-centre complex and mutable-source bit composition are from icekylinx #433. Zhihao Chen supplied #425/#386; Dylan Crow supplied #370; Jacob Sussman supplied E8 and compiler interfaces. All parent notices remain in the pinned sibling package. Adapted bit_global.py, bit_audit.py, bit_price.py and combined.py retain original author notices.
diff --git a/research/e8-early-reset-reuse/PROOF.md b/research/e8-early-reset-reuse/PROOF.md
new file mode 100644
index 0000000000..933ba6ab83
--- /dev/null
+++ b/research/e8-early-reset-reuse/PROOF.md
@@ -0,0 +1,9 @@
+# Earlier clean reset and physical slot reuse
+
+Select a helper whose last main read has completed and which is not read by the subsequent target decoder. Immediately after that last read, cancel its clean source content using the recorded three or four available parent rows. Parent frames must admit the reset before their next use. The slot may retain arbitrary helper dirt. A later logical helper whose first use has not occurred is assigned that physical slot. The selected intervals and eleven physical pairs are disjoint.
+
+The reconstruction checks each actual reset on source columns with the earlier physical aliases already applied. It emits every reset addition, including its frame transitions. The main helper word is inverted at the full frame after restoring the source basis. The initial target compensation is regenerated from the entire changed raw operator on every independent physical column; no old dirty response is reused. The full emitted forward and reflected words independently verify the target shear, restored sources, restored helpers, and erased private copy row.
+
+The global nine-stage dimension-64 geometry and data routes are inherited. New ownership is generated for R747: 6,723 complete rank-eight helper banks, 53,784 assignments, 14,403 live and 14,412 physical rows. All 72 invocations and reflected streams are emitted and independently decoded. The two exact moment engines use the reconstructed profile and positive fallback allowance. The changed prefix has 226 bits, charged at 256; the two-level coefficient has 488 bits, charged at 512. Six finite bootstrap levels and 47 strict outer inequalities give the selected conditional bound.
+
+The parent complex supplier is unchanged and fully replayed, including all Gaussian phase pairs, by verify.py. Parent all-size compiler, dirty-bank, compressed-window, restored-work, tape/common-grid, precision and analytic interfaces remain assumptions. This is not an unconditional multiplication theorem or new Lean proof.
diff --git a/research/e8-early-reset-reuse/README.md b/research/e8-early-reset-reuse/README.md
new file mode 100644
index 0000000000..5c976801cd
--- /dev/null
+++ b/research/e8-early-reset-reuse/README.md
@@ -0,0 +1,11 @@
+# Earlier clean resets on PR433
+
+Conditional kappa = 0.001128250848293019, approximately 0.659% above PR433. Eleven helpers removed, R758 to R747. The exact bit saving is 0.001129525236098815991751; the unchanged complex saving is 0.001183986549206329.
+
+Run `python -B research/e8-early-reset-reuse/verify.py /absolute/new/output` with Python 3.11 or 3.14. Standard library only. The wrapper freshly verifies the pinned parent with all phases before reconstructing and checking the changed bit program.
+
+At draft submission the changed emitted bit, independent bank audit, two rational moments and exact finite assembly passed locally against the previously fully replayed parent. The new uninterrupted wrapper and GitHub CI are pending. Local receipts distinguish that scope.
+
+The initial full Python3.14 wrapper passed. Python3.11 exposed the parent compressed-file metadata mismatch; the package now imports PR433's upstream decoded-witness hash fix at 6d9244518175caf9e0089f92486959bc2c317273. Fresh both-version replays are pending. The original failure and pass receipts are preserved.
+
+Both fresh portable full replays now passed locally on Python 3.11 and 3.14 against e48f24fd2393500c804a0cbab542e20de8ddee6e. See VALIDATION.json and local-evidence/FULL-PORTABLE-PYTHON*.json.
diff --git a/research/e8-early-reset-reuse/SELECTION.json b/research/e8-early-reset-reuse/SELECTION.json
new file mode 100644
index 0000000000..9df36fb9ef
--- /dev/null
+++ b/research/e8-early-reset-reuse/SELECTION.json
@@ -0,0 +1,141 @@
+{
+  "source_sha256": "015811014644ed62acba1da590d9cf6ebdfe834d89867f8ce2b68722609072ea",
+  "word_sha256": "98ffef9246c8bf6c537ab5e134321abea05cf0b7830c9e3fd92cbe4e88d8c308",
+  "R": 747,
+  "local_profile": {
+    "1": 2398,
+    "2": 865,
+    "3": 475,
+    "5": 153,
+    "4": 310,
+    "8": 9,
+    "7": 14
+  },
+  "global_profile": {
+    "1": 172656,
+    "2": 62280,
+    "3": 34200,
+    "5": 11016,
+    "4": 22320,
+    "8": 648,
+    "7": 6768,
+    "14": 3840,
+    "28": 3840,
+    "42": 3840
+  },
+  "live": 14403,
+  "entries": [
+    {
+      "position": 1032,
+      "new_helper": 949,
+      "retired_helper": 406,
+      "parents": [
+        411,
+        518
+      ],
+      "frame": 458
+    },
+    {
+      "position": 1036,
+      "new_helper": 950,
+      "retired_helper": 252,
+      "parents": [
+        0,
+        1,
+        512,
+        523
+      ],
+      "frame": 458
+    },
+    {
+      "position": 1038,
+      "new_helper": 957,
+      "retired_helper": 532,
+      "parents": [
+        533,
+        534
+      ],
+      "frame": 459
+    },
+    {
+      "position": 1053,
+      "new_helper": 936,
+      "retired_helper": 310,
+      "parents": [
+        315,
+        566
+      ],
+      "frame": 461
+    },
+    {
+      "position": 1069,
+      "new_helper": 937,
+      "retired_helper": 422,
+      "parents": [
+        427,
+        598
+      ],
+      "frame": 463
+    },
+    {
+      "position": 1085,
+      "new_helper": 933,
+      "retired_helper": 294,
+      "parents": [
+        299,
+        630
+      ],
+      "frame": 465
+    },
+    {
+      "position": 1094,
+      "new_helper": 935,
+      "retired_helper": 374,
+      "parents": [
+        379,
+        646
+      ],
+      "frame": 466
+    },
+    {
+      "position": 1103,
+      "new_helper": 934,
+      "retired_helper": 444,
+      "parents": [
+        439,
+        662
+      ],
+      "frame": 467
+    },
+    {
+      "position": 1112,
+      "new_helper": 932,
+      "retired_helper": 492,
+      "parents": [
+        487,
+        678
+      ],
+      "frame": 468
+    },
+    {
+      "position": 1121,
+      "new_helper": 944,
+      "retired_helper": 476,
+      "parents": [
+        471,
+        694
+      ],
+      "frame": 469
+    },
+    {
+      "position": 1128,
+      "new_helper": 942,
+      "retired_helper": 710,
+      "parents": [
+        455,
+        460
+      ],
+      "frame": 470
+    }
+  ]
+}
diff --git a/research/e8-early-reset-reuse/SOURCE.json b/research/e8-early-reset-reuse/SOURCE.json
new file mode 100644
index 0000000000..d9ed13ac34
--- /dev/null
+++ b/research/e8-early-reset-reuse/SOURCE.json
@@ -0,0 +1,7 @@
+{
+  "parent_pr": 433,
+  "parent_commit": "6d9244518175caf9e0089f92486959bc2c317273",
+  "parent_manifest_sha256": "3129eb4321f706542470f8443f66a6b4351a12a9ceec85e7f76aa19db1e1e32f",
+  "attribution": "Rohan Arun with substantial OpenAI Codex assistance. icekylinx PR433 split centres and source reuse; ai-nanachi PR426 clean reset principle and base bit word; Zhihao Chen PR425/386; Dylan Crow PR370; Jacob Sussman E8 and inherited framework.",
+  "parent_update": "Upstream PR433 gzip portability repair: bind decoded canonical witness rather than platform-dependent gzip header. No construction or price changes."
+}
diff --git a/research/e8-early-reset-reuse/VALIDATION.json b/research/e8-early-reset-reuse/VALIDATION.json
new file mode 100644
index 0000000000..2cfd52731f
--- /dev/null
+++ b/research/e8-early-reset-reuse/VALIDATION.json
@@ -0,0 +1,9 @@
+{
+  "status": "PASS_BOTH_FULL_LOCAL_REPLAYS",
+  "validated_code_head": "e48f24fd2393500c804a0cbab542e20de8ddee6e",
+  "python": [
+    "3.11",
+    "3.14"
+  ],
+  "scope": "Fresh full parent phases and changed bit program, independent audit, finite invoice and exact assembly; GitHub CI pending."
+}
diff --git a/research/e8-early-reset-reuse/bit_audit.py b/research/e8-early-reset-reuse/bit_audit.py
new file mode 100644
index 0000000000..155faf40b0
--- /dev/null
+++ b/research/e8-early-reset-reuse/bit_audit.py
@@ -0,0 +1,126 @@
+# Adapted with exact rational span checks by icekylinx; Codex assistance.
+"""Independent audit of the emitted bit template, including mutation controls.
+Prepared by Zhihao Chen with OpenAI Codex assistance; Apache-2.0.
+"""
+import argparse, copy, gzip, hashlib, json, struct, time
+from collections import Counter, defaultdict
+from pathlib import Path
+from fractions import Fraction as Q
+
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out
+    blob=gzip.decompress((out/'GLOBAL-TEMPLATE.json.gz').read_bytes()); t=json.loads(blob)
+    g=json.loads((out/'GLOBAL.json').read_text()); geo=json.loads((out/'GEOMETRY.json').read_text())
+    assert hashlib.sha256(blob).hexdigest()==g['template_sha256']
+    assert t['geometry_sha256']==sha(out/'GEOMETRY.json') and t['source_record_sha256']==sha(a.local_check/'records/249-records.bin')
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    records=list(struct.iter_unpack('<6i',(a.local_check/'records/249-records.bin').read_bytes()))
+    word=json.loads((a.local_check/'bit-source-centres.json').read_text())
+    assert g['word_sha256']==sha(a.local_check/'bit-source-centres.json')
+    def rank(rows):
+        piv={}
+        for rr in rows:
+            row=list(map(Q,rr))
+            for k,b in sorted(piv.items()):
+                q=row[k]
+                if q:row=[x-q*y for x,y in zip(row,b)]
+            k=next((j for j,x in enumerate(row) if x),None)
+            if k is not None:
+                q=row[k];piv[k]=[x/q for x in row]
+        return len(piv)
+    dimensions={};proj={}
+    for key,f in fs.items():
+        k=int(key);B=f['B'];roots=[word['lines'][j] for j in word['frames'][k]]
+        assert rank(B)==f['dim']==rank(B+roots)==rank(roots)
+        dimensions[k]=f['dim'];proj[k]=B
+    sets=[set(f) for f in word['frames']];pairs={}
+    for op,x,y,c,r,z in records:
+        if op==0:
+            assert sets[y]<=sets[c] and dimensions[c]-dimensions[y]==r
+            pairs[y,c]=r
+    # Positive definite rational form: exact inclusion implies commuting
+    # orthogonal projectors and rank(P_V-P_U)=dim(V)-dim(U), also in reflection.
+    assert len(proj)==944
+    expected={}
+    for rev in (False,True):
+        es=[]
+        for op,x,y,c,f,z in (reversed(records) if rev else records):
+            if op==0: es.append([0,x,c if rev else y,y if rev else c,f,int(rev)])
+            elif op==1: es.append([1,x,y,-c if rev else c,f,int(rev)])
+            elif op==(3 if rev else 2): es.append([2,x,y,c,f,abs(dimensions[c]-dimensions[f]),int(rev)])
+            else: es.append([3,x,y,c,f,z,int(rev)])
+        expected['reverse' if rev else 'forward']=es
+    assert t['local_programs']==expected
+
+    def validate(q,check_profile=True):
+        assert (q['m'],q['live'],q['replicas'],q['stages'])==(64,14403,8,9)
+        assert q['bank_padding'] is None and q['local_programs']==expected
+        hist=Counter(); occupation=defaultdict(set); calls=set()
+        for c in q['calls']:
+            st,rep,p=c['stage'],c['replica'],c['pair']; rev=c['orientation']=='reverse'
+            assert 0<=st<9 and 0<=rep<8 and p==max(0,(st-1)//2)
+            assert rev==(st in (1,3,5,7)) and (st,rep) not in calls; calls.add((st,rep))
+            own=c['owners']; assert len(own)==987
+            assert len({(f,tuple(r)) for f,r in own})==987
+            for i,(family,route) in enumerate(own):
+                assert 0<=family<14403
+                if i<240:
+                    side=i//120; side=1-side if rev else side
+                    assert family==rep*960+(2*p+side)*120+i%120 and route==['data',st,i%120]
+                else:
+                    j=i-240; bank,slot=divmod(rep*747+j,8)
+                    assert family==7680+st*747+bank and route==['bank',slot]
+                    assert slot not in occupation[family]; occupation[family].add(slot)
+            for e in q['local_programs'][c['orientation']]:
+                if e[0]==0 and e[4]: hist[e[4]]+=1
+                if e[0]==2: hist[e[5]]+=1
+        assert calls=={(s,r) for s in range(9) for r in range(8)}
+        assert set(occupation)==set(range(7680,14403)) and all(s==set(range(8)) for s in occupation.values())
+        levels=[-1]*4; scalar=[1<<i for i in range(8)]; seen=[]; br=0; exchanged=False
+        for e in q['schedule']:
+            if e['kind']=='local_cover_sweep':
+                s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1 and not exchanged
+                src,dst=(2*p+1,2*p) if rev else (2*p,2*p+1)
+                scalar[dst]^=scalar[src]; levels[p]=s; seen.append(s)
+            elif e['kind']=='idle':
+                p,src,dst,r=e['pair'],e['source_level'],e['target_level'],e['rank']
+                assert levels[p]==src and src<=dst<=8
+                assert r==7*(dst-src); levels[p]=dst
+                if r: hist[r]+=1920
+            elif e['kind']=='bridge':
+                d,s=e['dst'],e['src']; assert levels[d]==levels[s] and e['coefficient'] in (-1,1)
+                scalar[2*d]^=scalar[2*s]; scalar[2*s+1]^=scalar[2*d+1]; br+=1
+            else:
+                assert e['kind']=='exchange' and levels==[8]*4 and not exchanged
+                for p in range(4): scalar[2*p],scalar[2*p+1]=scalar[2*p+1],scalar[2*p]
+                exchanged=True
+        assert exchanged and scalar==[1<<i for i in range(8)] and seen==list(range(9)) and br==9
+        assert 64*14403-sum(r*n for r,n in hist.items())==2496
+        if check_profile: assert hist==Counter({int(k):v for k,v in g['profile'].items()})
+        return hist
+    hist=validate(t)
+    controls=[]
+    def rejects(name,mutator):
+        q=copy.deepcopy(t); mutator(q)
+        try: validate(q)
+        except (AssertionError,KeyError,IndexError): controls.append(name)
+        else: raise AssertionError('mutation accepted: '+name)
+    rejects('omit an idle child',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='idle')))
+    rejects('omit a bridge',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='bridge')))
+    rejects('omit terminal exchange',lambda q:q['schedule'].pop())
+    rejects('remove a local invocation',lambda q:q['calls'].pop())
+    rejects('re-use a helper bank slot',lambda q:q['calls'][0]['owners'].__setitem__(241,q['calls'][0]['owners'][240]))
+    rejects('understate live stock',lambda q:q.__setitem__('live',14402))
+    rejects('omit a local paid move',lambda q:q['local_programs']['forward'].pop(next(i for i,e in enumerate(q['local_programs']['forward']) if e[0]==0)))
+    rejects('wrong reflected copy charge',lambda q:q['local_programs']['reverse'][next(i for i,e in enumerate(q['local_programs']['reverse']) if e[0]==2)].__setitem__(5,0))
+    result=dict(status='PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT',template_sha256=g['template_sha256'],
+                source_frames=len(proj),exact_nested_frame_pairs=len(pairs),exact_reflected_pairs=len(pairs),
+                orthogonal_lift_argument='Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.',
+                exact_bank_families=6723,slots_per_bank=8,mutations_rejected=controls,
+                profile=dict(sorted(hist.items())),seconds=time.monotonic()-start)
+    (out/'AUDIT.json').write_text(json.dumps(result,indent=2)+'\n'); print(json.dumps(result),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-early-reset-reuse/bit_global.py b/research/e8-early-reset-reuse/bit_global.py
new file mode 100644
index 0000000000..311067a7a6
--- /dev/null
+++ b/research/e8-early-reset-reuse/bit_global.py
@@ -0,0 +1,226 @@
+# Adapted for the PR426/source-centre composition by icekylinx with Codex assistance.
+"""Source-bound compressed nine-stage bit template and exact scalar audits.
+
+Prepared by Zhihao Chen with OpenAI Codex assistance, Apache-2.0.
+The local E8 bit word is Dylan Crow's pinned PR #370 contribution.
+"""
+import argparse, gzip, hashlib, json, struct, time
+from collections import Counter
+from pathlib import Path
+
+H,V,R,L,K,T,M=8,120,747,9,4,8,64
+LOCAL=2*V+R; DATA=2*K*V*T; LIVE=DATA+L*R
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+def write(p,x): p.write_text(json.dumps(x,indent=2)+'\n')
+
+def recipe():
+    out=[dict(kind='local',stage=0,pair=0,reverse=False)]; stage=1
+    for j in range(K):
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=True)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=1))
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=False)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=-1))
+    for j in reversed(range(K-1)): out.append(dict(kind='bridge',dst=j+1,src=j,coefficient=1))
+    out.append(dict(kind='exchange'))
+    return out
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--source',type=Path,required=True)
+    ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out; out.mkdir(parents=True,exist_ok=True)
+    wp=a.source/'bit-source-centres.json'; w=json.loads(wp.read_bytes())
+    inherited=Path('inherited/bit-geometry.json.gz')
+    geo=json.loads(gzip.decompress(inherited.read_bytes()))
+    base=Path('work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz')
+    original=json.loads(gzip.decompress(base.read_bytes()))
+    assert geo['word_sha256']==sha(base)
+    assert w['lines']==original['lines'] and w['frames']==original['frames'] and w['form']==original['form']
+    geo['inherited_geometry_sha256']=sha(inherited);geo['word_sha256']=sha(wp)
+    geo['reuse_scope']='Unchanged ports, rational frames, compressed windows and whole rank-eight bank slots; changed owners are replayed separately.'
+    write(out/'GEOMETRY.json',geo)
+    rp=a.local_check/'records/249-records.bin';raw=rp.read_bytes();rec=list(struct.iter_unpack('<6i',raw))
+    state=json.loads((a.local_check/'records/249-states.json').read_text())
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    dims={int(f):z['dim'] for f,z in fs.items()}
+    assert (state['v'],state['n'])==(V,LOCAL)
+    expected_adds=sum(e[0]==1 for e in rec)
+    initial=[state['initial'][str(i)] for i in range(LOCAL)]
+    final=[state['final'][str(i)] for i in range(LOCAL)]
+    assert all(dims[initial[i]]==0 and dims[final[i]]==H for i in range(2*V,LOCAL))
+    streams={}; checks={}; localH=None
+    for reverse in (False,True):
+        cur=(final if reverse else initial)[:]+[-1]; val=[1<<i for i in range(LOCAL)]+[0]
+        norm=[1]*LOCAL+[0]; maxnorm=1; center=None; hist=Counter(); events=[]; copies=0; adds=0
+        dim=lambda f:H-dims[f] if reverse else dims[f]
+        for op,x,y,c,f,z in (reversed(rec) if reverse else rec):
+            if op==0:
+                oldf,newf=(c,y) if reverse else (y,c)
+                assert cur[x]==oldf and dim(newf)-dim(oldf)==f>=0
+                cur[x]=newf
+                if f: hist[f]+=1
+                events.append([0,x,oldf,newf,f,int(reverse)])
+            elif op==1:
+                assert cur[x]==cur[y]==f and x!=y and x<LOCAL
+                if center is not None: assert x!=center
+                if y==LOCAL: assert center is not None
+                if c&1: val[x]^=val[y]
+                norm[x]+=abs(c)*norm[y]; maxnorm=max(maxnorm,norm[x]); adds+=1
+                events.append([1,x,y,-c if reverse else c,f,int(reverse)])
+            elif op==(3 if reverse else 2):
+                assert center is None and y==LOCAL and cur[x]==c and val[LOCAL]==0
+                copy_rank=abs(dim(c)-dim(f)); assert copy_rank==8
+                assert z==(0 if reverse else copy_rank)
+                center=x; cur[LOCAL]=f; val[LOCAL]=val[x]; norm[LOCAL]=norm[x]
+                hist[copy_rank]+=1; copies+=1; events.append([2,x,LOCAL,c,f,copy_rank,int(reverse)])
+            else:
+                assert op==(2 if reverse else 3)
+                assert center==x and y==LOCAL and cur[x]==c and cur[LOCAL]==f
+                assert val[LOCAL]==val[x]
+                val[LOCAL]=0; norm[LOCAL]=0; cur[LOCAL]=-1; center=None
+                events.append([3,x,LOCAL,c,f,z,int(reverse)])
+        assert center is None and copies==9 and adds==expected_adds
+        assert cur[:LOCAL]==(initial if reverse else final)
+        for i in range(LOCAL):
+            want=(1<<i) ^ ((1<<(i-V)) if V<=i<2*V else 0)
+            assert val[i]==want
+        assert val[LOCAL]==0
+        if localH is None: localH=hist
+        else: assert localH==hist
+        key='reverse' if reverse else 'forward'; streams[key]=events
+        checks[key]=dict(copies=copies,adds=adds,records=len(events),all_columns=LOCAL,
+                         cancellation_free_row_l1=maxnorm,profile=dict(sorted(hist.items())),
+                         sha256=hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest())
+    assert sum(r*n for r,n in localH.items())==H*R+72+2*V*(H-1)==7728
+    assert localH==Counter({int(k):v for k,v in json.loads((Path(__file__).parent/"SELECTION.json").read_text())["local_profile"].items()})
+
+    events=recipe(); levels=[-1]*K; schedule=[]; bridge_controls=[]
+    # Full scalar replay on separate dirty helpers for all nine stages.
+    # Physical banking then uses the separately checked injective cover owners.
+    n=2*K*V+L*R; vals=[1<<i for i in range(n)]+[0]; temp=n
+    stages=[]
+    for e in events:
+        if e['kind']=='local':
+            s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1
+            def mapper(i):
+                if i==LOCAL: return temp
+                if i<2*V:
+                    side=i//V; side=1-side if rev else side
+                    return (2*p+side)*V+i%V
+                return 2*K*V+s*R+i-2*V
+            before=vals[:]; opened=False
+            for z in streams['reverse' if rev else 'forward']:
+                if z[0]==0: continue
+                x,y=mapper(z[1]),mapper(z[2])
+                if z[0]==1:
+                    if z[3]&1: vals[x]^=vals[y]
+                elif z[0]==2:
+                    assert not opened; vals[temp]=vals[x]; opened=True
+                else:
+                    assert opened and vals[temp]==vals[x]; vals[temp]=0; opened=False
+            assert not opened
+            d=(2*p+(0 if rev else 1))*V; src=(2*p+(1 if rev else 0))*V
+            for t in range(V): before[d+t]^=before[src+t]
+            assert vals==before
+            levels[p]=s; schedule.append(dict(kind='local_cover_sweep',**{k:v for k,v in e.items() if k!='kind'}))
+            if s in (1,3,5):
+                j=(s+1)//2; assert levels[j]==-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7*(s+1),source_level=-1,target_level=s))
+            elif s in (2,4,6):
+                j=s//2; assert levels[j]==s-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7,source_level=s-1,target_level=s))
+            elif s==8:
+                for j in range(4):
+                    oldlevel=levels[j]; assert oldlevel==2*j+2
+                    schedule.append(dict(kind='idle',pair=j,rank=7*(8-oldlevel),source_level=oldlevel,target_level=8))
+                    levels[j]=8
+            stages.append(dict(stage=s,all_columns=n,helper_columns=L*R,reverse=rev))
+        elif e['kind']=='bridge':
+            d,s=e['dst'],e['src']; assert levels[d]==levels[s]
+            for t in range(V): vals[2*d*V+t]^=vals[2*s*V+t]; vals[(2*s+1)*V+t]^=vals[(2*d+1)*V+t]
+            schedule.append(e)
+        else:
+            assert levels==[8]*4
+            for j in range(K):
+                for t in range(V):
+                    x=2*j*V+t; y=(2*j+1)*V+t; vals[x],vals[y]=vals[y],vals[x]
+            schedule.append(e)
+    assert vals==[1<<i for i in range(n)]+[0]
+    # Integer scalar eight-bank matrix, with each individual bridge shear omitted.
+    def small(skip=-1):
+        z=[[int(i==j) for j in range(8)] for i in range(8)]; count=0
+        def add(d,s,c): z[d]=[x+c*y for x,y in zip(z[d],z[s])]
+        for e in events:
+            if e['kind']=='local':
+                p=e['pair']; add(2*p,2*p+1,-1) if e['reverse'] else add(2*p+1,2*p,1)
+            elif e['kind']=='bridge':
+                d,s,c=e['dst'],e['src'],e['coefficient']
+                for x,y,sgn in [(2*d,2*s,c),(2*s+1,2*d+1,-c)]:
+                    if count!=skip: add(x,y,sgn)
+                    count+=1
+            else:
+                for j in range(4): z[2*j],z[2*j+1]=z[2*j+1],[-x for x in z[2*j]]
+        return z,count
+    ident=[[int(i==j) for j in range(8)] for i in range(8)]
+    z,nb=small(); assert z==ident and nb==18
+    for skip in range(nb): assert small(skip)[0]!=ident; bridge_controls.append(skip)
+
+    paid=Counter(); calls=[]; assignment=set(); expanded=hashlib.sha256(); full_event_count=0
+    for e in events:
+        if e['kind']!='local': continue
+        s,p,rev=e['stage'],e['pair'],e['reverse']; ori='reverse' if rev else 'forward'
+        for rep in range(T):
+            owners=[]
+            for i in range(2*V):
+                side=i//V; side=1-side if rev else side
+                owners.append([rep*(2*K*V)+(2*p+side)*V+i%V, ['data',s,i%V]])
+            for r in range(R):
+                bank,slot=divmod(rep*R+r,8)
+                owners.append([DATA+s*R+bank,['bank',slot]])
+                assignment.add((s,rep,r,bank,slot))
+            assert len({(f,tuple(route)) for f,route in owners})==LOCAL
+            assert all(0<=f<LIVE for f,route in owners)
+            # Stream one full renamed instruction program into a source-bound
+            # digest, including exact owner route descriptors and reflection.
+            for z in streams[ori]:
+                op=z[0]
+                if op==0: paid[z[4]]+=bool(z[4]); mapped=[op,owners[z[1]],*z[2:]]
+                else:
+                    ox=owners[z[1]]; oy=owners[z[2]] if z[2]<LOCAL else [LIVE,['private',0]]
+                    mapped=[op,ox,oy,*z[3:]]
+                    if op==2: paid[z[5]]+=1
+                expanded.update((json.dumps(mapped,separators=(',',':'))+'\n').encode()); full_event_count+=1
+            calls.append(dict(stage=s,replica=rep,pair=p,orientation=ori,owners=owners,local_hash=checks[ori]['sha256']))
+    paid.pop(0,None)
+    assert len(assignment)==L*T*R==53784 and len(calls)==72
+    for e in schedule:
+        if e['kind']=='idle' and e['rank']: paid[e['rank']]+=2*V*T
+    mass=sum(r*c for r,c in paid.items()); assert M*LIVE-mass==2496
+    assert dict(paid)=={int(k):v for k,v in json.loads((Path(__file__).parent/'SELECTION.json').read_text())['global_profile'].items()}
+    cf=checks['forward']['cancellation_free_row_l1']; cb=checks['reverse']['cancellation_free_row_l1']
+    prefix=(1<<nb)*cf**5*cb**4; charged_prefix=64*((prefix.bit_length()+63)//64);assert prefix<1<<charged_prefix
+    print('Fresh prefix bits',prefix.bit_length(),'charged',charged_prefix,flush=True)
+    template=dict(version='compressed-nine-e8-bit-v1',m=M,h=H,stages=L,replicas=T,live=LIVE,private_centre_reserve=9,
+                  cover='O(I_64/2,F_q) for admitted odd address primes q',loop_order='Each recipe phase: replicas then all cover classes; finish every local invocation before the next.',
+                  schedule=schedule,local_programs=streams,calls=calls,bank_padding=None,
+                  helper_route='owner (DATA + stage*747 + floor((747*replica+helper)/8), d*Pi_slot^-1)',
+                  data_route='owner (replica*960 + (2*pair+side)*120+port, d*rho_stage,port)',
+                  bit_operator='D_U exchanges the two address halves on projector U; D_I D_P = D_(I-P) exactly.',
+                  geometry_sha256=sha(out/'GEOMETRY.json'),source_record_sha256=sha(rp))
+    blob=json.dumps(template,separators=(',',':'),sort_keys=True).encode(); (out/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+    result=dict(status='PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE',h=H,m=M,v=V,R=R,replicas=T,live=LIVE,physical=LIVE+9,
+                word_sha256=sha(wp),source_records_sha256=sha(rp),local_checks=checks,scalar_stages=stages,
+                independent_unbanked_scalar_columns=n,all_scalar_columns_restored=True,
+                geometry_sha256=sha(out/'GEOMETRY.json'),template_sha256=hashlib.sha256(blob).hexdigest(),
+                emitted_program_sha256=expanded.hexdigest(),emitted_events=full_event_count,local_invocations=len(calls),
+                bank_assignments=len(assignment),banks_per_stage=R,whole_rank8_slots_per_bank=8,padding_calls=0,
+                profile=dict(sorted(paid.items())),paid_calls=sum(paid.values()),rank_mass=mass,deficit=2496,
+                maxchild=max(paid),halving_depth=2,halving_integer_inequality=[64**2,2*42**2],
+                local_additions=expected_adds,bridge_additions=18*V*T,copy_erase_episodes=9*72,
+                global_prefix_bound=str(prefix),global_prefix_bits=prefix.bit_length(),charged_prefix_bits=charged_prefix,
+                omitted_bridge_shears_rejected=bridge_controls,
+                scope='Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.',
+                seconds=time.monotonic()-start)
+    write(out/'GLOBAL.json',result)
+    print(json.dumps({k:v for k,v in result.items() if k not in ('local_checks','scalar_stages','global_prefix_bound')}),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-early-reset-reuse/bit_price.py b/research/e8-early-reset-reuse/bit_price.py
new file mode 100644
index 0000000000..005da012a3
--- /dev/null
+++ b/research/e8-early-reset-reuse/bit_price.py
@@ -0,0 +1,18 @@
+"""Exact price of the emitted bit program; no histogram supplied by discovery."""
+import json,importlib.util
+from fractions import Fraction as Q
+from pathlib import Path
+
+def load(name):
+ p=Path('work/pr361/code/engines')/(name+'.py');sp=importlib.util.spec_from_file_location('price_'+name,p);m=importlib.util.module_from_spec(sp);sp.loader.exec_module(m);return m
+p=Path('bit426-source-centres/global');g=json.loads((p/'GLOBAL.json').read_text());a=json.loads((p/'AUDIT.json').read_text())
+assert a['template_sha256']==g['template_sha256']
+H={int(r):n for r,n in a['profile'].items()};m,W=g['m'],g['live']
+M,B=load('moment'),load('base_two_moment');root=M.certify(H,m,W,True);lo,hi=Q(root['lower']),Q(root['upper'])
+fb=32*m*m*sum(H.values())
+def other(x):
+ l,u=B.moment(m,W,list(H.items()),x);a,b=B.moment(m,W,[(1,fb)],x);return l+a/10**16,u+b/10**16
+assert other(lo)[1]<1<other(hi)[0]
+root.update(source_template_sha256=g['template_sha256'],two_exact_engines=True)
+Path('BIT-PRICE.json').write_text(json.dumps(root,indent=2)+'\n')
+print('PASS two rational bit moments',root['lower'])
diff --git a/research/e8-early-reset-reuse/combined.py b/research/e8-early-reset-reuse/combined.py
new file mode 100644
index 0000000000..3dc894b938
--- /dev/null
+++ b/research/e8-early-reset-reuse/combined.py
@@ -0,0 +1,55 @@
+"""Fresh bit finite invoice and joint strict arithmetic for two changed suppliers.
+icekylinx, with Codex assistance. Inherited all-size interfaces remain conditional.
+"""
+import json,hashlib,importlib.util
+from pathlib import Path
+from fractions import Fraction as Q
+import os
+ROOT=Path(os.environ['E8_OUTPUT']);D=ROOT/'bit426-source-centres/global';C=ROOT/'split-centres'
+read=lambda p:json.loads(p.read_text())
+g=read(D/'GLOBAL.json');geo=read(D/'GEOMETRY.json');audit=read(D/'AUDIT.json')
+cx=read(C/'INTEGRATION.json');ca=read(C/'INDEPENDENT-REPLAY.json')
+assert audit['template_sha256']==g['template_sha256'] and ca['template_sha256']==cx['global_template_sha256']
+assert len(audit['mutations_rejected'])==8 and len(ca['mutation_controls_rejected'])==7
+P={int(r):z for r,z in audit['profile'].items()};m,W=64,14403;E=sum(P.values());T,L,R,V,K=8,9,747,120,4
+mass=sum(r*z for r,z in P.items());assert m*W-mass==2496 and g['live']==W
+physical=g['physical'];d=m*m;N=2*m
+unit=L*T*g['local_additions']+g['bridge_additions']
+J=8*T*L*(2*V+R)+8*(2*K*V*T)+2*g['bank_assignments']+2*g['copy_erase_episodes']
+high=16*(d+1)**2;good=8*m*m+8;compiler=128*N**3
+selectors=2*L*T*((W-1)+R*m*(geo['max_route_factors']+(m-1)+m))
+prefix=int(g['global_prefix_bound']);charged_prefix=64*((prefix.bit_length()+63)//64);assert prefix<1<<charged_prefix
+coefficient=unit+J*high+J*physical+E*(good+compiler)+16*m**3+g['copy_erase_episodes']+selectors+prefix+1
+two=(coefficient+1)**2*(E+1)**2
+charged_two=64*((two.bit_length()+63)//64);assert two<1<<charged_two and 2*max(P)**2<m*m
+row=2*(m*m+1)+9909+252;assert row==18355<20161
+assert geo['bad_prime_factors']==[2] and geo['route_denominators']==[1,2,4]
+def load(name):
+ p=ROOT/'work/pr361/code/engines'/(name+'.py');sp=importlib.util.spec_from_file_location('joint_'+name,p);mod=importlib.util.module_from_spec(sp);sp.loader.exec_module(mod);return mod
+M,Other,Outer=load('moment'),load('base_two_moment'),load('outer')
+root=M.certify(P,m,W,True);c=Q(root['lower']);grid=Q(1,10**18);b=Q(ca['complex_b'])
+fb=32*m*m*E
+lo,hi=Other.moment(m,W,list(P.items()),c);bl,bh=Other.moment(m,W,[(1,fb)],c)
+assert hi+bh/10**16<1
+eta=beta=Q(1,10**18);s=min(c,(1-beta)*b)-Q(1,10**24)
+assert 0<s<c and s<(1-beta)*b
+chain=[Q(384599,10**10)];cutoffs=[]
+def ceil(x):return -((-x.numerator)//x.denominator)
+for j in range(6):
+ old=chain[-1];a=(1-s)*s+s*old
+ gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+ cutoff=max(ceil(36/gap**2),ceil(2*(4+charged_two)/gap))
+ assert cutoff*gap**2>=36 and cutoff*gap>=2*(4+charged_two)
+ cutoffs.append(dict(gap=str(gap),cutoff_log2=str(cutoff)));chain.append(a)
+q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin/grid;k=grid*((ticks.numerator-1)//ticks.denominator)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}
+a=Outer.assembly(chain[-1],b,bridge,k,eta=eta,beta=beta)
+assert len(a['strict_constraints'])==47 and all(x>0 for x in a['strict_constraints'].values())
+controls=[]
+for name,kk,ee,bb in [('next_grid',k+grid,eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]:
+ try:Outer.assembly(chain[-1],b,bridge,kk,eta=ee,beta=bb)
+ except AssertionError:controls.append(name)
+ else:raise AssertionError(name)
+result=dict(status='PASS_CONDITIONAL_EARLY_RESET_REUSE_ASSEMBLY',kappa=str(k),kappa_decimal=format(float(k),'.18f'),bit_lower=str(c),complex_lower=str(b),binding_component='bit',gain_over_pr425_percent=float(100*(k/Q(1048005508028206,10**18)-1)),bit_invoice=dict(prefix_bits=prefix.bit_length(),charged_prefix_bits=charged_prefix,coefficient_bits=coefficient.bit_length(),two_level_coefficient_bits=two.bit_length(),charged_two_level_coefficient_bits=charged_two,row_coefficient=row,live=W,physical=physical),strict_outer_constraints={n:str(x) for n,x in a['strict_constraints'].items()},outer_controls=controls,bootstrap=cutoffs,bit_template_sha256=g['template_sha256'],complex_template_sha256=cx['global_template_sha256'],scope='Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim.')
+(ROOT/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n')
+print(result['status'],result['kappa_decimal'],result['gain_over_pr425_percent'],result['bit_invoice'])
diff --git a/research/e8-early-reset-reuse/local-evidence/ASSEMBLY.json b/research/e8-early-reset-reuse/local-evidence/ASSEMBLY.json
new file mode 100644
index 0000000000..7899c12d17
--- /dev/null
+++ b/research/e8-early-reset-reuse/local-evidence/ASSEMBLY.json
@@ -0,0 +1,103 @@
+{
+  "status": "PASS_CONDITIONAL_EARLY_RESET_REUSE_ASSEMBLY",
+  "kappa": "1128250848293019/1000000000000000000",
+  "kappa_decimal": "0.001128250848293019",
+  "bit_lower": "1129525236098815991751/1000000000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr425_percent": 7.656957873799007,
+  "bit_invoice": {
+    "prefix_bits": 226,
+    "charged_prefix_bits": 256,
+    "coefficient_bits": 226,
+    "two_level_coefficient_bits": 488,
+    "charged_two_level_coefficient_bits": 512,
+    "row_coefficient": 18355,
+    "live": 14403,
+    "physical": 14412
+  },
+  "strict_outer_constraints": {
+    "bit_positive": "18506141468243001171708721090504160753359281193270932320673716200550478228569658366279537613727959580145427271328281666596703824135534263924614730977/16384000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "892294153953493164291278909495839246640718806729067679326283799449521771430341633720462386272040419854572728671718333403296175864465736075385269023/16384000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "30066013450793671/1000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "892294153953493144892843287299344910640718806729067679326283799449521771430341633720462386272040419854572728671718333403296175864465736075385269023/16384000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_positive": "9253070734121500567348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023/8192000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_internal": "18506141468243001171708721090504160753359281193270932320673716200550478228569658366279537613727959580145427271328281666596703824135534263924614730977/8192000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_leaf": "446147076976746590952563111892673627029080493868694593022423092995693206388887017410709421705678576206823978063818746847075359260514534634396458647034263924614730977/8192000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_positive": "9253070734121502615348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023/8192000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_below_one": "8182746929265878497384651780922990920795029080493868694593022423092995693206388887017410709421705678576206823978063818746847075359260514534634396458647034263924614730977/8192000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_reservations": "1/4000000000000000000",
+    "lambda_above_tau": "18506141468243001171708721090504160753359281193270932320673716200550478228569658366279537613727959580145427271328281666596703824135534263924614730977/16384000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_sigma": "892294153953493182797420377738840418349439897233228432685564992720454092104057834270940614841698786134110342399677913548723447192747402672089093158534263924614730977/16384000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_internal": "18506141468243001171708721090504160753359281193270932320673716200550478228569658366279537613727959580145427271328281666596703824135534263924614730977/16384000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_prime_above_lambda": "18506141468243001171708721090504160753359281193270932320673716200550478228569658366279537613727959580145427271328281666596703824135534263924614730977/16384000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_leaf": "446147076976746590952563111892673627029080493868694593022423092995693206388887017410709421705678576206823978063818746847075359260514534634396458647034263924614730977/8192000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_reservations": "1/4000000000000000000",
+    "lambda_prime_below_one": "9253070734121500567348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023/8192000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "epsilon_positive": "8191999999999999991808000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/8201253070734121500567348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023",
+    "epsilon_below_one": "9253070734121508759348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023/8201253070734121500567348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023",
+    "guard_width": "9253070734121508759348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023/8201253070734121500567348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023",
+    "K_geometry": "6153253070734121502615348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023/8201253070734121500567348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023000000000000000000",
+    "K_dominates_log": "298486152713596858261133817512502470632990336423297619419569593576548431826888260502741412409135756167867272375543865463217697380751748781054158084305815184186507344194653674987571967/264556550668842629050559619970226099329192610306649396948612179900225945380439068160728686792848203916896554065223747782359771762604499531140825920688805346325012428033000000000000000000",
+    "record_suffix": "9253070734121508759348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023/8201253070734121500567348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023",
+    "phase_local": "74024565872972061873532681881951133072419136972041364050849695749903148941911326953710017832743458407756117597195128601430221103979702469771903690084240423237478610831034263924614730977/65610024565872972004538785752616072633639767356049050443255820615256034454348888903860714324626354571390345408175489450025223397125915883722924828330823725888603082152184000000000000000000",
+    "phase_boundary": "14804913174594405813704079789093026160605252132801009446193203545075585462800203865138558131659801295479791056803568581251503403246995491432041025425259712355012889083834263924614730977/13122004913174594400907757150523214526727953471209810088651164123051206890869777780772142864925270914278069081635097890005044679425183176744584965666164745177720616430436800000000000000000",
+    "gamma_sublinear": "1/2000000000000000000",
+    "cell_above_band": "16383999999999999975414746929265878499432651780922990920795029080493868694593022423092995693206388887017410709421705678576206823978063818746847075359260514534634396458647034263924614730977/32805012282936486002269392876308036316819883678024525221627910307628017227174444451930357162313177285695172704087744725012611698562957941861462414165411862944301541076092000000000000000000",
+    "prime_interval_packing": "9253070734121508759348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023/8201253070734121500567348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023",
+    "alpha_positive": "18506141468243009317443367419896657842593619935253531608984234307877308180244649058174274362977529864997061465578041082512673259542789677578282441966446006785166996693034263924614730977/16402506141468243001134696438154018158409941839012262610813955153814008613587222225965178581156588642847586352043872362506305849281478970930731207082705931472150770538046000000000000000000",
+    "alpha_below_one": "16383999999999999991817253070734121500567348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023/16402506141468243001134696438154018158409941839012262610813955153814008613587222225965178581156588642847586352043872362506305849281478970930731207082705931472150770538046000000000000000000",
+    "alpha_below_one_fourth": "4082120393898817740966230742118607881759891839817812121094504554145624845216560907433120370926169630846899526545390049544063789060826953055104519328710036861252525637818465736075385269023/16402506141468243001134696438154018158409941839012262610813955153814008613587222225965178581156588642847586352043872362506305849281478970930731207082705931472150770538046000000000000000000",
+    "delta_positive": "1/8000000000000000000",
+    "delta_below_one_eighth": "999999999999999999/8000000000000000000",
+    "short_record_fallback": "134065954450456131888572404073222057587195605953853045459726979682067836030854839827324250112657359613753045411329984324417514991266327925496392926819076909098625880785159609317507266039991394147465325581857236255532115555519907868899367780890770924744091711832220085615353750878175230822142166392507469830641670083374529/134369330310907846665295433221357716753694243545188455307787920620044358562506524475106742936834774162207427395943402393651657517313875729864550048421526990619859112247672832000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "small_field_exposure": "1/1000000000000000000",
+    "artificial_boundary": "459344196526983776126450045233130945570820183505623430783661477680566669551012043961606727517391669910070531137138798564473166705073135613542857400568808263504921467841530897208226155807069/65610024565872972004538785752616072633639767356049050443255820615256034454348888903860714324626354571390345408175489450025223397125915883722924828330823725888603082152184000000000000000000",
+    "literal_scalar_guard": "1",
+    "row_product_gap": "23971789/25",
+    "balanced_prefix_above_kappa": "9220264634419749410126248485777003611646590040381762946804723855588412103267248597113917235579943540037407401432945273428716916281235826485632259566734279018802352149563/8201253070734121500567348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023000000000000000000",
+    "coordinate_movement_above_kappa": "20879569810177875708721090504160753359281193270932320673716200550478228569658366279537613727959580145427271328281666596703824135534263924614730977/16384000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_phase_layer_above_kappa": "50950578184281395477945013334999726622080956043781582069887313934070389823681874206566397250082460930680711270550454608778199582024817051013332801269065664136348344027/410062653536706075028367410953850453960248545975306565270348878845350215339680555649129464528914716071189658801096809062657646232036974273268280177067648286803769263451150000000000000000",
+    "bulk_exposure_above_kappa": "20879569810177875708721090504160753359281193270932320673716200550478228569658366279537613727959580145427271328281666596703824135534263924614730977/16384000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "Gaussian_arithmetic_above_kappa": "32755851721687387778173246790830983497147865725523447047402902960172275292169933211998391431748076713180293331353881281163970707046189184558230058827109403470041890851389/65610024565872972004538785752616072633639767356049050443255820615256034454348888903860714324626354571390345408175489450025223397125915883722924828330823725888603082152184000000000000000000",
+    "scalar_work_above_kappa": "65560864004623873780442639667139019813967749403547972269030813267800292519344377663928748594061253998875466035441626006176582405609147126419692472992521266414343431927481/65610024565872972004538785752616072633639767356049050443255820615256034454348888903860714324626354571390345408175489450025223397125915883722924828330823725888603082152184000000000000000000",
+    "dimension_above_kappa": "8182746929265878492268916415342740330921277566270872306239612463474758640011112742605822812688954275690124059558007358784254476792205787963351312739882860749556874297711279018802352149563/8201253070734121500567348219077009079204970919506131305406977576907004306793611112982589290578294321423793176021936181253152924640739485465365603541352965736075385269023000000000000000000"
+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "19718173301699986490442310099608577089/16000000000000000000000000000000000000000000",
+      "cutoff_log2": "23703316064509"
+    },
+    {
+      "gap": "89088697416160189168478072742640881250923123343423452063/64000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "18578781647433489479"
+    },
+    {
+      "gap": "402511727930897263492893481780029509017558469228965731102330904495255713921/256000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "14562145083988389157871807"
+    },
+    {
+      "gap": "1818588618094756475300249931559443478956904117509927455038979846382951280845356947587831584607/1024000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "11413884584645035881423129400187"
+    },
+    {
+      "gap": "8216566952880397264033353325540771278429496754443877107508740488500708481207792267348207305960479962067658955969/4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "8946261732747165430949576222298741146"
+    },
+    {
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+}
diff --git a/research/e8-early-reset-reuse/local-evidence/BIT-AUDIT.json b/research/e8-early-reset-reuse/local-evidence/BIT-AUDIT.json
new file mode 100644
index 0000000000..5acb750852
--- /dev/null
+++ b/research/e8-early-reset-reuse/local-evidence/BIT-AUDIT.json
@@ -0,0 +1,33 @@
+{
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diff --git a/research/e8-early-reset-reuse/local-evidence/BIT-GLOBAL.json b/research/e8-early-reset-reuse/local-evidence/BIT-GLOBAL.json
new file mode 100644
index 0000000000..fd3faa8602
--- /dev/null
+++ b/research/e8-early-reset-reuse/local-evidence/BIT-GLOBAL.json
@@ -0,0 +1,164 @@
+{
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diff --git a/research/e8-early-reset-reuse/local-evidence/BIT-PRICE.json b/research/e8-early-reset-reuse/local-evidence/BIT-PRICE.json
new file mode 100644
index 0000000000..0ee06a110f
--- /dev/null
+++ b/research/e8-early-reset-reuse/local-evidence/BIT-PRICE.json
@@ -0,0 +1,17 @@
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new file mode 100644
index 0000000000..927c934e27
--- /dev/null
+++ b/research/e8-early-reset-reuse/local-evidence/FAILED-INLINING.json
@@ -0,0 +1,571 @@
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diff --git a/research/e8-early-reset-reuse/local-evidence/FAILED-LATE-RESET.json b/research/e8-early-reset-reuse/local-evidence/FAILED-LATE-RESET.json
new file mode 100644
index 0000000000..f01e4f53a2
--- /dev/null
+++ b/research/e8-early-reset-reuse/local-evidence/FAILED-LATE-RESET.json
@@ -0,0 +1,8 @@
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diff --git a/research/e8-early-reset-reuse/local-evidence/FULL-PORTABLE-PYTHON311.json b/research/e8-early-reset-reuse/local-evidence/FULL-PORTABLE-PYTHON311.json
new file mode 100644
index 0000000000..b91e7cc182
--- /dev/null
+++ b/research/e8-early-reset-reuse/local-evidence/FULL-PORTABLE-PYTHON311.json
@@ -0,0 +1,44 @@
+{
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+}
diff --git a/research/e8-early-reset-reuse/local-evidence/FULL-PORTABLE-PYTHON314.json b/research/e8-early-reset-reuse/local-evidence/FULL-PORTABLE-PYTHON314.json
new file mode 100644
index 0000000000..773987c837
--- /dev/null
+++ b/research/e8-early-reset-reuse/local-evidence/FULL-PORTABLE-PYTHON314.json
@@ -0,0 +1,44 @@
+{
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+}
diff --git a/research/e8-early-reset-reuse/local-evidence/FULL-PYTHON314-INITIAL.json b/research/e8-early-reset-reuse/local-evidence/FULL-PYTHON314-INITIAL.json
new file mode 100644
index 0000000000..39fe0d80ac
--- /dev/null
+++ b/research/e8-early-reset-reuse/local-evidence/FULL-PYTHON314-INITIAL.json
@@ -0,0 +1,44 @@
+{
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+  "kappa_decimal": "0.001128250848293019",
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+}
diff --git a/research/e8-early-reset-reuse/local-evidence/PARENT-FULL-REPLAY.json b/research/e8-early-reset-reuse/local-evidence/PARENT-FULL-REPLAY.json
new file mode 100644
index 0000000000..59ced26676
--- /dev/null
+++ b/research/e8-early-reset-reuse/local-evidence/PARENT-FULL-REPLAY.json
@@ -0,0 +1,120 @@
+{
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+    "Gaussian_arithmetic_above_kappa": "49929956359383891636682334467235976400846493161596454696927943987316335662954230095174784854400852306299403498179012231794056054820241901455974763560139756902928431597231181121226907/51257452682253575127867256701214029332254870510048632733197542663606075726316364959643880249784273294552016721137634553308103163360604369856156793527338835635083267030132419768134536000000000000000000",
+    "scalar_work_above_kappa": "3022347308020427168024638512713719642678957136664830842541068612764774941044496502999868999171719558143016474349913180337924305460021763455362126412952366988818802604491895640211767/2050298107290143005114690268048561173290194820401945309327901706544243029052654598385755209991370931782080668845505382132324126534424174794246271741093553425403330681205296790725381440000000000000000",
+    "dimension_above_kappa": "3196409207359151553231162974036146672459031212215382000019265285423173401803752699526640796382355306275012080586149285130394424095589341109716483649580049811311843280287131837920058593191496467269437/3203590792640848445491703543825876833265929406878039545824846416475379732894772809977742515611517080909501045071102159581756447710037773116009799595458677227192704189383276235508408500000000000000000"
+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "48640105104416009930955104551272628756769/40000000000000000000000000000000000000000000000",
+      "cutoff_log2": "24346328299693"
+    },
+    {
+      "gap": "10916033216189494908506938862091413300675156484737667525550897/8000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "19335382939135799529"
+    },
+    {
+      "gap": "2449825733746901655394438404809502019511708753179325050819248403056515410563319361/1600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "15355787073969246541017124"
+    },
+    {
+      "gap": "549801013506219857550281901936704203615404924098069138182437287931091972275689180385852832590942771793/320000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "12195269025875323655994833423982"
+    },
+    {
+      "gap": "123388839576821941106964776874551364767558290306753584545234931806617408234472738882773008179061080923160999418343337504609/64000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "9685246734476302780854842486398253310"
+    },
+    {
+      "gap": "27691483569705102945201339627252022591017013352985113602942786795000164759817249951996149235225861576966507630300630689893816878766552471016817/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "7691835588756193183914168151850588989363719"
+    }
+  ],
+  "bit_template_sha256": "c40f89a2ae3c2c5635ddf8f18d74f24567ddf67fc8c8e93a1fc7a1a8098e857e",
+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f",
+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim.",
+  "verification_steps": [
+    "hamming_packets",
+    "complex_construct",
+    "complex_audit",
+    "complex_emit",
+    "complex_phases",
+    "bit_construct",
+    "bit_export",
+    "bit_global",
+    "bit_audit",
+    "bit_price",
+    "complex_integrate",
+    "complex_replay",
+    "combined"
+  ],
+  "phase_mode": "full replay",
+  "manifest_sha256": "c903e548e42d04a243a034d320b15e6cb26b878c30f935181336ea6ea679a004"
+}
diff --git a/research/e8-early-reset-reuse/local-evidence/PYTHON311-GZIP-FAILURE.log b/research/e8-early-reset-reuse/local-evidence/PYTHON311-GZIP-FAILURE.log
new file mode 100644
index 0000000000..20a1987364
--- /dev/null
+++ b/research/e8-early-reset-reuse/local-evidence/PYTHON311-GZIP-FAILURE.log
@@ -0,0 +1,5 @@
+Traceback (most recent call last):
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/source433-review/research/split-centres-global/code/complex_phases.py", line 9, in <module>
+    assert sha(O/'CANONICAL-WORD.json.gz')==r['canonical_word_sha256']
+           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+AssertionError
diff --git a/research/e8-early-reset-reuse/local-evidence/PYTHON311-INITIAL-FAILURE.json b/research/e8-early-reset-reuse/local-evidence/PYTHON311-INITIAL-FAILURE.json
new file mode 100644
index 0000000000..d82c79a260
--- /dev/null
+++ b/research/e8-early-reset-reuse/local-evidence/PYTHON311-INITIAL-FAILURE.json
@@ -0,0 +1,4 @@
+{
+  "error": "RuntimeError(('full-parent433', 1, 'PASS hamming_packets\\nPASS complex_construct\\nPASS complex_audit\\nPASS complex_emit\\nTraceback (most recent call last):\\n  File \"/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/early-reuse-publication/research/split-centres-global/verify.py\", line 39, in <module>\\n    for name in (\\'complex_construct\\',\\'complex_audit\\',\\'complex_emit\\',\\'complex_phases\\',\\'bit_construct\\'):run(name,\\'code/\\'+name+\\'.py\\')\\n                                                                                                      ^^^^^^^^^^^^^^^^^^^^^^^^^^^^\\n  File \"/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/early-reuse-publication/research/split-centres-global/verify.py\", line 36, in run\\n    assert r.returncode==0,(name,str(out/(name+\\'.log\\')))\\n           ^^^^^^^^^^^^^^^\\nAssertionError: (\\'complex_phases\\', \\'/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/early-reuse-full311/baseline/complex_phases.log\\')\\n'))",
+  "completed": []
+}
diff --git a/research/e8-early-reset-reuse/replay.py b/research/e8-early-reset-reuse/replay.py
new file mode 100644
index 0000000000..84d4875764
--- /dev/null
+++ b/research/e8-early-reset-reuse/replay.py
@@ -0,0 +1,71 @@
+"""Reconstruct eleven chronological clean resets; regenerate arbitrary-dirt compensation.
+Rohan Arun with OpenAI Codex assistance, using icekylinx's PR433 and ai-nanachi's PR426.
+"""
+import copy,hashlib,json,sys
+from pathlib import Path
+from collections import defaultdict
+ROOT=Path(__file__).resolve().parent
+
+def reconstruct(raw,selection):
+ assert hashlib.sha256(raw).hexdigest()==selection['source_sha256']
+ w=json.loads(raw);v=w['v'];n=2*v+w['R'];entries=selection['entries'];cut=len(w['A'])-w['source_basis_gates'];assert all(d>=2*v for f,d,ss in w['A'][:cut])
+ removed={z['new_helper'] for z in entries};retired={z['retired_helper'] for z in entries}
+ assert len(removed)==len(retired)==len(entries) and not removed&retired
+ assert all(2*v<=x<n for x in removed|retired)
+ by=defaultdict(list)
+ for z in entries:
+  pos,h,dead=z['position'],z['new_helper'],z['retired_helper'];assert 0<pos<cut
+  assert all(h!=d and h not in ss for f,d,ss in w['A'][:pos])
+  assert all(dead!=d and dead not in ss for f,d,ss in w['A'][pos:]+w['B'])
+  assert h not in z['parents'] and dead not in z['parents'] and len(set(z['parents']))==len(z['parents'])
+  by[pos].append(z)
+ # Each reset must zero the actual clean form at its actual insertion time.
+ alias={z['new_helper']:z['retired_helper'] for z in entries}
+ role=lambda x:alias.get(x,x)
+ clean=[1<<i if i<v else 0 for i in range(n)];a=[]
+ for i,e in enumerate(w['A']):
+  for z in by[i]:
+   dead=z['retired_helper'];before=clean[dead];assert before
+   for parent in z['parents']:clean[dead]^=clean[role(parent)]
+   assert clean[dead]==0
+   a.append([z['frame'],dead,z['parents']])
+  f,d,ss=e
+  for q in ss:clean[role(d)]^=clean[role(q)]
+  a.append(e)
+ physical=[x for x in range(n) if x not in removed];mp={x:i for i,x in enumerate(physical)}
+ for z in entries:mp[z['new_helper']]=mp[z['retired_helper']]
+ def remap(gs):return [[f,mp[d],[mp[s] for s in ss]] for f,d,ss in gs]
+ c=copy.deepcopy(w);c['A']=remap(a);c['B']=remap(w['B']);c['C']=[[w['final'][0],d,ss] for f,d,ss in reversed(c['A'][:cut+len(entries)])];c['R']-=len(entries);c['start']=[w['start'][i] for i in physical];c['final']=[w['final'][i] for i in physical];c['ret']=[mp[x] for x in w['ret']]
+ nn=2*v+c['R'];vals=[1<<i for i in range(nn)]
+ for ph in ['A','B','C']:
+  if ph=='B':
+   totals=[vals[i] for i in c['ret']]
+   for t,ks in enumerate(c['scatter']):
+    for k in ks:vals[v+t]^=totals[k]
+  for f,d,ss in c[ph]:
+   assert d not in ss
+   for q in ss:vals[d]^=vals[q]
+ for i in list(range(v))+list(range(2*v,nn)):assert vals[i]==1<<i
+ D=[]
+ for t in range(v):
+  z=vals[v+t]^(1<<(v+t))^(1<<t);assert not z&((1<<(2*v))-1)
+  ss=[i for i in range(2*v,nn) if z>>i&1]
+  if ss:D.append([0,v+t,ss])
+ c['D']=D;raw=json.dumps(c,sort_keys=True,separators=(',',':')).encode();assert hashlib.sha256(raw).hexdigest()==selection['word_sha256'];return raw
+
+def controls(raw,sel):
+ rejected=[]
+ cases=[]
+ for label in ('missing reset parent','wrong insertion time','duplicate physical reuse'):
+  s=copy.deepcopy(sel)
+  if label=='missing reset parent':s['entries'][0]['parents'].pop()
+  elif label=='wrong insertion time':s['entries'][0]['position']=0
+  else:s['entries'][1]['new_helper']=s['entries'][0]['new_helper']
+  cases.append((label,s))
+ for label,s in cases:
+  try:reconstruct(raw,s)
+  except AssertionError:rejected.append(label)
+  else:raise AssertionError(label)
+ return rejected
+if __name__=='__main__':
+ raw=Path(sys.argv[1]).read_bytes();s=json.loads((ROOT/'SELECTION.json').read_text());out=Path(sys.argv[2]);data=reconstruct(raw,s);out.write_bytes(data);print(json.dumps(dict(status='PASS_EXACT_CHRONOLOGICAL_RECONSTRUCTION',helpers_removed=len(s['entries']),R=s['R'],sha256=hashlib.sha256(data).hexdigest(),controls=controls(raw,s))))
diff --git a/research/e8-early-reset-reuse/verify.py b/research/e8-early-reset-reuse/verify.py
new file mode 100644
index 0000000000..6fae5fc80e
--- /dev/null
+++ b/research/e8-early-reset-reuse/verify.py
@@ -0,0 +1,31 @@
+"""Fresh parent replay, chronological reset reconstruction, banks and exact assembly."""
+from pathlib import Path
+import hashlib,json,os,subprocess,sys,time
+assert __debug__
+ROOT=Path(__file__).resolve().parent;PARENT=ROOT.parent/'split-centres-global';out=Path(sys.argv[1]).resolve();assert not out.exists() and not out.is_relative_to(ROOT.parent)
+read=lambda p:json.loads(p.read_text());sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+def integrity():
+ assert {p.relative_to(ROOT).as_posix():sha(p) for p in ROOT.rglob('*') if p.is_file() and p.name!='MANIFEST.json'}==read(ROOT/'MANIFEST.json')['files']
+ assert sha(PARENT/'MANIFEST.json')==read(ROOT/'SOURCE.json')['parent_manifest_sha256']
+integrity();out.mkdir(parents=True);env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONINTMAXSTRDIGITS='0');env.pop('PYTHONOPTIMIZE',None);steps=[]
+def run(name,file,*args,cwd=None):
+ t=time.monotonic();log=out/(name+'.log');print('RUN',name,flush=True)
+ with log.open('w') as f:q=subprocess.run([sys.executable,'-B',str(file),*map(str,args)],cwd=cwd,env=env,stdout=f,stderr=subprocess.STDOUT)
+ if q.returncode:raise RuntimeError((name,q.returncode,log.read_text()[-2000:]))
+ steps.append(dict(name=name,seconds=time.monotonic()-t,log_sha256=sha(log)));print('PASS',name,flush=True)
+try:
+ base=out/'baseline';run('full-parent433',PARENT/'verify.py',base,'--replay-phases')
+ changed=out/'changed';changed.mkdir()
+ for name in ('work','inherited','split-centres'):(changed/name).symlink_to(base/name,target_is_directory=True)
+ bit=changed/'bit426-source-centres';bit.mkdir()
+ run('reconstruct',ROOT/'replay.py',base/'bit426-source-centres/bit-source-centres.json',bit/'bit-source-centres.json')
+ run('export',PARENT/'vendor/export_records.py',bit/'bit-source-centres.json',bit/'records')
+ run('global-program',ROOT/'bit_global.py','--source',bit,'--local-check',bit,'--out',bit/'global',cwd=changed)
+ run('independent-audit',ROOT/'bit_audit.py','--local-check',bit,'--out',bit/'global',cwd=changed)
+ run('two-moments',ROOT/'bit_price.py',cwd=changed)
+ env['E8_OUTPUT']=str(changed);run('finite-assembly',ROOT/'combined.py',cwd=changed)
+ actual=read(changed/'RESULT.json');expected=read(ROOT/'EXPECTED.json')
+ for k,v in expected.items():assert actual[k]==v,(k,actual[k],v)
+ integrity();result=dict(status='PASS_FULL_PARENT_AND_EARLY_RESET_REUSE',kappa=actual['kappa'],kappa_decimal=actual['kappa_decimal'],source_manifest_sha256=sha(ROOT/'MANIFEST.json'),checks=steps,parent_phase_mode=read(base/'RESULT.json')['phase_mode']);(out/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n')
+except BaseException as e:
+ (out/'FAILURE.json').write_text(json.dumps(dict(error=repr(e),completed=steps),indent=2)+'\n');raise
diff --git a/research/e8-eleven-hosting-selected-validation/MANIFEST.json b/research/e8-eleven-hosting-selected-validation/MANIFEST.json
new file mode 100644
index 0000000000..cd2efeb176
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/MANIFEST.json
@@ -0,0 +1,43 @@
+{
+  "README.md": "1b71ebafa3fb7abe657bd88eb955a590d515dfd2a81d42b344ef9b2607d32acf",
+  "precision/BEFORE-assemble.py": "150bc23a25485be70b9e0a5347f336338a7458efe2ebc800053da37df42d522e",
+  "precision/assemble.diff": "888cba9cdf619fcf6d694804a0b89b77494fbbed34cb8a9f5a2fca0c7fdb40c7",
+  "precision/python311/RECEIPT.json": "f57f1d8f895e18d6a7869cb1a86905a00bf983fcfaceaf4882418dc81e4a7cd5",
+  "precision/python311/RESULT.json": "dae8b568b730de0ea2377ecb77cc0a49751e1d58b647026d25392b6b7e4301ab",
+  "precision/python311/assembly.log": "8449240c9cd4c2a46279fea4f920de9572128cb7d54d6f0accea1ba9dd133be1",
+  "precision/python314/RECEIPT.json": "baf8e978f0e49a2256dfb294cfb9fc60197e903a980f1e5ab8b3b030440498cf",
+  "precision/python314/RESULT.json": "69f4ea305f053500fe127ad73a72b32bac5ad10cc7faf05122d2ee4a92e4a2fa",
+  "precision/python314/assembly.log": "8449240c9cd4c2a46279fea4f920de9572128cb7d54d6f0accea1ba9dd133be1",
+  "python311/AUDIT.json": "2e8f1476d3bc72a2cc3bf3cd035a1e67afae9b2a732fbaf5003b116edd65a743",
+  "python311/RANK147-PARENT-RECEIPT.json": "c642e7abf6b025b5e503b7afea9374d3b03ae325b769c73fdaebfad6b8210442",
+  "python311/RECEIPT.json": "378c5171909e3dca8767e89303e73b324e553663ec317e0072cede664c273dba",
+  "python311/RESULT.json": "f0e6bdf81e0fb96bef9c7ad8c6eaf856b88dd1c7836fd3059af132101aa61130",
+  "python311/TESTED-MANIFEST.json": "58048a268e837f4e8a30521435b2c3dad77fd0e74b38f020b7b7e11367ecf5b7",
+  "python311/emit.log": "086a680df0af21c572e1c8125a62e0c0ca6f853714f060f218f29704d3d6c142",
+  "python311/exact-assembly.log": "e02a0b68a7f72a453c470339dd48eab594e433c80809fdab196e58fc7ff10ee7",
+  "python311/geometry.log": "581f74eccaad91982180899bab2a0b9c4c50d8e2ffcb00651c4f357455835bb2",
+  "python311/independent-audit.log": "efd529d366c8e85dd3b823888fd656202cbc28ca9ef0f94509d03656fcfa179f",
+  "python311/parent-full.log": "27a703b99593110c92d28d2d6e61b431b71762be5a20e1cda2f25681d9edc430",
+  "python314/AUDIT.json": "8804e3ed7c133ff7278766f379e06561002c91608b35e5c80863b85d98aac4e1",
+  "python314/RANK147-PARENT-RECEIPT.json": "89314b23aa82c7cfadab792da26d45abf12e1719c5b230658947f4b4a6e6ccb4",
+  "python314/RECEIPT.json": "2bdfa38a351473dceef266986f0c4885a7652354713fe83b4b1cec00c6d054e8",
+  "python314/RESULT.json": "93170cf9d084d539015f81fd257f0021fabbf84f705dd13ff0ee6073fc2eb9dc",
+  "python314/TESTED-MANIFEST.json": "58048a268e837f4e8a30521435b2c3dad77fd0e74b38f020b7b7e11367ecf5b7",
+  "python314/emit.log": "756c3a1cf09ddc0c053685e16305414c3bc645d052a0ec8ae61515bb43c90342",
+  "python314/exact-assembly.log": "e02a0b68a7f72a453c470339dd48eab594e433c80809fdab196e58fc7ff10ee7",
+  "python314/geometry.log": "2045ec8f88fa42a4051f1309f6a994561b3328ba105ccd57204201bfc3f2121f",
+  "python314/independent-audit.log": "3e00eba9ad762570d30d84b32b588e8dbe8458ca7fe5d8010f64a703a97f761e",
+  "python314/parent-full.log": "2192bf17cc72cd10cba563cebc12ae214bdaa37c4c5f3ff4130e1fd5cbe6b715",
+  "research/FRAMES.json": "f3314e9d97b682a759297c61dcbf3c288630d84a2bcc439540a33a219523b1c4",
+  "research/GROUPS.json": "ee4ea310c3ad579da394337795e4ae466f0619e2889f54c0a447fd0cebf6f284",
+  "research/HOSTING-RESULT.json": "d7171db3712effc4c2c267230c5814adcaf816b85b7d7609d21b8881df2ec2d8",
+  "research/MIXED-GROUPS.json": "bcc26a92e220e3a36fedfe591eb372be975e5ee1d7820d600a8d1ed110aeb47b",
+  "research/PARTITIONS-SUMMARY.json": "9b3a478df5a3c7e33e5adfc1d6b892a980ab537920b3d410532281acc01bcd17",
+  "research/REPEATED-PARTITIONS.json": "6fa4ec52d91ffdcb5eb34579c931e9d1a58d07e7c3ca41f89f4709244ab3563b",
+  "research/SUMMARY.json": "39146dd50833c0b5ad35de1a85c7e6390c1aa939456b5b59ced23ae7c8fe0657",
+  "research/frames-initial-boundary-failure.log": "a5fac3e7d22349d74a5799a44ea0fe000ee5523c97fd6200f9c01f4587f47908",
+  "research/partitions.log": "c67a10987d4c28c334c3702e863c545e9045d896fdeebdf3ee6cc96876512e14",
+  "research/repeated-partitions.log": "df972e8ab60ffc60629aaa8e424fa3994cc2cc2b52659d60c66738a577bb726f",
+  "research/search_complex_output_partitions.py": "5508da1406a91ba48635e6699fe710d528d2e6c8b631255fded53d45eddcdc86",
+  "research/search_complex_same_partitions.py": "4488444d135eecbeead45c83ecc48edb5d7e777c029152d77c40df0b17c374e6"
+}
diff --git a/research/e8-eleven-hosting-selected-validation/README.md b/research/e8-eleven-hosting-selected-validation/README.md
new file mode 100644
index 0000000000..a499fe2be3
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/README.md
@@ -0,0 +1,7 @@
+# Verification evidence for PR447
+
+Uninterrupted full Python3.11.15 and3.14.8 wrappers passed for κ=0.001265848755025708, with the same tested manifest58048a268e837f4e8a30521435b2c3dad77fd0e74b38f020b7b7e11367ecf5b7. See python311/ and python314/ for receipts, full logs, exact results and tested manifests. Both nested nine-stage rank147 parents also passed.
+
+The current κ=0.001265848755025709 keeps the full rational complex lower endpoint. Only two executable assembly lines changed: remove truncation at1e-18; compare the refined endpoint >= the inherited weaker one. All supplier, geometry, program, ownership, phase and row-bound code/witnesses remain byte-identical to the full runs. precision/ retains the exact diff and both runtime receipts: both rational moments, both invoices, six bootstrap levels,47 strict outer constraints and controls pass against each fully verified supplier artifact. No fresh uninterrupted current-manifest wrapper is claimed. GitHub CI remains pending.
+
+The research/ directory contains subsequent negative screens, including failures and scope limits. OpenAI Codex assistance; inherited proof assumptions remain.
diff --git a/research/e8-eleven-hosting-selected-validation/precision/BEFORE-assemble.py b/research/e8-eleven-hosting-selected-validation/precision/BEFORE-assemble.py
new file mode 100644
index 0000000000..2df8f178ad
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/precision/BEFORE-assemble.py
@@ -0,0 +1,94 @@
+# Adapted from DaysSky PR442 with Claude assistance; Eleven-stage R740 integration by chafreaky with OpenAI Codex. Apache-2.0.
+"""Two exact moments for both hosted suppliers, fresh finite invoices with the hosted stock, and the strict outer
+assembly of #434 (six bootstrap levels, 47 inequalities, next-grid and parameter controls).
+usage: assemble.py VERIFIED444_DIR BIT_DIR"""
+import gzip, hashlib, importlib.util, json, math, sys
+from fractions import Fraction as Q
+from pathlib import Path
+parent444, bd = map(Path, sys.argv[1:3])
+upstream=parent444
+ap=bd/"AUDIT.json";outp=bd/"RESULT.json"
+from row_bound import bound as row_bound, controls as row_controls
+par=upstream / "changed"
+cd=upstream / "complex"
+def load(name):
+    sp = importlib.util.spec_from_file_location('hosted_' + name, par / 'work/pr361/code/engines' / (name + '.py'))
+    mod = importlib.util.module_from_spec(sp); sp.loader.exec_module(mod); return mod
+M, Other, Outer = load('moment'), load('base_two_moment'), load('outer')
+audit = json.loads(ap.read_text()); ua=json.loads((upstream/'AUDIT.json').read_text()); ur=json.loads((upstream/'RESULT.json').read_text()); bg = json.loads((bd / 'GLOBAL.json').read_text()); ch = json.loads((cd / 'HOSTED.json').read_text())
+assert audit['template_sha256'] == bg['template_sha256'] and ua['complex_template_sha256'] == ch['template_sha256']
+assert json.loads((upstream/'RECEIPT.json').read_text())['status']in ('PASS_FULL_RANK138_IDLE_HOSTING','PASS_FULL_HOSTING_SELECTED_KERNEL')
+# ---------------- bit: two moments and the parent's invoice formulas with the hosted stock
+P = {int(r): n for r, n in audit['profile'].items()}; m, W = 78, audit['live']; E = sum(P.values())
+geo = json.loads((bd / 'GEOMETRY.json').read_text());pg=bg
+T, L, R, V, K = 8, 11, 740, 120, 5
+assert pg["replicas"]==T and pg["R"]==R
+mass = sum(r * z for r, z in P.items()); assert m * W - mass == (2*K*V-L*72)*T
+physical = W + 9; d = m * m; N = 2 * m
+unit = L * T * pg['local_additions'] + pg['bridge_additions']
+J = 8 * T * L * (2 * V + R) + 8 * (2 * K * V * T) + 2 * L * T * R + 2 * pg['copy_erase_episodes']   # every helper route charged (bank or hosted)
+high = 16 * (d + 1) ** 2; good = 8 * m * m + 8; compiler = 128 * N ** 3
+selectors = 2 * L * T * ((W - 1) + R * m * (geo['max_route_factors'] + 144 + 2 + (m - 1) + m))   # 144: residual isometry; +2: hosted slot permutation and idle basis U_q
+prefix = int(pg['global_prefix_bound']); charged_prefix = 64 * ((prefix.bit_length() + 63) // 64)
+assert 1<<128 <= prefix < 1<<charged_prefix <= 1<<256
+coefficient = unit + J * high + J * physical + E * (good + compiler) + 16 * m ** 3 + pg['copy_erase_episodes'] + selectors + prefix + 1
+two = (coefficient + 1) ** 3 * (E + 1) ** 3; charged_two = 1024
+assert 1 << 512 <= two < 1 << charged_two and 2 * max(P) ** 3 < m ** 3
+rows = row_bound(m,physical,max(P),3);row=rows["complete_row_coefficient"]
+assert row==19431<20161
+row_rejected=row_controls()
+root = M.certify(P, m, W, True); c = Q(root['lower']); chi = Q(root['upper'])
+fb = 32 * m * m * E
+lo, hi = Other.moment(m, W, list(P.items()), c); bl, bh = Other.moment(m, W, [(1, fb)], c); assert hi + bh / 10 ** 16 < 1
+lo2, hi2 = Other.moment(m, W, list(P.items()), chi); bl2, bh2 = Other.moment(m, W, [(1, fb)], chi); assert lo2 + bl2 / 10 ** 16 > 1
+# ---------------- complex: two moments and the parent's invoice with the hosted stock
+PC = {int(r): n for r, n in ua['complex_profile'].items()}; mc, WC = 73, ua['complex_live']; EC = sum(PC.values())
+massc = sum(r * z for r, z in PC.items()); assert mc * WC - massc == 2496
+rc = M.certify(PC, mc, WC, True); b = Q(int(Q(rc['lower']) * 10 ** 18), 10 ** 18)
+assert b==Q(ur['complex_lower'])
+fbc = 32 * mc * mc * EC
+l3, h3 = Other.moment(mc, WC, list(PC.items()), b); b3, bh3 = Other.moment(mc, WC, [(1, fbc)], b); assert h3 + bh3 / 10 ** 16 < 1
+integ = json.loads((par / 'split-centres/INTEGRATION.json').read_text()); inv = integ['finite_invoice']
+physc = ch['physical']; Rc = 560; v = 120
+compilerc = 64 * (mc + 1) ** 3
+pervertex = inv['pervertex'] - integ['physical'] * (64 + 1) + physc * (64 + 1) - integ['live'] + WC   # stock-dependent terms re-based
+r_ = mc // 2; group = 2 ** (r_ * r_) * math.prod(2 ** (2 * i) - 1 for i in range(1, r_ + 1)); stock = group * physc
+smass = group * massc; logical = group * max(pervertex, inv['pervertex']) + 64; router = compilerc * (logical + 1) * (stock + 1) ** 2
+GG, EE, C0 = 1 << 30000, 1 << 100000, 1 << 210000; BB = smass + EE
+literal = 2 * GG * stock ** 2 + 8 * smass + 4 * stock + 4 + 32 * mc
+assert logical < 1 << 6050 and router < GG and literal < EE and BB < 1 << 100001 and 32 * mc * BB * BB < C0 and 2 * BB + 18 < C0
+depth = 2; assert mc ** depth > 2 * max(PC) ** depth
+rowc = depth * stock.bit_length() + 9909 + 252; assert rowc < 20161
+# ---------------- outer assembly exactly as #434's combined.py
+eta = beta = Q(1, 10 ** 18); grid = Q(1, 10 ** 18); s = min(c, (1 - beta) * b) - Q(1, 10 ** 24)
+assert 0 < s < c and s < (1 - beta) * b
+chain = [Q(384599, 10 ** 10)]; cutoffs = []
+def ceil(x): return -((-x.numerator) // x.denominator)
+for j in range(6):
+    old = chain[-1]; a = (1 - s) * s + s * old
+    gap = min(s - a, 1 - a - s, 1 - a - s * (1 - old), 1 - s); assert old < a < s < 1 - a and gap > 0
+    cutoff = max(ceil(36 / gap ** 2), ceil(2 * (4 + charged_two) / gap)); assert cutoff * gap ** 2 >= 36 and cutoff * gap >= 2 * (4 + charged_two)
+    cutoffs.append(dict(gap=str(gap), cutoff_log2=str(cutoff))); chain.append(a)
+q = chain[-1] * (1 - 2 * eta); margin = (1 - eta) * q / (1 + q); ticks = margin / grid; k = grid * ((ticks.numerator - 1) // ticks.denominator)
+bridge = {'semantic': {'C0': {'base': 2, 'exponent': 210000}, 'strict_literal_gap': 1}, 'rows': {'degree_gap': Q(10 ** 6) - Q(51 * 20161, 25)}}
+a = Outer.assembly(chain[-1], b, bridge, k, eta=eta, beta=beta)
+assert len(a['strict_constraints']) == 47 and all(x > 0 for x in a['strict_constraints'].values())
+controls = []
+for name, kk, ee, bb in [('next_grid', k + grid, eta, beta), ('zero_eta', k, Q(0), beta), ('zero_beta', k, eta, Q(0)), ('unit_beta', k, eta, Q(1))]:
+    try: Outer.assembly(chain[-1], b, bridge, kk, eta=ee, beta=bb)
+    except AssertionError: controls.append(name)
+    else: raise AssertionError(name)
+parent_k = Q('315841366195289/250000000000000000')
+assert json.loads((parent444/'RECEIPT.json').read_text())['status']in ('PASS_FULL_RANK138_IDLE_HOSTING','PASS_FULL_HOSTING_SELECTED_KERNEL')
+res = dict(status='PASS_CONDITIONAL_ELEVEN_STAGE_HOSTING_ASSEMBLY', kappa=str(k), kappa_decimal=format(float(k), '.18f'),
+           bit_lower=str(c), complex_lower=str(b), binding_component='bit' if c < (1 - beta) * b else 'complex',
+           gain_over_pr445_percent=float(100 * (k / parent_k - 1)),
+           bit=dict(live=W, physical=physical, maxchild=max(P), rank_mass=mass, hosted_residuals=audit['hosted_residuals'],
+                    prefix_bits=prefix.bit_length(), charged_prefix_bits=charged_prefix, coefficient_bits=coefficient.bit_length(),
+                    three_level_coefficient_bits=two.bit_length(), charged_three_level_coefficient_bits=charged_two, row_coefficient=row),
+           complex=dict(live=WC, physical=physc, maxchild=max(PC), rank_mass=massc, hosted_residuals=ua['complex_hosted_residuals'],
+                        physical_stock_bits=stock.bit_length(), router_bits=router.bit_length(), literal_bits=literal.bit_length(), row_coefficient=rowc),
+           strict_outer_constraints={n: str(x) for n, x in a['strict_constraints'].items()}, outer_controls=controls, bootstrap=cutoffs,
+           bit_template_sha256=bg['template_sha256'], complex_template_sha256=ch['template_sha256'], emitted_program_sha256=bg['emitted_program_sha256'], bank_assignments=audit['bank_assignments'], bit_profile=audit['profile'], parent_kappa=str(parent_k), additional_interface='PR442 idle-data hosting during untouched windows',row_bound=rows,row_controls=row_rejected, halving_depth=3, finite_controls=['old 128-bit prefix charge insufficient','old 512-bit composite charge insufficient'])
+outp.write_text(json.dumps(res, indent=2) + '\n')
+print(res['status'], res['kappa_decimal'], 'binding', res['binding_component'], 'gain over #445 %.4f%%' % res['gain_over_pr445_percent'])
diff --git a/research/e8-eleven-hosting-selected-validation/precision/assemble.diff b/research/e8-eleven-hosting-selected-validation/precision/assemble.diff
new file mode 100644
index 0000000000..f3336f5818
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/precision/assemble.diff
@@ -0,0 +1,13 @@
+--- verified-before/assemble.py
++++ precision/assemble.py
+@@ -44,8 +44,8 @@
+ # ---------------- complex: two moments and the parent's invoice with the hosted stock
+ PC = {int(r): n for r, n in ua['complex_profile'].items()}; mc, WC = 73, ua['complex_live']; EC = sum(PC.values())
+ massc = sum(r * z for r, z in PC.items()); assert mc * WC - massc == 2496
+-rc = M.certify(PC, mc, WC, True); b = Q(int(Q(rc['lower']) * 10 ** 18), 10 ** 18)
+-assert b==Q(ur['complex_lower'])
++rc = M.certify(PC, mc, WC, True); b = Q(rc['lower'])
++assert b>=Q(ur['complex_lower'])
+ fbc = 32 * mc * mc * EC
+ l3, h3 = Other.moment(mc, WC, list(PC.items()), b); b3, bh3 = Other.moment(mc, WC, [(1, fbc)], b); assert h3 + bh3 / 10 ** 16 < 1
+ integ = json.loads((par / 'split-centres/INTEGRATION.json').read_text()); inv = integ['finite_invoice']
diff --git a/research/e8-eleven-hosting-selected-validation/precision/python311/RECEIPT.json b/research/e8-eleven-hosting-selected-validation/precision/python311/RECEIPT.json
new file mode 100644
index 0000000000..d8ba207fce
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/precision/python311/RECEIPT.json
@@ -0,0 +1,18 @@
+{
+  "status": "PASS_REVISED_EXACT_ASSEMBLY_AGAINST_FULLY_VERIFIED_SUPPLIERS",
+  "python": "3.11.15",
+  "supplier_full_receipt_sha256": "378c5171909e3dca8767e89303e73b324e553663ec317e0072cede664c273dba",
+  "prior_tested_manifest": "58048a268e837f4e8a30521435b2c3dad77fd0e74b38f020b7b7e11367ecf5b7",
+  "old_assembly_sha256": "150bc23a25485be70b9e0a5347f336338a7458efe2ebc800053da37df42d522e",
+  "new_assembly_sha256": "7f5b02e2f48c0b5e1ae8dc12fd953b2bb262287277910115bee5fffae4a73817",
+  "kappa": "1265848755025709/1000000000000000000",
+  "complex_lower": "79215822439319966337/62500000000000000000000",
+  "input_sha256": {
+    "GLOBAL.json": "4c71526402774c619212991d08708e11629946072bb78b799b8cacf45d8bab30",
+    "GEOMETRY.json": "77adc647850dcf0522869e6c007e08108222d49a458b8dedbfe8d028c2d160be",
+    "AUDIT.json": "2e8f1476d3bc72a2cc3bf3cd035a1e67afae9b2a732fbaf5003b116edd65a743"
+  },
+  "result_sha256": "dae8b568b730de0ea2377ecb77cc0a49751e1d58b647026d25392b6b7e4301ab",
+  "strict_outer_constraints": 47,
+  "scope": "Full unchanged suppliers passed; the two-line assembly refinement is rerun in both versions. This is not a fresh uninterrupted full-wrapper run of the changed manifest."
+}
diff --git a/research/e8-eleven-hosting-selected-validation/precision/python311/RESULT.json b/research/e8-eleven-hosting-selected-validation/precision/python311/RESULT.json
new file mode 100644
index 0000000000..4414ee735e
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/precision/python311/RESULT.json
@@ -0,0 +1,154 @@
+{
+  "status": "PASS_CONDITIONAL_ELEVEN_STAGE_HOSTING_ASSEMBLY",
+  "kappa": "1265848755025709/1000000000000000000",
+  "kappa_decimal": "0.001265848755025709",
+  "bit_lower": "1267514693114214441041/1000000000000000000000000",
+  "complex_lower": "79215822439319966337/62500000000000000000000",
+  "binding_component": "complex",
+  "gain_over_pr445_percent": 0.19656151080425197,
+  "bit": {
+    "live": 9600,
+    "physical": 9609,
+    "maxchild": 56,
+    "rank_mass": 745536,
+    "hosted_residuals": 65120,
+    "prefix_bits": 153,
+    "charged_prefix_bits": 192,
+    "coefficient_bits": 153,
+    "three_level_coefficient_bits": 514,
+    "charged_three_level_coefficient_bits": 1024,
+    "row_coefficient": 19431
+  },
+  "complex": {
+    "live": 8400,
+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
+  },
+  "strict_outer_constraints": {
+    "bit_positive": "4721630957086084243016630892729619412794522938894421719114608588019406415676289654518536543712476039477685177526932922689268369962070727619992859322184404727257879456878020964682741220072360294059935536891135637625523295955093071402198116561532831993561153303849754778784168608924033/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "23705571408295771212205477061105578280885391411980593584323710345481463456287523960522314822473067077310731630037929272380007140677815595272742120543121979035317258779927639705940064463108864362374476704044906928597801883438467168006438846696150245221215831391075967/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "1873909177560680033663/62500000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "18983940451209686945483274760080187655885391411980593584323710345481463456287523960522314822473067077310731630037929272380007140677815595272742120543121979035317258779927639705940064463108864362374476704044906928597801883438467168006438846696150245221215831391075967/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_positive": "2360815478543042116786684489278725463380630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_internal": "4721630957086084243016630892729619412794522938894421719114608588019406415676289654518536543712476039477685177526932922689268369962070727619992859322184404727257879456878020964682741220072360294059935536891135637625523295955093071402198116561532831993561153303849754778784168608924033/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_leaf": "14213601182690927715758268272769713240737218644884718511276463760760138143820051634779693954949009578133050992545897558879271940300978525256363919593745394244916508846841840817652773451626792475247173888913589101924424237674326655405417539909607954604169068999387738278784168608924033/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_positive": "2360815478543042582447971797017983275880630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_below_one": "1860284333752413988667552028202982016724119369423282408553237218644884718511276463760760138143820051634779693954949009578133050992545897558879271940300978525256363919593745394244916508846841840817652773451626792475247173888913589101924424237674326655405417539909607954604169068999387738278784168608924033/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_reservations": "1/4000000000000000000",
+    "lambda_above_tau": "4721630957086084243016630892729619412794522938894421719114608588019406415676289654518536543712476039477685177526932922689268369962070727619992859322184404727257879456878020964682741220072360294059935536891135637625523295955093071402198116561532831993561153303849754778784168608924033/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_sigma": "28427202365381855455222107953835197693679914350875015303438318933500869871963813615040851366185543116788416807564862195069275510639886322892734979865306383762575138236805660670622805683181224656434412240936042566223325179393560239408636963257683077214776984694925721778784168608924033/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_internal": "4721630957086084243016630892729619412794522938894421719114608588019406415676289654518536543712476039477685177526932922689268369962070727619992859322184404727257879456878020964682741220072360294059935536891135637625523295955093071402198116561532831993561153303849754778784168608924033/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_prime_above_lambda": "4721630957086084243016630892729619412794522938894421719114608588019406415676289654518536543712476039477685177526932922689268369962070727619992859322184404727257879456878020964682741220072360294059935536891135637625523295955093071402198116561532831993561153303849754778784168608924033/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_leaf": "14213601182690927715758268272769713240737218644884718511276463760760138143820051634779693954949009578133050992545897558879271940300978525256363919593745394244916508846841840817652773451626792475247173888913589101924424237674326655405417539909607954604169068999387738278784168608924033/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_reservations": "1/4000000000000000000",
+    "lambda_prime_below_one": "2360815478543042116786684489278725463380630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "epsilon_positive": "1862645149230957029387354850769042968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/1865005964709500073366786684489278725463380630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967",
+    "epsilon_below_one": "2360815478543043979431833720235756713380630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967/1865005964709500073366786684489278725463380630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967",
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+}
diff --git a/research/e8-eleven-hosting-selected-validation/precision/python311/assembly.log b/research/e8-eleven-hosting-selected-validation/precision/python311/assembly.log
new file mode 100644
index 0000000000..9f548bcb3b
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/precision/python311/assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_ELEVEN_STAGE_HOSTING_ASSEMBLY 0.001265848755025709 binding complex gain over #445 0.1966%
diff --git a/research/e8-eleven-hosting-selected-validation/precision/python314/RECEIPT.json b/research/e8-eleven-hosting-selected-validation/precision/python314/RECEIPT.json
new file mode 100644
index 0000000000..ff90dc0b56
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/precision/python314/RECEIPT.json
@@ -0,0 +1,18 @@
+{
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+  "python": "3.14.8",
+  "supplier_full_receipt_sha256": "2bdfa38a351473dceef266986f0c4885a7652354713fe83b4b1cec00c6d054e8",
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+  "old_assembly_sha256": "150bc23a25485be70b9e0a5347f336338a7458efe2ebc800053da37df42d522e",
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+  "kappa": "1265848755025709/1000000000000000000",
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+  "input_sha256": {
+    "GLOBAL.json": "f7e6aa31c6b36286e00d88aa8f9ed9bf20aee4e6702322d5907d57b9ddb5ffef",
+    "GEOMETRY.json": "7c2d5dadb344160ca6f40feb89401711e02f9d496b43a04fcfc1925ed506c6d4",
+    "AUDIT.json": "8804e3ed7c133ff7278766f379e06561002c91608b35e5c80863b85d98aac4e1"
+  },
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+  "strict_outer_constraints": 47,
+  "scope": "Full unchanged suppliers passed; the two-line assembly refinement is rerun in both versions. This is not a fresh uninterrupted full-wrapper run of the changed manifest."
+}
diff --git a/research/e8-eleven-hosting-selected-validation/precision/python314/RESULT.json b/research/e8-eleven-hosting-selected-validation/precision/python314/RESULT.json
new file mode 100644
index 0000000000..d1d30c76f2
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/precision/python314/RESULT.json
@@ -0,0 +1,154 @@
+{
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+}
diff --git a/research/e8-eleven-hosting-selected-validation/precision/python314/assembly.log b/research/e8-eleven-hosting-selected-validation/precision/python314/assembly.log
new file mode 100644
index 0000000000..9f548bcb3b
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/precision/python314/assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_ELEVEN_STAGE_HOSTING_ASSEMBLY 0.001265848755025709 binding complex gain over #445 0.1966%
diff --git a/research/e8-eleven-hosting-selected-validation/python311/AUDIT.json b/research/e8-eleven-hosting-selected-validation/python311/AUDIT.json
new file mode 100644
index 0000000000..5636bdc234
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python311/AUDIT.json
@@ -0,0 +1,51 @@
+{
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+  "deficit": 3264,
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+  "halving_depth": 3,
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+    "wrong residual width",
+    "duplicate helper",
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+    "cross-replica host",
+    "cross-replica data",
+    "wrong hosted coordinate",
+    "helper changed to bank",
+    "wrong call orientation",
+    "duplicate call",
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+    "omitted bridge",
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+    "omitted terminal exchange",
+    "understated live stock",
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+    "omitted local instruction",
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+}
diff --git a/research/e8-eleven-hosting-selected-validation/python311/RANK147-PARENT-RECEIPT.json b/research/e8-eleven-hosting-selected-validation/python311/RANK147-PARENT-RECEIPT.json
new file mode 100644
index 0000000000..fb73eac6bc
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python311/RANK147-PARENT-RECEIPT.json
@@ -0,0 +1,54 @@
+{
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+}
diff --git a/research/e8-eleven-hosting-selected-validation/python311/RECEIPT.json b/research/e8-eleven-hosting-selected-validation/python311/RECEIPT.json
new file mode 100644
index 0000000000..e93de5f067
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python311/RECEIPT.json
@@ -0,0 +1,33 @@
+{
+  "status": "PASS_FULL_ELEVEN_HOSTING_SELECTED",
+  "python": "3.11.15",
+  "kappa": "316462188756427/250000000000000000",
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+}
diff --git a/research/e8-eleven-hosting-selected-validation/python311/RESULT.json b/research/e8-eleven-hosting-selected-validation/python311/RESULT.json
new file mode 100644
index 0000000000..5530ca21fc
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python311/RESULT.json
@@ -0,0 +1,154 @@
+{
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+}
diff --git a/research/e8-eleven-hosting-selected-validation/python311/TESTED-MANIFEST.json b/research/e8-eleven-hosting-selected-validation/python311/TESTED-MANIFEST.json
new file mode 100644
index 0000000000..ccc12498de
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python311/TESTED-MANIFEST.json
@@ -0,0 +1,53 @@
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+  "evidence/audit.log": "a4b1b1eed31c07f9a3e495205bfffde4ec861aba9cf750a7b1fea5a9922ea38d",
+  "evidence/eleven-kernel-screen-first-failure.log": "cd53bd73b6a2dd53879d9f048368bf8f68204ef7daf4b0be849f7bd725a65eb7",
+  "evidence/eleven-kernel-screen.log": "54ded773480d897867a969444794ea5fdcf2fd03de062c4012f63e28d86d09b0",
+  "evidence/emit-missing-engines.log": "4e3419b3e32b60bbefe52a30f5661a8f6f53f060b99eccf32d11c9db0098d0e9",
+  "evidence/emit-missing-vendor.log": "407732b01762f5f843f54dd629820173e5958d35e0126e2c857249aad4e776a9",
+  "evidence/emit.log": "3d3853b873beb8705f798c2abdd8ac4564497f51d2c4d56419743603d6d063ae",
+  "evidence/geometry.log": "46d842d677e5faf5b8224d247f0549a00f3db138168a13802f0aebb7bc5ace46",
+  "evidence/hosted147-full314.log": "5424d4caeeb8f868adb0aee4014f42715711d4044564b3ed6b865bec16f3a028",
+  "evidence/screen_eleven_kernels.py": "80cc77ba27382ac57f7c804f6c78d880442644710e437a9859bd964106b216b7",
+  "upstream445/EXPECTED.json": "1a2e35da8c586be03201a8d102c72f681b0b6698bbcb3a2ea286d8b0d9c0c1e4",
+  "upstream445/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "upstream445/MANIFEST.json": "4d53297535ffb17603f916fa59cdc4b7f941c3166fe9f8e576f9588fd2fb79a6",
+  "upstream445/NOTICE.md": "b80411c1db53d12bf43d6cbb8bf2804102f2e57be2a2f55dd7820c6c2f2b9570",
+  "upstream445/PROOF.md": "4aede2a05d9570cc5d8a19032513c973137ee9083f079ae845b04f3f362e2ca0",
+  "upstream445/README.md": "15e76f8a2200af0f871b04d410ebd7fac059b800b5ec4a1f376a333c9f5638bf",
+  "upstream445/SOURCE.json": "976eebfec20d467f3384194fc03bd6f5b289a615e3b2deb70a7be910aaee8579",
+  "upstream445/code/assemble.py": "42dbfaddd284088474a80f0b6e894332b6737b8e9f9b5c45260e21c5df139792",
+  "upstream445/code/audit.py": "9900a1b2f1f314f2b93ca8f99b5516ed2e1a7295d668ea51df2df89cef84e381",
+  "upstream445/code/emit.py": "ac63ee481f3d75cb9f0658faaa2412db81d55bc44d9f1ff1c0329ce1e75aa0d4",
+  "upstream445/code/geometry.py": "9554182d67e434ea84b4430f909a2c400abc755d8487b51454a8e6968e62859d",
+  "upstream445/code/row_bound.py": "de4a9b9cd797e1a05da56f62cfe725c8728cea3a4aa031b7d1b0a68f869760d6",
+  "upstream445/data/selection.json": "52dbbb68e8c147690d15eaa1d952df05d074b0c121885a4159d9f6732f391872",
+  "upstream445/proof/INHERITED-ROW-DIVISOR.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8",
+  "upstream445/proof/UPSTREAM-PR234-NOTICE.md": "ce978c8dfc8a2b36eed7a53014b1a792248b22ef4cee3edd8adab825a571c429",
+  "upstream445/verify.py": "4a161d35c65fa1d35e655c3957c05a8164a003ca05c3effe9fee7dc8d0f38090",
+  "verify.py": "fcc35e955bd667350f999a540011df92e2e1d774fc78703f53bfbabf949643af"
+}
diff --git a/research/e8-eleven-hosting-selected-validation/python311/emit.log b/research/e8-eleven-hosting-selected-validation/python311/emit.log
new file mode 100644
index 0000000000..3d4ae136d1
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python311/emit.log
@@ -0,0 +1 @@
+{"status": "PASS_SOURCE_BOUND_ELEVEN_STAGE_HOSTED_BIT_TEMPLATE", "h": 8, "m": 78, "v": 120, "R": 740, "replicas": 8, "live": 9600, "physical": 9609, "word_sha256": "5b9a54c97eea0ef3729b164d81fde4e289105d134d0567c83bedc67cdac3298a", "source_records_sha256": "f9e0f3cdbc6a4eb5bfaf3fd843731a79c26740a6c4715079f2228e94b8706403", "independent_unbanked_scalar_columns": 9340, "all_scalar_columns_restored": true, "geometry_sha256": "77adc647850dcf0522869e6c007e08108222d49a458b8dedbfe8d028c2d160be", "template_sha256": "ddd133d2f4de89a6d26ba062d043e703ca5cb50f07c6956035be9972416cfd0a", "emitted_program_sha256": "4ab6c4a1cecef52521cff258e2722f8755e65f5c9f8d87344ee78a1388bc57ec", "emitted_events": 1740288, "local_invocations": 88, "bank_assignments": 0, "hosted_residuals": 65120, "banks_per_stage": 0, "entrance_rank_total": 147, "residual_bank_slots": false, "padding_calls": 0, "profile": {"1": 223960, "2": 93568, "3": 23528, "4": 34296, "5": 9504, "6": 2000, "7": 5112, "8": 792, "49": 8, "56": 440}, "paid_calls": 393208, "rank_mass": 745536, "deficit": 3264, "maxchild": 56, "halving_depth": 3, "halving_integer_inequality": [474552, 351232], "local_additions": 15446, "bridge_additions": 23040, "copy_erase_episodes": 792, "global_prefix_bits": 153, "charged_prefix_bits": 192, "omitted_bridge_shears_rejected": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], "scope": "Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; idle-data hosting follows conditionally from PR442 plus injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.", "seconds": 3.501204374944791}
diff --git a/research/e8-eleven-hosting-selected-validation/python311/exact-assembly.log b/research/e8-eleven-hosting-selected-validation/python311/exact-assembly.log
new file mode 100644
index 0000000000..ee608c69b0
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python311/exact-assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_ELEVEN_STAGE_HOSTING_ASSEMBLY 0.001265848755025708 binding complex gain over #445 0.1966%
diff --git a/research/e8-eleven-hosting-selected-validation/python311/geometry.log b/research/e8-eleven-hosting-selected-validation/python311/geometry.log
new file mode 100644
index 0000000000..32076b0043
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python311/geometry.log
@@ -0,0 +1,5 @@
+compressed geometry 1
+compressed geometry 31
+compressed geometry 61
+compressed geometry 91
+{"status": "PASS_COMPRESSED_ELEVEN_BIT_GEOMETRY", "h": 8, "m": 78, "stages": 11, "word_sha256": "1fb726ea3818fe0837cceb0dd22a71a0814f064e5e781628104610d6468e0e55", "local_window": "U direct_sum E_s, with E_s the first s exterior coordinate 7-blocks", "ambient_form": "I_78/2", "bank_slots": [], "route_checks": 1320, "exact_bit_endpoint_operator_checks": 240, "max_route_factors": 77, "route_denominators": [1, 2, 4], "bad_prime_factors": [2], "missing_route_factor_controls": 120, "bank_free": true, "scope": "All port isometries, stage boundary identities, nested idle ranks, exact bit endpoint operators and coordinate embeddings. No residual banks are used. Full local-word scalar and chronological lowering are checked separately.", "seconds": 2.2424576670164242}
diff --git a/research/e8-eleven-hosting-selected-validation/python311/independent-audit.log b/research/e8-eleven-hosting-selected-validation/python311/independent-audit.log
new file mode 100644
index 0000000000..823bb8a742
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python311/independent-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_ELEVEN_STAGE_HOSTING_AUDIT", "template_sha256": "ddd133d2f4de89a6d26ba062d043e703ca5cb50f07c6956035be9972416cfd0a", "emitted_program_sha256": "4ab6c4a1cecef52521cff258e2722f8755e65f5c9f8d87344ee78a1388bc57ec", "emitted_events": 1740288, "profile": {"1": 223960, "2": 93568, "3": 23528, "4": 34296, "5": 9504, "6": 2000, "7": 5112, "8": 792, "49": 8, "56": 440}, "live": 9600, "physical": 9609, "hosted_residuals": 65120, "bank_assignments": 0, "rank_mass": 745536, "deficit": 3264, "maxchild": 56, "geometry_routes": 1320, "halving_depth": 3, "mutations_rejected": ["slot outside window", "copy outside family", "negative slot offset", "wrong residual width", "duplicate helper", "missing helper", "cross-replica host", "cross-replica data", "wrong hosted coordinate", "helper changed to bank", "wrong call orientation", "duplicate call", "dropped final stage", "wrong idle rank", "omitted bridge", "wrong bridge sign", "omitted terminal exchange", "understated live stock", "missing remainder summary", "wrong residual isometry", "omitted local instruction", "wrong reflected copy rank"]}
diff --git a/research/e8-eleven-hosting-selected-validation/python311/parent-full.log b/research/e8-eleven-hosting-selected-validation/python311/parent-full.log
new file mode 100644
index 0000000000..bdf568c03b
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python311/parent-full.log
@@ -0,0 +1,72 @@
+RUN parent-full
+PASS parent-full
+RUN kernel-rebuild
+PASS kernel-rebuild
+RUN export-records
+PASS export-records
+RUN bit-global-64
+PASS bit-global-64
+RUN bit-global-audit
+PASS bit-global-audit
+RUN bit-hosting
+PASS bit-hosting
+RUN complex-hosting
+PASS complex-hosting
+RUN independent-hosting-audit
+PASS independent-hosting-audit
+RUN exact-assembly
+PASS exact-assembly
+{
+  "status": "PASS_FULL_HOSTING_SELECTED_KERNEL",
+  "python": "3.11.15",
+  "kappa": "312258824824501/250000000000000000",
+  "kappa_decimal": "0.001249035299298004",
+  "manifest_sha256": "b32a601147fbe042af3799bae4a73d27f7a433e76aa83650ba24566b329c184b",
+  "checks": [
+    {
+      "name": "parent-full",
+      "seconds": 384.16,
+      "log_sha256": "0ccab4b740f5eef349efd4a265373b1f35e388b25e939cc2507b67f353560fbf"
+    },
+    {
+      "name": "kernel-rebuild",
+      "seconds": 16.11,
+      "log_sha256": "c04d4e939822acd4f0f91c7690293f2b321c9e1fb2de342ce61b997d19e686d9"
+    },
+    {
+      "name": "export-records",
+      "seconds": 0.58,
+      "log_sha256": "76145fe1bd54c65d5f4041e92b2589cb0dede760b5030bbe2042c3e502119594"
+    },
+    {
+      "name": "bit-global-64",
+      "seconds": 21.0,
+      "log_sha256": "abcd082928a955fed95f4bd2402b2e47e6d52d424fc7ff2337a1ab094788e70e"
+    },
+    {
+      "name": "bit-global-audit",
+      "seconds": 24.7,
+      "log_sha256": "063d820aecc7c53677fba23c24d907f74e6b8e1a12099f83a444d6936756c86b"
+    },
+    {
+      "name": "bit-hosting",
+      "seconds": 3.39,
+      "log_sha256": "20295c72cee3f6a3856f68889c5ae1a6874bd5892bef548122cc69842555f933"
+    },
+    {
+      "name": "complex-hosting",
+      "seconds": 0.39,
+      "log_sha256": "3b42f65586cb5c37e06df560fae4dcde1c42526238697a73d103f9895df24fcd"
+    },
+    {
+      "name": "independent-hosting-audit",
+      "seconds": 14.63,
+      "log_sha256": "1359977f74843042c039a81bf2c687cd0b931916b906fe7ca60efd9f745e9c52"
+    },
+    {
+      "name": "exact-assembly",
+      "seconds": 0.24,
+      "log_sha256": "4813c9b302a6b07e1d276c9b939926cf8ebce5197d75703cdb061794827a21b2"
+    }
+  ]
+}
diff --git a/research/e8-eleven-hosting-selected-validation/python314/AUDIT.json b/research/e8-eleven-hosting-selected-validation/python314/AUDIT.json
new file mode 100644
index 0000000000..aaa516cf66
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python314/AUDIT.json
@@ -0,0 +1,51 @@
+{
+  "status": "PASS_INDEPENDENT_ELEVEN_STAGE_HOSTING_AUDIT",
+  "template_sha256": "fda4ef5f1fd3559cade37d9c94ac9d790768df22047c2df2652683412466aba9",
+  "emitted_program_sha256": "4ab6c4a1cecef52521cff258e2722f8755e65f5c9f8d87344ee78a1388bc57ec",
+  "emitted_events": 1740288,
+  "profile": {
+    "1": 223960,
+    "2": 93568,
+    "3": 23528,
+    "4": 34296,
+    "5": 9504,
+    "6": 2000,
+    "7": 5112,
+    "8": 792,
+    "49": 8,
+    "56": 440
+  },
+  "live": 9600,
+  "physical": 9609,
+  "hosted_residuals": 65120,
+  "bank_assignments": 0,
+  "rank_mass": 745536,
+  "deficit": 3264,
+  "maxchild": 56,
+  "geometry_routes": 1320,
+  "halving_depth": 3,
+  "mutations_rejected": [
+    "slot outside window",
+    "copy outside family",
+    "negative slot offset",
+    "wrong residual width",
+    "duplicate helper",
+    "missing helper",
+    "cross-replica host",
+    "cross-replica data",
+    "wrong hosted coordinate",
+    "helper changed to bank",
+    "wrong call orientation",
+    "duplicate call",
+    "dropped final stage",
+    "wrong idle rank",
+    "omitted bridge",
+    "wrong bridge sign",
+    "omitted terminal exchange",
+    "understated live stock",
+    "missing remainder summary",
+    "wrong residual isometry",
+    "omitted local instruction",
+    "wrong reflected copy rank"
+  ]
+}
diff --git a/research/e8-eleven-hosting-selected-validation/python314/RANK147-PARENT-RECEIPT.json b/research/e8-eleven-hosting-selected-validation/python314/RANK147-PARENT-RECEIPT.json
new file mode 100644
index 0000000000..5dfd747494
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python314/RANK147-PARENT-RECEIPT.json
@@ -0,0 +1,54 @@
+{
+  "status": "PASS_FULL_HOSTING_SELECTED_KERNEL",
+  "python": "3.14.8",
+  "kappa": "312258824824501/250000000000000000",
+  "kappa_decimal": "0.001249035299298004",
+  "manifest_sha256": "b32a601147fbe042af3799bae4a73d27f7a433e76aa83650ba24566b329c184b",
+  "checks": [
+    {
+      "name": "parent-full",
+      "seconds": 274.75,
+      "log_sha256": "35391ae8f6164bddc0d5fe070bbc68bacb30595536143d37614b4e997ca5bccf"
+    },
+    {
+      "name": "kernel-rebuild",
+      "seconds": 9.94,
+      "log_sha256": "c04d4e939822acd4f0f91c7690293f2b321c9e1fb2de342ce61b997d19e686d9"
+    },
+    {
+      "name": "export-records",
+      "seconds": 0.36,
+      "log_sha256": "76145fe1bd54c65d5f4041e92b2589cb0dede760b5030bbe2042c3e502119594"
+    },
+    {
+      "name": "bit-global-64",
+      "seconds": 20.89,
+      "log_sha256": "37892007ce1ec64720e6b0d20bb34d1030e151892587463dd8c7c6f4915dc4a4"
+    },
+    {
+      "name": "bit-global-audit",
+      "seconds": 13.55,
+      "log_sha256": "3cb0e4fd1dc3dc183bff3e988cc5bf9eed80ae882aa30e02ab14c0331f88dca2"
+    },
+    {
+      "name": "bit-hosting",
+      "seconds": 2.16,
+      "log_sha256": "20295c72cee3f6a3856f68889c5ae1a6874bd5892bef548122cc69842555f933"
+    },
+    {
+      "name": "complex-hosting",
+      "seconds": 0.37,
+      "log_sha256": "3b42f65586cb5c37e06df560fae4dcde1c42526238697a73d103f9895df24fcd"
+    },
+    {
+      "name": "independent-hosting-audit",
+      "seconds": 6.6,
+      "log_sha256": "1359977f74843042c039a81bf2c687cd0b931916b906fe7ca60efd9f745e9c52"
+    },
+    {
+      "name": "exact-assembly",
+      "seconds": 0.22,
+      "log_sha256": "4813c9b302a6b07e1d276c9b939926cf8ebce5197d75703cdb061794827a21b2"
+    }
+  ]
+}
diff --git a/research/e8-eleven-hosting-selected-validation/python314/RECEIPT.json b/research/e8-eleven-hosting-selected-validation/python314/RECEIPT.json
new file mode 100644
index 0000000000..4754753e58
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python314/RECEIPT.json
@@ -0,0 +1,33 @@
+{
+  "status": "PASS_FULL_ELEVEN_HOSTING_SELECTED",
+  "python": "3.14.8",
+  "kappa": "316462188756427/250000000000000000",
+  "manifest_sha256": "58048a268e837f4e8a30521435b2c3dad77fd0e74b38f020b7b7e11367ecf5b7",
+  "checks": [
+    {
+      "name": "parent-full",
+      "seconds": 328.89,
+      "log_sha256": "2192bf17cc72cd10cba563cebc12ae214bdaa37c4c5f3ff4130e1fd5cbe6b715"
+    },
+    {
+      "name": "geometry",
+      "seconds": 2.33,
+      "log_sha256": "2045ec8f88fa42a4051f1309f6a994561b3328ba105ccd57204201bfc3f2121f"
+    },
+    {
+      "name": "emit",
+      "seconds": 3.34,
+      "log_sha256": "756c3a1cf09ddc0c053685e16305414c3bc645d052a0ec8ae61515bb43c90342"
+    },
+    {
+      "name": "independent-audit",
+      "seconds": 6.55,
+      "log_sha256": "3e00eba9ad762570d30d84b32b588e8dbe8458ca7fe5d8010f64a703a97f761e"
+    },
+    {
+      "name": "exact-assembly",
+      "seconds": 0.25,
+      "log_sha256": "e02a0b68a7f72a453c470339dd48eab594e433c80809fdab196e58fc7ff10ee7"
+    }
+  ]
+}
diff --git a/research/e8-eleven-hosting-selected-validation/python314/RESULT.json b/research/e8-eleven-hosting-selected-validation/python314/RESULT.json
new file mode 100644
index 0000000000..087e197b6c
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python314/RESULT.json
@@ -0,0 +1,154 @@
+{
+  "status": "PASS_CONDITIONAL_ELEVEN_STAGE_HOSTING_ASSEMBLY",
+  "kappa": "316462188756427/250000000000000000",
+  "kappa_decimal": "0.001265848755025708",
+  "bit_lower": "1267514693114214441041/1000000000000000000000000",
+  "complex_lower": "1267453159029119/1000000000000000000",
+  "binding_component": "complex",
+  "gain_over_pr445_percent": 0.1965615108041728,
+  "bit": {
+    "live": 9600,
+    "physical": 9609,
+    "maxchild": 56,
+    "rank_mass": 745536,
+    "hosted_residuals": 65120,
+    "prefix_bits": 153,
+    "charged_prefix_bits": 192,
+    "coefficient_bits": 153,
+    "three_level_coefficient_bits": 514,
+    "charged_three_level_coefficient_bits": 1024,
+    "row_coefficient": 19431
+  },
+  "complex": {
+    "live": 8400,
+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
+  },
+  "strict_outer_constraints": {
+    "bit_positive": "1267453159029118993636584129273575974277156296177030459740728443275374931273908992545463023755416291367880514466331552246861631100778856205365772854913694471018734377815249453006044134546927457676478839335758769886625685298693906301814628191855821439/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "6363415870726424025722843703822969540259271556724625068726091007454536976244583708632119485533668447753138368899221143794634227145086305528981265622184750546993955865453072542323521160664241230113374314701306093698185371808144178561/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "29982546840970881/1000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
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+    "factor_two_power": 78,
+    "cover_exponent": 3081,
+    "physical_families": 9609,
+    "physical_exponent": 9,
+    "stock_exponent": 3090,
+    "halving_depth": 3,
+    "complete_row_coefficient": 19431,
+    "retained_row_coefficient": 20161
+  },
+  "row_controls": [
+    "false two-level halving",
+    "understated row reserve"
+  ],
+  "halving_depth": 3,
+  "finite_controls": [
+    "old 128-bit prefix charge insufficient",
+    "old 512-bit composite charge insufficient"
+  ]
+}
diff --git a/research/e8-eleven-hosting-selected-validation/python314/TESTED-MANIFEST.json b/research/e8-eleven-hosting-selected-validation/python314/TESTED-MANIFEST.json
new file mode 100644
index 0000000000..ccc12498de
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python314/TESTED-MANIFEST.json
@@ -0,0 +1,53 @@
+{
+  "AUDIT.json": "268269736a1427572a01ac660888af19d12194bdfa3f6c9b5311752f77c1cbc8",
+  "CERTIFICATE.json": "b27a4ef11a3550b8f3246f6982cbb49b7f0076837256893aaed470fe6e52e735",
+  "EXPECTED.json": "ba660caab38f1b8f15288ae66c5d7ef3fdecea6d59e0889a144675b2f18a0e15",
+  "GLOBAL.json": "64f0863ce8897335ebfb0e78a5a356a0ca9f3ebf07b7a54b5332403d1ca93bdc",
+  "INHERITED-HOSTING-PROOF.md": "4f06d1dead63c62b076f0a6c1521c68c0b0544aa2c5df5e74a408fdfc34f91c4",
+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "NOTICE.md": "28662fdf0a5dc6adaa13e491e2a7023ec9846bcb83ab183f8da393555fa96dab",
+  "PROOF.md": "07bdc9ceb83831b2ca116ebc17955e39e782b01c2eab85eaf0bdfc6357a2b163",
+  "README.md": "d0bad14c41740a680cfe34a91f0b290321101878883d3d1c1eb10c047e2fb59e",
+  "SOURCE.json": "470735692afc6deeba3ff5992a26282d92a485c34848bc00bf4cc7009230aebb",
+  "VALIDATION.json": "7824817182a9904e6b116779a6a857bf3ae3d09229e05b76cf4310c42302b1a9",
+  "code/assemble.py": "150bc23a25485be70b9e0a5347f336338a7458efe2ebc800053da37df42d522e",
+  "code/audit.py": "9900a1b2f1f314f2b93ca8f99b5516ed2e1a7295d668ea51df2df89cef84e381",
+  "code/bank_routes.py": "7c6997c455bd55acca3a1603797c34e7733d557c27a7694a1429ff15773a505d",
+  "code/e8core.py": "1cb286196c1530d06f50f0997febc5993b388f33464e295611b920ba30a24eeb",
+  "code/emit.py": "515d7021293e23aba1165ee270e17c375072e7128ed7b3c738768b6f6b7e9af8",
+  "code/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+  "code/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+  "code/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+  "code/geometry.py": "9554182d67e434ea84b4430f909a2c400abc755d8487b51454a8e6968e62859d",
+  "code/hosting_core.py": "d8b90cd5d152df3c7c351230863d9e61816ad5e1f21d69bea1a86a5daad559a3",
+  "code/row_bound.py": "de4a9b9cd797e1a05da56f62cfe725c8728cea3a4aa031b7d1b0a68f869760d6",
+  "code/tile_m.py": "d6ae4a556472d403773cd2117c992bfc10e1187112da1b3893f3fae628a131dd",
+  "data/selection.json": "b81758d0cce18e6c1abd07e716f05064aaa9b43819d6b70f7f52b4f2e4f01a9b",
+  "evidence/assembly.log": "e02a0b68a7f72a453c470339dd48eab594e433c80809fdab196e58fc7ff10ee7",
+  "evidence/audit.log": "a4b1b1eed31c07f9a3e495205bfffde4ec861aba9cf750a7b1fea5a9922ea38d",
+  "evidence/eleven-kernel-screen-first-failure.log": "cd53bd73b6a2dd53879d9f048368bf8f68204ef7daf4b0be849f7bd725a65eb7",
+  "evidence/eleven-kernel-screen.log": "54ded773480d897867a969444794ea5fdcf2fd03de062c4012f63e28d86d09b0",
+  "evidence/emit-missing-engines.log": "4e3419b3e32b60bbefe52a30f5661a8f6f53f060b99eccf32d11c9db0098d0e9",
+  "evidence/emit-missing-vendor.log": "407732b01762f5f843f54dd629820173e5958d35e0126e2c857249aad4e776a9",
+  "evidence/emit.log": "3d3853b873beb8705f798c2abdd8ac4564497f51d2c4d56419743603d6d063ae",
+  "evidence/geometry.log": "46d842d677e5faf5b8224d247f0549a00f3db138168a13802f0aebb7bc5ace46",
+  "evidence/hosted147-full314.log": "5424d4caeeb8f868adb0aee4014f42715711d4044564b3ed6b865bec16f3a028",
+  "evidence/screen_eleven_kernels.py": "80cc77ba27382ac57f7c804f6c78d880442644710e437a9859bd964106b216b7",
+  "upstream445/EXPECTED.json": "1a2e35da8c586be03201a8d102c72f681b0b6698bbcb3a2ea286d8b0d9c0c1e4",
+  "upstream445/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "upstream445/MANIFEST.json": "4d53297535ffb17603f916fa59cdc4b7f941c3166fe9f8e576f9588fd2fb79a6",
+  "upstream445/NOTICE.md": "b80411c1db53d12bf43d6cbb8bf2804102f2e57be2a2f55dd7820c6c2f2b9570",
+  "upstream445/PROOF.md": "4aede2a05d9570cc5d8a19032513c973137ee9083f079ae845b04f3f362e2ca0",
+  "upstream445/README.md": "15e76f8a2200af0f871b04d410ebd7fac059b800b5ec4a1f376a333c9f5638bf",
+  "upstream445/SOURCE.json": "976eebfec20d467f3384194fc03bd6f5b289a615e3b2deb70a7be910aaee8579",
+  "upstream445/code/assemble.py": "42dbfaddd284088474a80f0b6e894332b6737b8e9f9b5c45260e21c5df139792",
+  "upstream445/code/audit.py": "9900a1b2f1f314f2b93ca8f99b5516ed2e1a7295d668ea51df2df89cef84e381",
+  "upstream445/code/emit.py": "ac63ee481f3d75cb9f0658faaa2412db81d55bc44d9f1ff1c0329ce1e75aa0d4",
+  "upstream445/code/geometry.py": "9554182d67e434ea84b4430f909a2c400abc755d8487b51454a8e6968e62859d",
+  "upstream445/code/row_bound.py": "de4a9b9cd797e1a05da56f62cfe725c8728cea3a4aa031b7d1b0a68f869760d6",
+  "upstream445/data/selection.json": "52dbbb68e8c147690d15eaa1d952df05d074b0c121885a4159d9f6732f391872",
+  "upstream445/proof/INHERITED-ROW-DIVISOR.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8",
+  "upstream445/proof/UPSTREAM-PR234-NOTICE.md": "ce978c8dfc8a2b36eed7a53014b1a792248b22ef4cee3edd8adab825a571c429",
+  "upstream445/verify.py": "4a161d35c65fa1d35e655c3957c05a8164a003ca05c3effe9fee7dc8d0f38090",
+  "verify.py": "fcc35e955bd667350f999a540011df92e2e1d774fc78703f53bfbabf949643af"
+}
diff --git a/research/e8-eleven-hosting-selected-validation/python314/emit.log b/research/e8-eleven-hosting-selected-validation/python314/emit.log
new file mode 100644
index 0000000000..05171f4eb7
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python314/emit.log
@@ -0,0 +1 @@
+{"status": "PASS_SOURCE_BOUND_ELEVEN_STAGE_HOSTED_BIT_TEMPLATE", "h": 8, "m": 78, "v": 120, "R": 740, "replicas": 8, "live": 9600, "physical": 9609, "word_sha256": "ee4cda817d5220fdbba1d116556e3dacb3da553ed81af43e74f19365e1393a5c", "source_records_sha256": "f9e0f3cdbc6a4eb5bfaf3fd843731a79c26740a6c4715079f2228e94b8706403", "independent_unbanked_scalar_columns": 9340, "all_scalar_columns_restored": true, "geometry_sha256": "7c2d5dadb344160ca6f40feb89401711e02f9d496b43a04fcfc1925ed506c6d4", "template_sha256": "fda4ef5f1fd3559cade37d9c94ac9d790768df22047c2df2652683412466aba9", "emitted_program_sha256": "4ab6c4a1cecef52521cff258e2722f8755e65f5c9f8d87344ee78a1388bc57ec", "emitted_events": 1740288, "local_invocations": 88, "bank_assignments": 0, "hosted_residuals": 65120, "banks_per_stage": 0, "entrance_rank_total": 147, "residual_bank_slots": false, "padding_calls": 0, "profile": {"1": 223960, "2": 93568, "3": 23528, "4": 34296, "5": 9504, "6": 2000, "7": 5112, "8": 792, "49": 8, "56": 440}, "paid_calls": 393208, "rank_mass": 745536, "deficit": 3264, "maxchild": 56, "halving_depth": 3, "halving_integer_inequality": [474552, 351232], "local_additions": 15446, "bridge_additions": 23040, "copy_erase_episodes": 792, "global_prefix_bits": 153, "charged_prefix_bits": 192, "omitted_bridge_shears_rejected": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], "scope": "Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; idle-data hosting follows conditionally from PR442 plus injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.", "seconds": 3.272205875022337}
diff --git a/research/e8-eleven-hosting-selected-validation/python314/exact-assembly.log b/research/e8-eleven-hosting-selected-validation/python314/exact-assembly.log
new file mode 100644
index 0000000000..ee608c69b0
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python314/exact-assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_ELEVEN_STAGE_HOSTING_ASSEMBLY 0.001265848755025708 binding complex gain over #445 0.1966%
diff --git a/research/e8-eleven-hosting-selected-validation/python314/geometry.log b/research/e8-eleven-hosting-selected-validation/python314/geometry.log
new file mode 100644
index 0000000000..e77285823f
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python314/geometry.log
@@ -0,0 +1,5 @@
+compressed geometry 1
+compressed geometry 31
+compressed geometry 61
+compressed geometry 91
+{"status": "PASS_COMPRESSED_ELEVEN_BIT_GEOMETRY", "h": 8, "m": 78, "stages": 11, "word_sha256": "1fb726ea3818fe0837cceb0dd22a71a0814f064e5e781628104610d6468e0e55", "local_window": "U direct_sum E_s, with E_s the first s exterior coordinate 7-blocks", "ambient_form": "I_78/2", "bank_slots": [], "route_checks": 1320, "exact_bit_endpoint_operator_checks": 240, "max_route_factors": 77, "route_denominators": [1, 2, 4], "bad_prime_factors": [2], "missing_route_factor_controls": 120, "bank_free": true, "scope": "All port isometries, stage boundary identities, nested idle ranks, exact bit endpoint operators and coordinate embeddings. No residual banks are used. Full local-word scalar and chronological lowering are checked separately.", "seconds": 1.990845499909483}
diff --git a/research/e8-eleven-hosting-selected-validation/python314/independent-audit.log b/research/e8-eleven-hosting-selected-validation/python314/independent-audit.log
new file mode 100644
index 0000000000..0f828a3424
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python314/independent-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_ELEVEN_STAGE_HOSTING_AUDIT", "template_sha256": "fda4ef5f1fd3559cade37d9c94ac9d790768df22047c2df2652683412466aba9", "emitted_program_sha256": "4ab6c4a1cecef52521cff258e2722f8755e65f5c9f8d87344ee78a1388bc57ec", "emitted_events": 1740288, "profile": {"1": 223960, "2": 93568, "3": 23528, "4": 34296, "5": 9504, "6": 2000, "7": 5112, "8": 792, "49": 8, "56": 440}, "live": 9600, "physical": 9609, "hosted_residuals": 65120, "bank_assignments": 0, "rank_mass": 745536, "deficit": 3264, "maxchild": 56, "geometry_routes": 1320, "halving_depth": 3, "mutations_rejected": ["slot outside window", "copy outside family", "negative slot offset", "wrong residual width", "duplicate helper", "missing helper", "cross-replica host", "cross-replica data", "wrong hosted coordinate", "helper changed to bank", "wrong call orientation", "duplicate call", "dropped final stage", "wrong idle rank", "omitted bridge", "wrong bridge sign", "omitted terminal exchange", "understated live stock", "missing remainder summary", "wrong residual isometry", "omitted local instruction", "wrong reflected copy rank"]}
diff --git a/research/e8-eleven-hosting-selected-validation/python314/parent-full.log b/research/e8-eleven-hosting-selected-validation/python314/parent-full.log
new file mode 100644
index 0000000000..75502053f5
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/python314/parent-full.log
@@ -0,0 +1,72 @@
+RUN parent-full
+PASS parent-full
+RUN kernel-rebuild
+PASS kernel-rebuild
+RUN export-records
+PASS export-records
+RUN bit-global-64
+PASS bit-global-64
+RUN bit-global-audit
+PASS bit-global-audit
+RUN bit-hosting
+PASS bit-hosting
+RUN complex-hosting
+PASS complex-hosting
+RUN independent-hosting-audit
+PASS independent-hosting-audit
+RUN exact-assembly
+PASS exact-assembly
+{
+  "status": "PASS_FULL_HOSTING_SELECTED_KERNEL",
+  "python": "3.14.8",
+  "kappa": "312258824824501/250000000000000000",
+  "kappa_decimal": "0.001249035299298004",
+  "manifest_sha256": "b32a601147fbe042af3799bae4a73d27f7a433e76aa83650ba24566b329c184b",
+  "checks": [
+    {
+      "name": "parent-full",
+      "seconds": 274.75,
+      "log_sha256": "35391ae8f6164bddc0d5fe070bbc68bacb30595536143d37614b4e997ca5bccf"
+    },
+    {
+      "name": "kernel-rebuild",
+      "seconds": 9.94,
+      "log_sha256": "c04d4e939822acd4f0f91c7690293f2b321c9e1fb2de342ce61b997d19e686d9"
+    },
+    {
+      "name": "export-records",
+      "seconds": 0.36,
+      "log_sha256": "76145fe1bd54c65d5f4041e92b2589cb0dede760b5030bbe2042c3e502119594"
+    },
+    {
+      "name": "bit-global-64",
+      "seconds": 20.89,
+      "log_sha256": "37892007ce1ec64720e6b0d20bb34d1030e151892587463dd8c7c6f4915dc4a4"
+    },
+    {
+      "name": "bit-global-audit",
+      "seconds": 13.55,
+      "log_sha256": "3cb0e4fd1dc3dc183bff3e988cc5bf9eed80ae882aa30e02ab14c0331f88dca2"
+    },
+    {
+      "name": "bit-hosting",
+      "seconds": 2.16,
+      "log_sha256": "20295c72cee3f6a3856f68889c5ae1a6874bd5892bef548122cc69842555f933"
+    },
+    {
+      "name": "complex-hosting",
+      "seconds": 0.37,
+      "log_sha256": "3b42f65586cb5c37e06df560fae4dcde1c42526238697a73d103f9895df24fcd"
+    },
+    {
+      "name": "independent-hosting-audit",
+      "seconds": 6.6,
+      "log_sha256": "1359977f74843042c039a81bf2c687cd0b931916b906fe7ca60efd9f745e9c52"
+    },
+    {
+      "name": "exact-assembly",
+      "seconds": 0.22,
+      "log_sha256": "4813c9b302a6b07e1d276c9b939926cf8ebce5197d75703cdb061794827a21b2"
+    }
+  ]
+}
diff --git a/research/e8-eleven-hosting-selected-validation/research/FRAMES.json b/research/e8-eleven-hosting-selected-validation/research/FRAMES.json
new file mode 100644
index 0000000000..aea7b92bab
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/research/FRAMES.json
@@ -0,0 +1,8 @@
+{
+  "status": "SINGLE_FRAME_NOMINATIONS_ONLY",
+  "source_sha256": "ee208ff20bfe04f774eccc3be8d6700d7bf8d84bdd8aa4f03b2e7149b6b53ca6",
+  "tested_gates": 3576,
+  "positive": 0,
+  "best": [],
+  "seconds": 0.05604195594787598
+}
diff --git a/research/e8-eleven-hosting-selected-validation/research/GROUPS.json b/research/e8-eleven-hosting-selected-validation/research/GROUPS.json
new file mode 100644
index 0000000000..1006cc59bb
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/research/GROUPS.json
@@ -0,0 +1,8 @@
+{
+  "status": "EXACT_BOUNDARY_GROUP_NOMINATIONS_ONLY",
+  "source_sha256": "ee208ff20bfe04f774eccc3be8d6700d7bf8d84bdd8aa4f03b2e7149b6b53ca6",
+  "groups_tested": 9278,
+  "positive": 0,
+  "best": [],
+  "seconds": 0.13321614265441895
+}
diff --git a/research/e8-eleven-hosting-selected-validation/research/HOSTING-RESULT.json b/research/e8-eleven-hosting-selected-validation/research/HOSTING-RESULT.json
new file mode 100644
index 0000000000..75eb488e26
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/research/HOSTING-RESULT.json
@@ -0,0 +1,40 @@
+{
+  "status": "PASS_EXACT_HOSTING_REPRICE_SCREEN",
+  "old_profile": {
+    "1": 138384,
+    "2": 56448,
+    "3": 15936,
+    "4": 16128,
+    "5": 32064,
+    "7": 3840,
+    "8": 7488
+  },
+  "new_profile": {
+    "1": 138384,
+    "2": 56448,
+    "3": 15936,
+    "4": 16128,
+    "5": 32064,
+    "7": 3840,
+    "8": 7488
+  },
+  "same_profile": true,
+  "old_live": 8400,
+  "new_live": 8400,
+  "hosted": 34560,
+  "cert": {
+    "lower": "0.001267453159029119461392",
+    "upper": "0.001267453159029119461393",
+    "lower_endpoint_residual_upper": "-1.560392349260697269557963458425144401950988674518821955340796287641640E-24",
+    "upper_endpoint_residual_lower": "1.658001749272704377336676268808635955400703370759321539044253081981942E-24",
+    "strict_rational_signs": true,
+    "moment_minus_one_at_current_k_required_rate": [
+      "-0.001839747154796185709271198752349970490608609234245079438495876559575395",
+      "-0.001839747154796185709271198752349970490608609234245079438495876559501211"
+    ],
+    "nominal_k_ceiling_interval": [
+      "0.001265848755025709048498315842978032572884126495378666492505294890821053",
+      "0.001265848755025709048499313312882895592066167056819089691650101211377309"
+    ]
+  }
+}
diff --git a/research/e8-eleven-hosting-selected-validation/research/MIXED-GROUPS.json b/research/e8-eleven-hosting-selected-validation/research/MIXED-GROUPS.json
new file mode 100644
index 0000000000..c0315657bc
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/research/MIXED-GROUPS.json
@@ -0,0 +1,8 @@
+{
+  "status": "MIXED_GROUP_NOMINATIONS_REQUIRING_PHASE_AND_SCALAR_REPLAY",
+  "source_sha256": "ee208ff20bfe04f774eccc3be8d6700d7bf8d84bdd8aa4f03b2e7149b6b53ca6",
+  "groups_tested": 155055,
+  "positive": 0,
+  "best": [],
+  "seconds": 2.358466148376465
+}
diff --git a/research/e8-eleven-hosting-selected-validation/research/PARTITIONS-SUMMARY.json b/research/e8-eleven-hosting-selected-validation/research/PARTITIONS-SUMMARY.json
new file mode 100644
index 0000000000..c02261bf18
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/research/PARTITIONS-SUMMARY.json
@@ -0,0 +1,8 @@
+{
+  "status": "PARTITION_SCREEN_COMPLETE",
+  "tested": 71,
+  "positive": 0,
+  "best": [],
+  "failures": [],
+  "seconds": 11.959186249994673
+}
diff --git a/research/e8-eleven-hosting-selected-validation/research/REPEATED-PARTITIONS.json b/research/e8-eleven-hosting-selected-validation/research/REPEATED-PARTITIONS.json
new file mode 100644
index 0000000000..36659f854e
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/research/REPEATED-PARTITIONS.json
@@ -0,0 +1,197 @@
+[
+  {
+    "tag": "baseline",
+    "R": 560,
+    "live": 8400,
+    "hosted": 34560,
+    "local_profile": {
+      "1": 1912,
+      "2": 784,
+      "3": 168,
+      "4": 224,
+      "5": 392,
+      "8": 24
+    },
+    "global_profile": {
+      "1": 138384,
+      "2": 56448,
+      "3": 15936,
+      "4": 16128,
+      "5": 32064,
+      "8": 7488,
+      "7": 3840
+    },
+    "cert": {
+      "lower": "0.001267453159029119461392",
+      "upper": "0.001267453159029119461393",
+      "lower_endpoint_residual_upper": "-1.560392349260697269557963458425144401950988674518821955340796287641640E-24",
+      "upper_endpoint_residual_lower": "1.658001749272704377336676268808635955400703370759321539044253081981942E-24",
+      "strict_rational_signs": true,
+      "moment_minus_one_at_current_k_required_rate": [
+        "-0.001839747154796185709271198752349970490608609234245079438495876559575395",
+        "-0.001839747154796185709271198752349970490608609234245079438495876559501211"
+      ],
+      "nominal_k_ceiling_interval": [
+        "0.001265848755025709048498315842978032572884126495378666492505294890821053",
+        "0.001265848755025709048499313312882895592066167056819089691650101211377309"
+      ]
+    },
+    "status": "EXACT_CLEAN_WORD_AND_AGGREGATE_ONLY"
+  },
+  {
+    "tag": "one-repeat",
+    "R": 564,
+    "live": 8436,
+    "hosted": 34560,
+    "local_profile": {
+      "1": 1912,
+      "2": 784,
+      "3": 168,
+      "4": 228,
+      "5": 396,
+      "8": 24
+    },
+    "global_profile": {
+      "1": 138420,
+      "2": 56448,
+      "3": 15936,
+      "4": 16416,
+      "5": 32352,
+      "8": 7488,
+      "7": 3840
+    },
+    "cert": {
+      "lower": "0.001262735056192039022966",
+      "upper": "0.001262735056192039022967",
+      "lower_endpoint_residual_upper": "-1.073645547464586287803425473517020835084694461125894787310608990677155E-24",
+      "upper_endpoint_residual_lower": "2.142958401984943792617846404736515231663919150576370658372673839197819E-24",
+      "strict_rational_signs": true,
+      "moment_minus_one_at_current_k_required_rate": [
+        "-0.001823577818941551852760771358844940767655025172333057881319619554428218",
+        "-0.001823577818941551852760771358844940767655025172333057881319619554354034"
+      ],
+      "nominal_k_ceiling_interval": [
+        "0.001261142567261501898013729794856003324883759049831550126197378335007974",
+        "0.001261142567261501898014727274161349376838894860316937104579560947708714"
+      ]
+    },
+    "status": "EXACT_CLEAN_WORD_AND_AGGREGATE_ONLY"
+  },
+  {
+    "tag": "all-00",
+    "R": 616,
+    "live": 8904,
+    "hosted": 34560,
+    "local_profile": {
+      "1": 1912,
+      "2": 784,
+      "3": 168,
+      "4": 280,
+      "5": 448,
+      "8": 24
+    },
+    "global_profile": {
+      "1": 138888,
+      "2": 56448,
+      "3": 15936,
+      "4": 20160,
+      "5": 36096,
+      "8": 7488,
+      "7": 3840
+    },
+    "cert": {
+      "lower": "0.001204447696176195679627",
+      "upper": "0.001204447696176195679628",
+      "lower_endpoint_residual_upper": "-2.403606883932876983689619393270963208086419656768483802752924165186441E-24",
+      "upper_endpoint_residual_lower": "7.910475981247765152543847224673886090903905529355202063904649293340578E-25",
+      "strict_rational_signs": true,
+      "moment_minus_one_at_current_k_required_rate": [
+        "-0.001625274643365853612538548608311557372941258375298831236705146849890305",
+        "-0.001625274643365853612538548608311557372941258375298831236705146849816120"
+      ],
+      "nominal_k_ceiling_interval": [
+        "0.001202998747106740116645598536019984919664003708157000354387040774405950",
+        "0.001202998747106740116646596131469696691724156878133504187077220465294133"
+      ]
+    },
+    "status": "EXACT_CLEAN_WORD_AND_AGGREGATE_ONLY"
+  },
+  {
+    "tag": "all-11",
+    "R": 616,
+    "live": 8904,
+    "hosted": 34560,
+    "local_profile": {
+      "1": 1912,
+      "2": 784,
+      "3": 168,
+      "4": 280,
+      "5": 448,
+      "8": 24
+    },
+    "global_profile": {
+      "1": 138888,
+      "2": 56448,
+      "3": 15936,
+      "4": 20160,
+      "5": 36096,
+      "8": 7488,
+      "7": 3840
+    },
+    "cert": {
+      "lower": "0.001204447696176195679627",
+      "upper": "0.001204447696176195679628",
+      "lower_endpoint_residual_upper": "-2.403606883932876983689619393270963208086419656768483802752924165186441E-24",
+      "upper_endpoint_residual_lower": "7.910475981247765152543847224673886090903905529355202063904649293340578E-25",
+      "strict_rational_signs": true,
+      "moment_minus_one_at_current_k_required_rate": [
+        "-0.001625274643365853612538548608311557372941258375298831236705146849890305",
+        "-0.001625274643365853612538548608311557372941258375298831236705146849816120"
+      ],
+      "nominal_k_ceiling_interval": [
+        "0.001202998747106740116645598536019984919664003708157000354387040774405950",
+        "0.001202998747106740116646596131469696691724156878133504187077220465294133"
+      ]
+    },
+    "status": "EXACT_CLEAN_WORD_AND_AGGREGATE_ONLY"
+  },
+  {
+    "tag": "all-22",
+    "R": 616,
+    "live": 8904,
+    "hosted": 34560,
+    "local_profile": {
+      "1": 1912,
+      "2": 784,
+      "3": 168,
+      "4": 280,
+      "5": 448,
+      "8": 24
+    },
+    "global_profile": {
+      "1": 138888,
+      "2": 56448,
+      "3": 15936,
+      "4": 20160,
+      "5": 36096,
+      "8": 7488,
+      "7": 3840
+    },
+    "cert": {
+      "lower": "0.001204447696176195679627",
+      "upper": "0.001204447696176195679628",
+      "lower_endpoint_residual_upper": "-2.403606883932876983689619393270963208086419656768483802752924165186441E-24",
+      "upper_endpoint_residual_lower": "7.910475981247765152543847224673886090903905529355202063904649293340578E-25",
+      "strict_rational_signs": true,
+      "moment_minus_one_at_current_k_required_rate": [
+        "-0.001625274643365853612538548608311557372941258375298831236705146849890305",
+        "-0.001625274643365853612538548608311557372941258375298831236705146849816120"
+      ],
+      "nominal_k_ceiling_interval": [
+        "0.001202998747106740116645598536019984919664003708157000354387040774405950",
+        "0.001202998747106740116646596131469696691724156878133504187077220465294133"
+      ]
+    },
+    "status": "EXACT_CLEAN_WORD_AND_AGGREGATE_ONLY"
+  }
+]
diff --git a/research/e8-eleven-hosting-selected-validation/research/SUMMARY.json b/research/e8-eleven-hosting-selected-validation/research/SUMMARY.json
new file mode 100644
index 0000000000..67a7692e19
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/research/SUMMARY.json
@@ -0,0 +1,25 @@
+{
+  "status": "COMPLEX_FRONTIER_SCREEN_COMPLETE",
+  "timestamp": "2026-10-11T14:35:50.696789+00:00",
+  "source_word_sha256": "ee208ff20bfe04f774eccc3be8d6700d7bf8d84bdd8aa4f03b2e7149b6b53ca6",
+  "single_frames": {
+    "tested": 3576,
+    "positive": 0
+  },
+  "same_frame_groups": {
+    "tested": 9278,
+    "positive": 0
+  },
+  "mixed_frame_groups": {
+    "tested": 155055,
+    "positive": 0
+  },
+  "hosting_same_profile": true,
+  "precision_candidate_kappa": "1265848755025709/1000000000000000000",
+  "precision_candidate_decimal": "0.001265848755025709",
+  "precision_scope": "Exact assembly with full certified complex endpoint, not a new supplier or full-wrapper pass",
+  "active_full_runs": {
+    "python311": 95864,
+    "python314": 97171
+  }
+}
diff --git a/research/e8-eleven-hosting-selected-validation/research/frames-initial-boundary-failure.log b/research/e8-eleven-hosting-selected-validation/research/frames-initial-boundary-failure.log
new file mode 100644
index 0000000000..dc802600e7
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/research/frames-initial-boundary-failure.log
@@ -0,0 +1,5 @@
+Traceback (most recent call last):
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/complex447-search/frames.py", line 48, in <module>
+    assert span(lo)<=ss[f]<=span(hi),(part,i)
+           ^^^^^^^^^^^^^^^^^^^^^^^^^
+AssertionError: ('A', 2675)
diff --git a/research/e8-eleven-hosting-selected-validation/research/partitions.log b/research/e8-eleven-hosting-selected-validation/research/partitions.log
new file mode 100644
index 0000000000..90ab613511
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/research/partitions.log
@@ -0,0 +1,72 @@
+baseline CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block0-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block0-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block0-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block0-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block0-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block1-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block1-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block1-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block1-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block1-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block2-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block2-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block2-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block2-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block2-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block3-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block3-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block3-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block3-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block3-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block4-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block4-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block4-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block4-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block4-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block5-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block5-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block5-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block5-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block5-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block6-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block6-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block6-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block6-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block6-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block7-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block7-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block7-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block7-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block7-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block8-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block8-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block8-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block8-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block8-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block9-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block9-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block9-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block9-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block9-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block10-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block10-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block10-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block10-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block10-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block11-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block11-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block11-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block11-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block11-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block12-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block12-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block12-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block12-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block12-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block13-02 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block13-10 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block13-12 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block13-20 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+block13-21 CLEAN_WORD_PASS_NOMINATION_ONLY 0.0
+FINAL 71 0
diff --git a/research/e8-eleven-hosting-selected-validation/research/repeated-partitions.log b/research/e8-eleven-hosting-selected-validation/research/repeated-partitions.log
new file mode 100644
index 0000000000..1de28f3b4c
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/research/repeated-partitions.log
@@ -0,0 +1,5 @@
+baseline 560 8400 0.001267453159029119461392
+one-repeat 564 8436 0.001262735056192039022966
+all-00 616 8904 0.001204447696176195679627
+all-11 616 8904 0.001204447696176195679627
+all-22 616 8904 0.001204447696176195679627
diff --git a/research/e8-eleven-hosting-selected-validation/research/search_complex_output_partitions.py b/research/e8-eleven-hosting-selected-validation/research/search_complex_output_partitions.py
new file mode 100644
index 0000000000..18fda68579
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/research/search_complex_output_partitions.py
@@ -0,0 +1,36 @@
+"""Exact clean-word search over #433 target-pair partition choices.
+Scores the current hosted profile; improvements still need arbitrary-dirt and phase replay.
+"""
+from pathlib import Path
+from collections import Counter
+import os,json,gzip,hashlib,itertools,contextlib,io,time
+r=Path.cwd();assert os.path.ismount('/Volumes/SP AI 01_16') and os.access(r,os.W_OK)
+source=r/'early-reuse-publication/research/split-centres-global/code/complex_construct.py';raw=source.read_text();out=r/'complex447-partitions';out.mkdir(exist_ok=True)
+raw=raw.replace("INPUT=Path('work/complex-network/hamming');OUT=Path('split-centres');OUT.mkdir(exist_ok=True);", "INPUT=INPUT_OVERRIDE;OUT=OUT_OVERRIDE;OUT.mkdir(exist_ok=True);")
+raw=raw.replace('selected=(pi==parity)',"selected=(pi==CHOICES[tuple(c)][parity])")
+code=compile(raw,str(source),'exec');modules=json.loads(gzip.decompress((r/'hosted138-screen/work/complex-network/hamming/PACKET-PROGRAMS.json.gz').read_bytes()));blocks=sorted(tuple(z['receipt']['block']) for z in modules)
+baseline=json.loads((r/'hosted138-screen/split-centres/LOCAL-CHECKS.json').read_text())['forward']['paid_profile'];baseline={int(k):v for k,v in baseline.items()};reference=json.loads((r/'hosted138-screen/complex/HOSTED.json').read_text());paid={int(k):v for k,v in reference['global_profile'].items()};c=.001267453159029119
+import math
+cost=lambda H:sum(k*n*math.expm1(c*math.log(73/k)) for k,n in H.items())
+basecost=cost(paid);results=[];start=time.monotonic()
+configs=[('baseline',{b:(0,1) for b in blocks})]
+for i,b in enumerate(blocks):
+ for x,y in itertools.permutations(range(3),2):
+  if (x,y)==(0,1):continue
+  choices={bb:(0,1) for bb in blocks};choices[b]=(x,y);configs.append((f'block{i}-{x}{y}',choices))
+for tag,choices in configs:
+ d=out/tag
+ try:
+  with contextlib.redirect_stdout(io.StringIO()):exec(code,dict(INPUT_OVERRIDE=(r/'hosted138-screen/work/complex-network/hamming').resolve(),OUT_OVERRIDE=d,CHOICES=choices))
+  report=json.loads((d/'FULL-DISCOVERY.json').read_text());H={int(k):v for k,v in report['local_profile'].items()};assert report['R']==560
+  if tag=='baseline':assert H==baseline
+  P=Counter(paid)
+  for k,n in baseline.items():P[k]-=72*n
+  for k,n in H.items():P[k]+=72*n
+  assert all(n>=0 for n in P.values()) and sum(k*n for k,n in P.items())==73*8400-2496
+  score=cost(P);result=dict(tag=tag,score=score,delta=score-basecost,profile=H,choices=[[list(b),list(xy)] for b,xy in choices.items()],status='CLEAN_WORD_PASS_NOMINATION_ONLY')
+ except Exception as e:result=dict(tag=tag,status='FAIL',error=repr(e))
+ results.append(result);print(tag,result['status'],result.get('delta'),flush=True)
+ (out/'PROGRESS.json').write_text(json.dumps(dict(source_sha256=hashlib.sha256(source.read_bytes()).hexdigest(),reference_cost=basecost,results=results),indent=2)+'\n')
+positives=[x for x in results if x.get('delta',0)<-1e-12]
+(out/'SUMMARY.json').write_text(json.dumps(dict(status='PARTITION_SCREEN_COMPLETE',tested=len(results),positive=len(positives),best=sorted(positives,key=lambda x:x['delta']),failures=[x for x in results if x['status']=='FAIL'],seconds=time.monotonic()-start),indent=2)+'\n');print('FINAL',len(results),len(positives),flush=True)
diff --git a/research/e8-eleven-hosting-selected-validation/research/search_complex_same_partitions.py b/research/e8-eleven-hosting-selected-validation/research/search_complex_same_partitions.py
new file mode 100644
index 0000000000..f0a0599ded
--- /dev/null
+++ b/research/e8-eleven-hosting-selected-validation/research/search_complex_same_partitions.py
@@ -0,0 +1,33 @@
+"""Allow repeated target partitions and price extra helpers under hosting; nomination only."""
+from pathlib import Path
+import json,gzip,contextlib,io,math,sys,time
+from collections import Counter
+r=Path.cwd();out=r/'complex447-same-partitions';out.mkdir(exist_ok=True)
+s=(r/'early-reuse-publication/research/split-centres-global/code/complex_construct.py').read_text().replace("INPUT=Path('work/complex-network/hamming');OUT=Path('split-centres');OUT.mkdir(exist_ok=True);", "INPUT=INPUT_OVERRIDE;OUT=OUT_OVERRIDE;OUT.mkdir(exist_ok=True);").replace('selected=(pi==parity)',"selected=(pi==CHOICES[tuple(c)][parity])").replace('assert len(cur)-240==560,(len(cur)-240)','assert len(cur)>240')
+code=compile(s,'complex_construct_variable_partitions','exec');inp=(r/'hosted138-screen/work/complex-network/hamming').resolve();modules=json.loads(gzip.decompress((inp/'PACKET-PROGRAMS.json.gz').read_bytes()));blocks=sorted(tuple(z['receipt']['block']) for z in modules)
+sys.path.insert(0,str(r/'complex447-search'));import hosting_core as HC
+sys.path.insert(0,str(r/'source443-review/code/engines'));import moment as M
+c=.001267453159029119;HC.cost=lambda rank,m:rank*math.expm1(c*math.log(m/rank))/c if rank else 0.
+t=json.loads(gzip.decompress((r/'hosted138-screen/split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes()));ranks={z['child']:z['rank'] for z in t['idle_children']};pairs={e['stage']:e['pair'] for e in t['recipe'] if e['kind']=='local'};sched=[]
+for e in t['execution_schedule']:
+ if e['kind']=='local_cover_sweep':sched.append(dict(kind='local',stage=e['stage'],pair=pairs[e['stage']]))
+ elif e['kind']=='bridge':sched.append(dict(kind='bridge',dst=e['dst'],src=e['src']))
+ elif e['kind']=='idle_cover_sweep':
+  for ch in e['child_indices']:
+   if ch in ranks:sched.append(dict(kind='idle',pair=e['pair'],rank=ranks[ch],idx=ch))
+win={k:x for k,x in HC.windows(sched).items() if x[1]>=9 and x[2]};cache={};results=[]
+configs=[('baseline',{b:(0,1) for b in blocks}),('one-repeat',{b:((0,0) if b==blocks[0] else (0,1)) for b in blocks})]+[(f'all-{x}{x}',{b:(x,x) for b in blocks}) for x in range(3)]
+for tag,choices in configs:
+ d=out/tag
+ with contextlib.redirect_stdout(io.StringIO()):exec(code,dict(INPUT_OVERRIDE=inp,OUT_OVERRIDE=d,CHOICES=choices))
+ a=json.loads((d/'FULL-DISCOVERY.json').read_text());R=a['R'];H={int(k):v for k,v in a['local_profile'].items()}
+ if R not in cache:
+  ys,zs,val=HC.solve(win,120,{(s,9):R for s in range(9)},73,pad_value=HC.cost(1,73)/8);slots,rem=HC.expand(win,ys,zs,{s:[(h,9) for h in range(R)] for s in range(9)},120);cache[R]=(ys,zs,val,slots,rem)
+ ys,zs,val,slots,rem=cache[R];unhosted=9*R-len(slots);W=7680+unhosted;P=Counter({k:n*72 for k,n in H.items()});P[1]+=unhosted
+ for it in t['idle_children']:
+  rr=rem.get((it['child'],it['port']),it['rank'])
+  if rr:P[rr]+=8
+ assert 73*W-sum(k*n for k,n in P.items())==2496
+ cert=M.certify(P,73,W,True);res=dict(tag=tag,R=R,live=W,hosted=len(slots)*8,local_profile=H,global_profile=dict(P),cert=cert,status='EXACT_CLEAN_WORD_AND_AGGREGATE_ONLY')
+ (d/'HOSTED-PRICE.json').write_text(json.dumps(res,indent=2)+'\n');HC.save_selection(d/'HOSTING-SELECTION.json','complex',ys,zs,val);results.append(res);print(tag,R,W,cert['lower'],flush=True)
+(out/'SUMMARY.json').write_text(json.dumps(results,indent=2)+'\n')
diff --git a/research/e8-eleven-hosting-selected/AUDIT.json b/research/e8-eleven-hosting-selected/AUDIT.json
new file mode 100644
index 0000000000..4627979822
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/AUDIT.json
@@ -0,0 +1,51 @@
+{
+  "status": "PASS_INDEPENDENT_ELEVEN_STAGE_HOSTING_AUDIT",
+  "template_sha256": "8d3580817dc305ec62d4a9bc2f3ceec6f571be1da91db464a9050b47e9036bbe",
+  "emitted_program_sha256": "4ab6c4a1cecef52521cff258e2722f8755e65f5c9f8d87344ee78a1388bc57ec",
+  "emitted_events": 1740288,
+  "profile": {
+    "1": 223960,
+    "2": 93568,
+    "3": 23528,
+    "4": 34296,
+    "5": 9504,
+    "6": 2000,
+    "7": 5112,
+    "8": 792,
+    "49": 8,
+    "56": 440
+  },
+  "live": 9600,
+  "physical": 9609,
+  "hosted_residuals": 65120,
+  "bank_assignments": 0,
+  "rank_mass": 745536,
+  "deficit": 3264,
+  "maxchild": 56,
+  "geometry_routes": 1320,
+  "halving_depth": 3,
+  "mutations_rejected": [
+    "slot outside window",
+    "copy outside family",
+    "negative slot offset",
+    "wrong residual width",
+    "duplicate helper",
+    "missing helper",
+    "cross-replica host",
+    "cross-replica data",
+    "wrong hosted coordinate",
+    "helper changed to bank",
+    "wrong call orientation",
+    "duplicate call",
+    "dropped final stage",
+    "wrong idle rank",
+    "omitted bridge",
+    "wrong bridge sign",
+    "omitted terminal exchange",
+    "understated live stock",
+    "missing remainder summary",
+    "wrong residual isometry",
+    "omitted local instruction",
+    "wrong reflected copy rank"
+  ]
+}
diff --git a/research/e8-eleven-hosting-selected/CERTIFICATE.json b/research/e8-eleven-hosting-selected/CERTIFICATE.json
new file mode 100644
index 0000000000..d1d30c76f2
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/CERTIFICATE.json
@@ -0,0 +1,154 @@
+{
+  "status": "PASS_CONDITIONAL_ELEVEN_STAGE_HOSTING_ASSEMBLY",
+  "kappa": "1265848755025709/1000000000000000000",
+  "kappa_decimal": "0.001265848755025709",
+  "bit_lower": "1267514693114214441041/1000000000000000000000000",
+  "complex_lower": "79215822439319966337/62500000000000000000000",
+  "binding_component": "complex",
+  "gain_over_pr445_percent": 0.19656151080425197,
+  "bit": {
+    "live": 9600,
+    "physical": 9609,
+    "maxchild": 56,
+    "rank_mass": 745536,
+    "hosted_residuals": 65120,
+    "prefix_bits": 153,
+    "charged_prefix_bits": 192,
+    "coefficient_bits": 153,
+    "three_level_coefficient_bits": 514,
+    "charged_three_level_coefficient_bits": 1024,
+    "row_coefficient": 19431
+  },
+  "complex": {
+    "live": 8400,
+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
+  },
+  "strict_outer_constraints": {
+    "bit_positive": "4721630957086084243016630892729619412794522938894421719114608588019406415676289654518536543712476039477685177526932922689268369962070727619992859322184404727257879456878020964682741220072360294059935536891135637625523295955093071402198116561532831993561153303849754778784168608924033/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "23705571408295771212205477061105578280885391411980593584323710345481463456287523960522314822473067077310731630037929272380007140677815595272742120543121979035317258779927639705940064463108864362374476704044906928597801883438467168006438846696150245221215831391075967/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "1873909177560680033663/62500000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "18983940451209686945483274760080187655885391411980593584323710345481463456287523960522314822473067077310731630037929272380007140677815595272742120543121979035317258779927639705940064463108864362374476704044906928597801883438467168006438846696150245221215831391075967/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_positive": "2360815478543042116786684489278725463380630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_internal": "4721630957086084243016630892729619412794522938894421719114608588019406415676289654518536543712476039477685177526932922689268369962070727619992859322184404727257879456878020964682741220072360294059935536891135637625523295955093071402198116561532831993561153303849754778784168608924033/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_leaf": "14213601182690927715758268272769713240737218644884718511276463760760138143820051634779693954949009578133050992545897558879271940300978525256363919593745394244916508846841840817652773451626792475247173888913589101924424237674326655405417539909607954604169068999387738278784168608924033/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_positive": "2360815478543042582447971797017983275880630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_below_one": "1860284333752413988667552028202982016724119369423282408553237218644884718511276463760760138143820051634779693954949009578133050992545897558879271940300978525256363919593745394244916508846841840817652773451626792475247173888913589101924424237674326655405417539909607954604169068999387738278784168608924033/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_reservations": "1/4000000000000000000",
+    "lambda_above_tau": "4721630957086084243016630892729619412794522938894421719114608588019406415676289654518536543712476039477685177526932922689268369962070727619992859322184404727257879456878020964682741220072360294059935536891135637625523295955093071402198116561532831993561153303849754778784168608924033/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_sigma": "28427202365381855455222107953835197693679914350875015303438318933500869871963813615040851366185543116788416807564862195069275510639886322892734979865306383762575138236805660670622805683181224656434412240936042566223325179393560239408636963257683077214776984694925721778784168608924033/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_internal": "4721630957086084243016630892729619412794522938894421719114608588019406415676289654518536543712476039477685177526932922689268369962070727619992859322184404727257879456878020964682741220072360294059935536891135637625523295955093071402198116561532831993561153303849754778784168608924033/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_prime_above_lambda": "4721630957086084243016630892729619412794522938894421719114608588019406415676289654518536543712476039477685177526932922689268369962070727619992859322184404727257879456878020964682741220072360294059935536891135637625523295955093071402198116561532831993561153303849754778784168608924033/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_leaf": "14213601182690927715758268272769713240737218644884718511276463760760138143820051634779693954949009578133050992545897558879271940300978525256363919593745394244916508846841840817652773451626792475247173888913589101924424237674326655405417539909607954604169068999387738278784168608924033/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_reservations": "1/4000000000000000000",
+    "lambda_prime_below_one": "2360815478543042116786684489278725463380630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967/1862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "epsilon_positive": "1862645149230957029387354850769042968750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/1865005964709500073366786684489278725463380630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967",
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+    "guard_width": "2360815478543043979431833720235756713380630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967/1865005964709500073366786684489278725463380630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967",
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+    "delta_positive": "1/8000000000000000000",
+    "delta_below_one_eighth": "999999999999999999/8000000000000000000",
+    "short_record_fallback": "6930088034009105798023708111692435196955552149556253087199349785849940897995706471261027431127870643844901693342737108275707705529890700781595392029635126865598362396597221833222723881261204310103651595840452469696915125094496475730783791137376889176850664727186651522474760850996412111715602190635734754931595221464414975629304939800383351588309136278042132832541676673833437286281560604216841697310719529148078209597162801376835112883596447585736198489405068437778599041298850219217355636138681012465311021017103961697858164136050772408162805440755664741613275556876236701007565964985089/6947688626905903493489275442396397610989885891142180530156056513470095699611021340784579000831320689489023037422638350806634683189742648754718631728362372050969437064253742269259257209126495417886775830940802423375669219013625423975570409604630147459337795004585355689361061643811360976551532117244139190763235092163085937500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+    "literal_scalar_guard": "1",
+    "row_product_gap": "23971789/25",
+    "balanced_prefix_above_kappa": "1936541361599938238709033288540658000499011801206998066772423702345580429101509756370917767105050622202881799589364612402433960287760299129937426782586605084328184238481301522970754103950554827387884928987678706802736338442313246590109517091167525603317238251045319564368073201433186692831253395742964397/1865005964709500073366786684489278725463380630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967000000000000000000",
+    "coordinate_movement_above_kappa": "5976870668718423800856356596806912794522938894421719114608588019406415676289654518536543712476039477685177526932922689268369962070727619992859322184404727257879456878020964682741220072360294059935536891135637625523295955093071402198116561532831993561153303849754778784168608924033/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_phase_layer_above_kappa": "7153539689043816534224660405137927503563117063028047532566092099046514761278622013167790524887067383766149354431362198056701128030619668881669872288758360958454815807504691721567061279739666820553770243930549927798351233122683569203394132884185225872265579095492751897224227043257443111003756435188843/186500596470950007336678668448927872546338063057671759144676278135511528148872353623923986185617994836522030604505099042186694900745410244112072805969902147474363608040625460575508349115315815918234722654837320752475282611108641089807557576232567334459458246009039204539583093100061226172121583139107596700000000000000000",
+    "bulk_exposure_above_kappa": "5976870668718423800856356596806912794522938894421719114608588019406415676289654518536543712476039477685177526932922689268369962070727619992859322184404727257879456878020964682741220072360294059935536891135637625523295955093071402198116561532831993561153303849754778784168608924033/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "Gaussian_arithmetic_above_kappa": "6167301069252005542838332885878870376675191256772396576945575711989067025368460369771142827559505235796952866489661947110136937264811880833895773962197733300907293505819139154990615375838647823191343299159563616798126576983073918230498257917711838103564993707910596287965430956462432234043948008988335341/14920047717676000586934293475914229803707045044613740731574102250840922251909788289913918894849439586921762448360407923374935592059632819528965824477592171797949088643250036846040667929225265273458777812386985660198022608888691287184604606098605386756756659680723136363166647448004898093769726651128607736000000000000000000",
+    "scalar_work_above_kappa": "13627324928090005836305479623835985278528713779079266942732626837409528151323354514728102274984225029257834090669865908797604733294628290598378686200993819199881837827444157578010949340451280459920732205353056446897137881427419561822800560967014531481943323548272164469548754680464881280928811334552639209/14920047717676000586934293475914229803707045044613740731574102250840922251909788289913918894849439586921762448360407923374935592059632819528965824477592171797949088643250036846040667929225265273458777812386985660198022608888691287184604606098605386756756659680723136363166647448004898093769726651128607736000000000000000000",
+    "dimension_above_kappa": "1860284333752413987344464378648745450745652657963940409052249019851882785283700166106340567245329808005697461059999631781014850581910509961313232228061277655193790702180350478573100747328143363788406877402181619863132102876592295904660762679987573245514934631077133557921407320044707302646857370042110725831253395742964397/1865005964709500073366786684489278725463380630576717591446762781355115281488723536239239861856179948365220306045050990421866949007454102441120728059699021474743636080406254605755083491153158159182347226548373207524752826111086410898075575762325673344594582460090392045395830931000612261721215831391075967000000000000000000"
+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "6084731986648243566095196451386160927799499851857157302451725850342813197569/3906250000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "14836780197380"
+    },
+    {
+      "gap": "482007048645177890006028469670812911168993343898915952762061335116135880346291986119085127031870806916107589765247/244140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "9235827787851545884"
+    },
+    {
+      "gap": "38182584779977073239836692054683233293135163201113383270550675434201115625418946664378777838616516927722383093357333882798661663919669805727482227509761/15258789062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "5749260539824950511327760"
+    },
+    {
+      "gap": "3024664856204944855019991806475746930649809456135947463826689575195074874654190665711231803441232234678309970305204565316873845088735151893940148902472642089913451052766544313604022141084543/953674316406250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "3578888380559265369049383003892"
+    },
+    {
+      "gap": "239601314187582169723952440922470383041161064239717289659446974659654573306683437230015831614583925826622244259104097470050221021571687376437109446835536878765763871633353099724503711287858088742345989062661383654089904568971009/59604644775390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "2227841641856102698350997063607860703"
+    },
+    {
+      "gap": "18980215160911225031420774760080187655885391411980593584323710345481463456287523960522314822473067077310731630037929272380007140677815595272742120543121979035317258779927639705940064463108864362374476704044906928597801883438467168006438846696150245221215831391075967/3725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1386821228666677298327686419515294231005143"
+    }
+  ],
+  "bit_template_sha256": "fda4ef5f1fd3559cade37d9c94ac9d790768df22047c2df2652683412466aba9",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f",
+  "emitted_program_sha256": "4ab6c4a1cecef52521cff258e2722f8755e65f5c9f8d87344ee78a1388bc57ec",
+  "bank_assignments": 0,
+  "bit_profile": {
+    "1": 223960,
+    "2": 93568,
+    "3": 23528,
+    "4": 34296,
+    "5": 9504,
+    "6": 2000,
+    "7": 5112,
+    "8": 792,
+    "49": 8,
+    "56": 440
+  },
+  "parent_kappa": "315841366195289/250000000000000000",
+  "additional_interface": "PR442 idle-data hosting during untouched windows",
+  "row_bound": {
+    "method": "successive nonzero-norm vectors in nondegenerate complements",
+    "minimum_q": 3,
+    "column_exponent": 3003,
+    "factor_two_power": 78,
+    "cover_exponent": 3081,
+    "physical_families": 9609,
+    "physical_exponent": 9,
+    "stock_exponent": 3090,
+    "halving_depth": 3,
+    "complete_row_coefficient": 19431,
+    "retained_row_coefficient": 20161
+  },
+  "row_controls": [
+    "false two-level halving",
+    "understated row reserve"
+  ],
+  "halving_depth": 3,
+  "finite_controls": [
+    "old 128-bit prefix charge insufficient",
+    "old 512-bit composite charge insufficient"
+  ]
+}
diff --git a/research/e8-eleven-hosting-selected/EXPECTED.json b/research/e8-eleven-hosting-selected/EXPECTED.json
new file mode 100644
index 0000000000..346f07f860
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/EXPECTED.json
@@ -0,0 +1,58 @@
+{
+  "kappa": "1265848755025709/1000000000000000000",
+  "kappa_decimal": "0.001265848755025709",
+  "bit_lower": "1267514693114214441041/1000000000000000000000000",
+  "complex_lower": "79215822439319966337/62500000000000000000000",
+  "binding_component": "complex",
+  "bit_profile": {
+    "1": 223960,
+    "2": 93568,
+    "3": 23528,
+    "4": 34296,
+    "5": 9504,
+    "6": 2000,
+    "7": 5112,
+    "8": 792,
+    "49": 8,
+    "56": 440
+  },
+  "bit": {
+    "live": 9600,
+    "physical": 9609,
+    "maxchild": 56,
+    "rank_mass": 745536,
+    "hosted_residuals": 65120,
+    "prefix_bits": 153,
+    "charged_prefix_bits": 192,
+    "coefficient_bits": 153,
+    "three_level_coefficient_bits": 514,
+    "charged_three_level_coefficient_bits": 1024,
+    "row_coefficient": 19431
+  },
+  "complex": {
+    "live": 8400,
+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
+  },
+  "row_bound": {
+    "method": "successive nonzero-norm vectors in nondegenerate complements",
+    "minimum_q": 3,
+    "column_exponent": 3003,
+    "factor_two_power": 78,
+    "cover_exponent": 3081,
+    "physical_families": 9609,
+    "physical_exponent": 9,
+    "stock_exponent": 3090,
+    "halving_depth": 3,
+    "complete_row_coefficient": 19431,
+    "retained_row_coefficient": 20161
+  },
+  "halving_depth": 3,
+  "bank_assignments": 0
+}
diff --git a/research/e8-eleven-hosting-selected/GLOBAL.json b/research/e8-eleven-hosting-selected/GLOBAL.json
new file mode 100644
index 0000000000..bb475726c3
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/GLOBAL.json
@@ -0,0 +1,184 @@
+{
+  "status": "PASS_SOURCE_BOUND_ELEVEN_STAGE_HOSTED_BIT_TEMPLATE",
+  "h": 8,
+  "m": 78,
+  "v": 120,
+  "R": 740,
+  "replicas": 8,
+  "live": 9600,
+  "physical": 9609,
+  "word_sha256": "ee4cda817d5220fdbba1d116556e3dacb3da553ed81af43e74f19365e1393a5c",
+  "source_records_sha256": "f9e0f3cdbc6a4eb5bfaf3fd843731a79c26740a6c4715079f2228e94b8706403",
+  "local_checks": {
+    "forward": {
+      "copies": 9,
+      "adds": 15446,
+      "records": 19776,
+      "all_columns": 980,
+      "cancellation_free_row_l1": 780,
+      "profile": {
+        "1": 2545,
+        "2": 1022,
+        "3": 266,
+        "4": 357,
+        "5": 108,
+        "7": 14,
+        "8": 9
+      },
+      "sha256": "975c00710ab47e3dd7eec27827a4152a584066032ec379a6222c3b40400162f1"
+    },
+    "reverse": {
+      "copies": 9,
+      "adds": 15446,
+      "records": 19776,
+      "all_columns": 980,
+      "cancellation_free_row_l1": 18238,
+      "profile": {
+        "1": 2545,
+        "2": 1022,
+        "3": 266,
+        "4": 357,
+        "5": 108,
+        "7": 14,
+        "8": 9
+      },
+      "sha256": "615a5a33a8240555011a5a248a08ba028334daea98f78b79973ce4315020fbac"
+    }
+  },
+  "scalar_stages": [
+    {
+      "stage": 0,
+      "all_columns": 9340,
+      "helper_columns": 8140,
+      "reverse": false
+    },
+    {
+      "stage": 1,
+      "all_columns": 9340,
+      "helper_columns": 8140,
+      "reverse": true
+    },
+    {
+      "stage": 2,
+      "all_columns": 9340,
+      "helper_columns": 8140,
+      "reverse": false
+    },
+    {
+      "stage": 3,
+      "all_columns": 9340,
+      "helper_columns": 8140,
+      "reverse": true
+    },
+    {
+      "stage": 4,
+      "all_columns": 9340,
+      "helper_columns": 8140,
+      "reverse": false
+    },
+    {
+      "stage": 5,
+      "all_columns": 9340,
+      "helper_columns": 8140,
+      "reverse": true
+    },
+    {
+      "stage": 6,
+      "all_columns": 9340,
+      "helper_columns": 8140,
+      "reverse": false
+    },
+    {
+      "stage": 7,
+      "all_columns": 9340,
+      "helper_columns": 8140,
+      "reverse": true
+    },
+    {
+      "stage": 8,
+      "all_columns": 9340,
+      "helper_columns": 8140,
+      "reverse": false
+    },
+    {
+      "stage": 9,
+      "all_columns": 9340,
+      "helper_columns": 8140,
+      "reverse": true
+    },
+    {
+      "stage": 10,
+      "all_columns": 9340,
+      "helper_columns": 8140,
+      "reverse": false
+    }
+  ],
+  "independent_unbanked_scalar_columns": 9340,
+  "all_scalar_columns_restored": true,
+  "geometry_sha256": "49bc07c36f27dc960c8c14e15b4eec75251dc845209809bc3ef677c8a271a7bc",
+  "template_sha256": "8d3580817dc305ec62d4a9bc2f3ceec6f571be1da91db464a9050b47e9036bbe",
+  "emitted_program_sha256": "4ab6c4a1cecef52521cff258e2722f8755e65f5c9f8d87344ee78a1388bc57ec",
+  "emitted_events": 1740288,
+  "local_invocations": 88,
+  "bank_assignments": 0,
+  "hosted_residuals": 65120,
+  "banks_per_stage": 0,
+  "entrance_rank_total": 147,
+  "residual_bank_slots": false,
+  "padding_calls": 0,
+  "profile": {
+    "1": 223960,
+    "2": 93568,
+    "3": 23528,
+    "4": 34296,
+    "5": 9504,
+    "6": 2000,
+    "7": 5112,
+    "8": 792,
+    "49": 8,
+    "56": 440
+  },
+  "paid_calls": 393208,
+  "rank_mass": 745536,
+  "deficit": 3264,
+  "maxchild": 56,
+  "halving_depth": 3,
+  "halving_integer_inequality": [
+    474552,
+    351232
+  ],
+  "local_additions": 15446,
+  "bridge_additions": 23040,
+  "copy_erase_episodes": 792,
+  "global_prefix_bound": "7623836413012276914350637325689921994752000000",
+  "global_prefix_bits": 153,
+  "charged_prefix_bits": 192,
+  "omitted_bridge_shears_rejected": [
+    0,
+    1,
+    2,
+    3,
+    4,
+    5,
+    6,
+    7,
+    8,
+    9,
+    10,
+    11,
+    12,
+    13,
+    14,
+    15,
+    16,
+    17,
+    18,
+    19,
+    20,
+    21,
+    22,
+    23
+  ],
+  "scope": "Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; idle-data hosting follows conditionally from PR442 plus injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.",
+  "seconds": 3.2126199159538373
+}
diff --git a/research/e8-eleven-hosting-selected/INHERITED-HOSTING-PROOF.md b/research/e8-eleven-hosting-selected/INHERITED-HOSTING-PROOF.md
new file mode 100644
index 0000000000..ff3eba6770
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/INHERITED-HOSTING-PROOF.md
@@ -0,0 +1,109 @@
+# Idle-axis hosting: helper residuals on pending idle coordinates
+
+This package changes only the global nine-stage templates of #434's two suppliers. Both local words are unchanged:
+
+- the complex word is #433's split-centre word, R = 560, m = 73;
+- the bit word is #434's early-reset kernel word, R = 747, m = 64.
+
+So are their local programs, scalar replays, data routes, bridges, terminal exchange and cover correction. What
+changes is where whole dirty-helper residuals live. Many of them move from bank streams onto coordinates of *idle*
+data families that would otherwise be advanced later by an idle child.
+
+## 1. The two inherited facts used
+
+**(a) Dirty invocations act on a helper stream as its residual.** The complete dirty local invocation is block
+diagonal on helpers at its endpoint and admits arbitrary correlated helper values (#425/#433, #386/#434). On the
+physical stream that owns a helper residual of width w, it acts as an exact coordinate factor on w coordinates:
+
+- complex: P_g C_block P_g⁻¹ (PR425-COMPLEX §5, INHERITED-COMPLEX-GEOMETRY);
+- bit: D_P with P the width-w coordinate projector (PR386-BIT-GEOMETRY; mixed widths 8 − entrance rank, #434).
+
+This holds whatever the stream held before. Banks rely on exactly this: eight sequential residuals and a pad tile a
+bank stream.
+
+**(b) An idle child is a product of coordinate factors.** Advancing a data pair from level a to level b applies, on
+every physical data stream (F, g) of that pair, the commuting product of coordinate factors on its pending set S:
+
+- complex: C over S, in the basis U_q ⊕ I used by the inherited idle factorisation;
+- bit: D_{P_V−P_U}, an orthogonal coordinate projector difference.
+
+Factors on disjoint coordinate sets commute and multiply:
+
+- complex: C_{S'}·C_{S∖S'} = C_S;
+- bit: D_{P'}·D_{P−P'} = D_P for P' ≤ P (the parent's identity D_I·D_P = D_{I−P}).
+
+## 2. Hosting lemma
+
+Fix a data family F (replica r, pair j, side, port) and an idle child Γ that advances pair j at recipe position τ.
+Let λ be the position of the last local invocation or bridge that names pair j before τ; idle children do not
+count as touches, since they act on other coordinates or on the other member. Let ι be any local invocation with
+λ < ι < τ. Then:
+
+1. ι is an invocation on another pair, and nothing touches F between ι and τ.
+2. A helper residual of ι, of width w, may be owned by stream (F, d·σ⁻¹) instead of a bank slot. Here d is the
+   invocation's cover class, and σ is a coordinate isometry carrying the local residual block onto a set S' ⊂ S of
+   w pending coordinates. When S' meets the local block of a level −1 advance, σ is composed with U_q ⊕ I.
+3. Γ is replaced by Γ' acting on S ∖ ⋃S' over all hosted residuals of F, which have pairwise disjoint S'.
+
+The complete program's operator is unchanged:
+
+- By (a), ι applies exactly the factor on S' to (F, d·σ⁻¹), for any prior contents.
+- Nothing else acts on F between ι and τ, so this factor may be moved to τ.
+- By (b), the moved factors times Γ' equal Γ.
+
+Distinct slots of one invocation have distinct σ, so distinct physical classes for every d. They are also disjoint
+from the invocation's own data owners, because pair j is not active, and from bank owners, because the families
+differ. Residuals of different invocations on F occupy disjoint coordinates. They are sequential, exactly as the
+parent's banks are co-owned sequentially by different cover classes.
+
+Two further points:
+
+- **Phases.** The stored Z₄ translations after Γ remain valid, because Γ'·∏(hosted factors) = Γ as exact operators.
+  The final X_δ(g) correction still applies to every live family; hosting changes no data endpoint.
+- **Reflection.** The inverse-transpose program reverses chronology and reflects each factor. The window condition
+  (no touch strictly between ι and τ) is symmetric, so hosting commutes with reflection.
+
+## 3. What is checked here
+
+- `bit_hosted.py` and `complex_hosted.py` read #434's freshly regenerated templates and compute windows from each
+  recipe. They apply a frozen integer-programme selection (`SELECTION.json`; `--discover` recomputes it with scipy)
+  and emit new owners, remainder children and banks.
+  - Bit: unhosted residuals keep an exact width-64 tiling with no padding.
+  - Complex: eight per bank plus one paid pad; a final partial bank pays the larger pad.
+- `audit.py` shares no code with the generators. It re-derives every window from the template schedule. For every
+  replica and invocation it checks that:
+  - each helper has exactly one owner;
+  - each hosted slot is inside its child's pending set, disjoint from other slots, outside the active pair, and in
+    window;
+  - every remainder child is exact, and the bank tiling is exact.
+
+  It also recomputes the paid profile and the rank deficit 2496, and rejects nine mutations.
+- `assemble.py` prices both suppliers with the two inherited rational moment engines and recomputes both finite
+  invoices with the hosted stock. Route charging is conservative: two extra route factors per helper selector, and
+  the parent's larger complex per-vertex bill is kept. It then runs #434's strict outer assembly: six bootstrap
+  levels and 47 inequalities. The next grid point and the zero-η, zero-β and unit-β controls are rejected.
+
+## 4. Result
+
+| | live stock | max child | hosted residuals | certified saving |
+| --- | ---: | ---: | ---: | --- |
+| bit | 14,259 → 9,457 | 42 → 8 | 39,568 of 53,784 | c = 1239085165241180038597/10²⁴ |
+| complex | 12,720 → 8,400 | 48 → 8 | 34,560 of 40,320 | b = 1267453159029119/10¹⁸ |
+
+κ = 618775866623647/(5·10¹⁷) ≈ 1.237551733247294·10⁻³, bit-bound, +9.218% over #434.
+
+## 5. Scope
+
+This is a written finite extension of the inherited correlated dirty-bank and compressed-window interfaces. The
+streams that own residuals now include data streams during idle windows. It is the principal new review point.
+
+All other interfaces remain inherited assumptions: the all-size compiler, restored-work, tape/common-grid, precision
+and analytic interfaces.
+
+No Lean proof and no unconditional integer-multiplication theorem is claimed. The global operator identity is argued
+from (a) and (b) and checked combinatorially. It is not replayed numerically on the 2⁷³- and 2⁶⁴-point address
+spaces; neither parent does that either.
+
+## R740 composition and additional scope
+
+The above argument is inherited from PR442 and remains an explicit additional hosting assumption. Here the bit local word has R740 and matches PR441 after two joint B-frame sweeps. The assignment is regenerated for its actual residual-width census, rather than transferred by helper index. Parent residual isometries remain checked, and the finite selector invoice retains the parent extra-helper-route bound of 144 in addition to the two hosting factors. All host windows, owners, disjoint intervals, remainders and bank coverage are independently rechecked. Original PR442 numerical values above describe its historical R747 construction; EXPECTED.json and CERTIFICATE.json describe this R740 composition.
diff --git a/research/e8-eleven-hosting-selected/LICENSE b/research/e8-eleven-hosting-selected/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/e8-eleven-hosting-selected/MANIFEST.json b/research/e8-eleven-hosting-selected/MANIFEST.json
new file mode 100644
index 0000000000..9df17d56c4
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/MANIFEST.json
@@ -0,0 +1,54 @@
+{
+  "AUDIT.json": "268269736a1427572a01ac660888af19d12194bdfa3f6c9b5311752f77c1cbc8",
+  "CERTIFICATE.json": "69f4ea305f053500fe127ad73a72b32bac5ad10cc7faf05122d2ee4a92e4a2fa",
+  "EXPECTED.json": "eb56fd0d039fe58a25dc61bc664e15b4401cbcb47ba7650adec13f78c9e94022",
+  "GLOBAL.json": "64f0863ce8897335ebfb0e78a5a356a0ca9f3ebf07b7a54b5332403d1ca93bdc",
+  "INHERITED-HOSTING-PROOF.md": "4f06d1dead63c62b076f0a6c1521c68c0b0544aa2c5df5e74a408fdfc34f91c4",
+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "NOTICE.md": "28662fdf0a5dc6adaa13e491e2a7023ec9846bcb83ab183f8da393555fa96dab",
+  "PROOF.md": "2de7aac6f650c3ed818fc512034d909eeb0aae7105efcb5b92c71c2a60514bca",
+  "README.md": "9b4184c204a44d1bf4fb05bafab2c1f8d4170c81cd746244339b3f17ae010570",
+  "SOURCE.json": "470735692afc6deeba3ff5992a26282d92a485c34848bc00bf4cc7009230aebb",
+  "VALIDATION.json": "e67ce1a2c0daa97002e0fb27cbd2de4100fdf36b2140f477e0f39a0f3aa8b879",
+  "code/assemble.py": "7f5b02e2f48c0b5e1ae8dc12fd953b2bb262287277910115bee5fffae4a73817",
+  "code/audit.py": "9900a1b2f1f314f2b93ca8f99b5516ed2e1a7295d668ea51df2df89cef84e381",
+  "code/bank_routes.py": "7c6997c455bd55acca3a1603797c34e7733d557c27a7694a1429ff15773a505d",
+  "code/e8core.py": "1cb286196c1530d06f50f0997febc5993b388f33464e295611b920ba30a24eeb",
+  "code/emit.py": "515d7021293e23aba1165ee270e17c375072e7128ed7b3c738768b6f6b7e9af8",
+  "code/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+  "code/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+  "code/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+  "code/geometry.py": "9554182d67e434ea84b4430f909a2c400abc755d8487b51454a8e6968e62859d",
+  "code/hosting_core.py": "d8b90cd5d152df3c7c351230863d9e61816ad5e1f21d69bea1a86a5daad559a3",
+  "code/row_bound.py": "de4a9b9cd797e1a05da56f62cfe725c8728cea3a4aa031b7d1b0a68f869760d6",
+  "code/tile_m.py": "d6ae4a556472d403773cd2117c992bfc10e1187112da1b3893f3fae628a131dd",
+  "data/selection.json": "b81758d0cce18e6c1abd07e716f05064aaa9b43819d6b70f7f52b4f2e4f01a9b",
+  "evidence/assembly.log": "8449240c9cd4c2a46279fea4f920de9572128cb7d54d6f0accea1ba9dd133be1",
+  "evidence/audit.log": "a4b1b1eed31c07f9a3e495205bfffde4ec861aba9cf750a7b1fea5a9922ea38d",
+  "evidence/draft-assembly.log": "e02a0b68a7f72a453c470339dd48eab594e433c80809fdab196e58fc7ff10ee7",
+  "evidence/eleven-kernel-screen-first-failure.log": "cd53bd73b6a2dd53879d9f048368bf8f68204ef7daf4b0be849f7bd725a65eb7",
+  "evidence/eleven-kernel-screen.log": "54ded773480d897867a969444794ea5fdcf2fd03de062c4012f63e28d86d09b0",
+  "evidence/emit-missing-engines.log": "4e3419b3e32b60bbefe52a30f5661a8f6f53f060b99eccf32d11c9db0098d0e9",
+  "evidence/emit-missing-vendor.log": "407732b01762f5f843f54dd629820173e5958d35e0126e2c857249aad4e776a9",
+  "evidence/emit.log": "3d3853b873beb8705f798c2abdd8ac4564497f51d2c4d56419743603d6d063ae",
+  "evidence/geometry.log": "46d842d677e5faf5b8224d247f0549a00f3db138168a13802f0aebb7bc5ace46",
+  "evidence/hosted147-full314.log": "5424d4caeeb8f868adb0aee4014f42715711d4044564b3ed6b865bec16f3a028",
+  "evidence/screen_eleven_kernels.py": "80cc77ba27382ac57f7c804f6c78d880442644710e437a9859bd964106b216b7",
+  "upstream445/EXPECTED.json": "1a2e35da8c586be03201a8d102c72f681b0b6698bbcb3a2ea286d8b0d9c0c1e4",
+  "upstream445/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "upstream445/MANIFEST.json": "4d53297535ffb17603f916fa59cdc4b7f941c3166fe9f8e576f9588fd2fb79a6",
+  "upstream445/NOTICE.md": "b80411c1db53d12bf43d6cbb8bf2804102f2e57be2a2f55dd7820c6c2f2b9570",
+  "upstream445/PROOF.md": "4aede2a05d9570cc5d8a19032513c973137ee9083f079ae845b04f3f362e2ca0",
+  "upstream445/README.md": "15e76f8a2200af0f871b04d410ebd7fac059b800b5ec4a1f376a333c9f5638bf",
+  "upstream445/SOURCE.json": "976eebfec20d467f3384194fc03bd6f5b289a615e3b2deb70a7be910aaee8579",
+  "upstream445/code/assemble.py": "42dbfaddd284088474a80f0b6e894332b6737b8e9f9b5c45260e21c5df139792",
+  "upstream445/code/audit.py": "9900a1b2f1f314f2b93ca8f99b5516ed2e1a7295d668ea51df2df89cef84e381",
+  "upstream445/code/emit.py": "ac63ee481f3d75cb9f0658faaa2412db81d55bc44d9f1ff1c0329ce1e75aa0d4",
+  "upstream445/code/geometry.py": "9554182d67e434ea84b4430f909a2c400abc755d8487b51454a8e6968e62859d",
+  "upstream445/code/row_bound.py": "de4a9b9cd797e1a05da56f62cfe725c8728cea3a4aa031b7d1b0a68f869760d6",
+  "upstream445/data/selection.json": "52dbbb68e8c147690d15eaa1d952df05d074b0c121885a4159d9f6732f391872",
+  "upstream445/proof/INHERITED-ROW-DIVISOR.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8",
+  "upstream445/proof/UPSTREAM-PR234-NOTICE.md": "ce978c8dfc8a2b36eed7a53014b1a792248b22ef4cee3edd8adab825a571c429",
+  "upstream445/verify.py": "4a161d35c65fa1d35e655c3957c05a8164a003ca05c3effe9fee7dc8d0f38090",
+  "verify.py": "fcc35e955bd667350f999a540011df92e2e1d774fc78703f53bfbabf949643af"
+}
diff --git a/research/e8-eleven-hosting-selected/NOTICE.md b/research/e8-eleven-hosting-selected/NOTICE.md
new file mode 100644
index 0000000000..793fb1baa3
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/NOTICE.md
@@ -0,0 +1,3 @@
+Prepared by Rohan Arun with substantial OpenAI Codex assistance: hosting-aware rank147 selection, eleven-stage integration and exact checks. Apache-2.0.
+
+The eleven-stage geometry, emitter, independent audit and elementary row bound are adapted from chafreaky PR445 with disclosed OpenAI Codex assistance, pinned at 40ab91daf2b5e87fc4071dedae1699d5d7e7cecc. Original files and notices remain in upstream445. The rank147 word is from our PR434; credit chafreaky PR443/444/417/439, eumemic PR436/440/441, DaysSky PR442 with Anthropic Claude assistance, icekylinx PR433, retained PR426/389/376/370, PR425/386 and Jacob Sussman contributions, and Henry Grant PR234's row interface. Parent source pins, licenses and assistance disclosures are retained unchanged.
diff --git a/research/e8-eleven-hosting-selected/PROOF.md b/research/e8-eleven-hosting-selected/PROOF.md
new file mode 100644
index 0000000000..2415bf9ce9
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/PROOF.md
@@ -0,0 +1,9 @@
+# Conditional composition
+
+Use the rank147 local word reconstructed from the frozen PR436/PR443 precursor in sibling `e8-hosting-selected-kernel`. Its exact local certificate has 123 pivots, 118 donor slots and scalar ADD count 15446. The word hash is `f5ae52ba95d0edd76f85fdb4da04cd78ad46b55c9ad3b86cc098146b62032336`.
+
+Apply the pinned PR445 eleven-stage construction (retained verbatim in `upstream445`). Recompute the assignment with the new residual-width census: 617 width8, 115 width7 and eight width4 helpers per stage. Freeze the resulting integer selection and independently expand/check every occurrence. The solver is only a discovery tool; the verifier uses no optimization oracle. The first unconstrained assignment left one helper unhosted and was rejected; the retained selection passes complete ownership coverage.
+
+The bit lower endpoint is 0.001267514693114214441041. The same complex supplier has certified lower endpoint 0.001267453159029119461392, which is smaller. Keeping this full rational endpoint (rather than truncating at1e-18) gains one κ grid step without a new supplier. The finite invoice retains the residual route allowance144 plus two hosting factors, three-level halving, a 1024-bit coefficient charge and complete row coefficient19431 below20161. Fresh strict outer assembly yields κ=0.001265848755025709.
+
+All proof-scope qualifications and source notices in the parent and PR445 remain. The elementary all-q orthogonal-cover argument is in `upstream445/PROOF.md` and `code/row_bound.py`; no finite sample is substituted for that argument. See `INHERITED-HOSTING-PROOF.md` for the additional conditional operator interface.
diff --git a/research/e8-eleven-hosting-selected/README.md b/research/e8-eleven-hosting-selected/README.md
new file mode 100644
index 0000000000..a95f38cefb
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/README.md
@@ -0,0 +1,18 @@
+# Eleven-stage hosting with the rank147 kernel
+
+Draft conditional κ = **0.001265848755025709**, 0.19656151% above PR445 at `40ab91daf2b5e87fc4071dedae1699d5d7e7cecc`.
+The complex supplier now binds. This combines PR434's hosting-selected rank147 word with PR445's eleven-stage dimension78 construction and complete orthogonal-cover row estimate. All 65,120 helper occurrences fit into idle data coordinates, leaving 9,600 live and 9,609 physical families.
+
+Exact changed-component checks have passed: 1,320 geometry routes, 9,340 unbanked columns, the signed ten-wire identity and 24 omitted-shear controls, all emitted instructions, all hosted owners and 22 mutation controls. Both rational moment engines, the refreshed finite invoices, six bootstrap levels, 47 strict outer inequalities and next-grid controls passed. The already fully verified rank138 parent supplies the unchanged complex certificate.
+
+**Full uninterrupted Python3.11.15 and3.14.8 runs passed at the preceding 708 endpoint.** Retaining the full certified complex lower endpoint instead of rounding it down at1e-18 raises the last κ grid digit to709. The only executable change is a two-line assembly refinement; both versions independently reran the two exact moments, invoices,47 inequalities and controls against their fully verified supplier artifacts. Receipts and the exact code diff are in sibling `e8-eleven-hosting-selected-validation/`. A fresh uninterrupted wrapper at the revised manifest has not been run; GitHub CI remains pending. The earlier SSD failure log is preserved.
+
+Reproduce after installing `sympy`:
+
+```
+python -B research/e8-eleven-hosting-selected/verify.py /absolute/new/output
+```
+
+The wrapper first rebuilds the whole rank147 parent, including the rank138 lineage and the complex phase audit, then runs the new geometry, program, independent ownership audit, invoice and exact assembly. The retained full-run receipts bind the unchanged suppliers; separate precision receipts bind the revised assembly.
+
+Scope: retains the additional PR442 idle-data hosting assumption, the inherited all-size compiler, dirty-helper/compressed-window, restored-work, tape/common-grid, precision, row-divisor and analytic interfaces. Finite audits do not establish the hosting operator extension. This is not an unconditional multiplication theorem, an improvement under only PR441's assumptions, or a new Lean proof.
diff --git a/research/e8-eleven-hosting-selected/SOURCE.json b/research/e8-eleven-hosting-selected/SOURCE.json
new file mode 100644
index 0000000000..db504435d7
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/SOURCE.json
@@ -0,0 +1,8 @@
+{
+  "parent_pr": 434,
+  "parent_commit": "6c0c0522665dda10201673c17fbb589f737d226c",
+  "parent_manifest_sha256": "b32a601147fbe042af3799bae4a73d27f7a433e76aa83650ba24566b329c184b",
+  "eleven_pr": 445,
+  "eleven_commit": "40ab91daf2b5e87fc4071dedae1699d5d7e7cecc",
+  "upstream445_manifest_sha256": "4d53297535ffb17603f916fa59cdc4b7f941c3166fe9f8e576f9588fd2fb79a6"
+}
diff --git a/research/e8-eleven-hosting-selected/VALIDATION.json b/research/e8-eleven-hosting-selected/VALIDATION.json
new file mode 100644
index 0000000000..aa139e9870
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/VALIDATION.json
@@ -0,0 +1,14 @@
+{
+  "status": "FULL_UNCHANGED_SUPPLIERS_AND_REVISED_ASSEMBLY_PASS_BOTH_PYTHONS",
+  "python_versions": [
+    "3.11.15",
+    "3.14.8"
+  ],
+  "kappa": "1265848755025709/1000000000000000000",
+  "previous_uninterrupted_manifest": "58048a268e837f4e8a30521435b2c3dad77fd0e74b38f020b7b7e11367ecf5b7",
+  "changed_code": [
+    "code/assemble.py: retain certified complex rational endpoint and compare it to weaker inherited bound"
+  ],
+  "fresh_current_manifest_uninterrupted_wrapper": "not rerun",
+  "github_ci": "pending"
+}
diff --git a/research/e8-eleven-hosting-selected/code/assemble.py b/research/e8-eleven-hosting-selected/code/assemble.py
new file mode 100644
index 0000000000..0117a300c7
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/code/assemble.py
@@ -0,0 +1,94 @@
+# Adapted from DaysSky PR442 with Claude assistance; Eleven-stage R740 integration by chafreaky with OpenAI Codex. Apache-2.0.
+"""Two exact moments for both hosted suppliers, fresh finite invoices with the hosted stock, and the strict outer
+assembly of #434 (six bootstrap levels, 47 inequalities, next-grid and parameter controls).
+usage: assemble.py VERIFIED444_DIR BIT_DIR"""
+import gzip, hashlib, importlib.util, json, math, sys
+from fractions import Fraction as Q
+from pathlib import Path
+parent444, bd = map(Path, sys.argv[1:3])
+upstream=parent444
+ap=bd/"AUDIT.json";outp=bd/"RESULT.json"
+from row_bound import bound as row_bound, controls as row_controls
+par=upstream / "changed"
+cd=upstream / "complex"
+def load(name):
+    sp = importlib.util.spec_from_file_location('hosted_' + name, par / 'work/pr361/code/engines' / (name + '.py'))
+    mod = importlib.util.module_from_spec(sp); sp.loader.exec_module(mod); return mod
+M, Other, Outer = load('moment'), load('base_two_moment'), load('outer')
+audit = json.loads(ap.read_text()); ua=json.loads((upstream/'AUDIT.json').read_text()); ur=json.loads((upstream/'RESULT.json').read_text()); bg = json.loads((bd / 'GLOBAL.json').read_text()); ch = json.loads((cd / 'HOSTED.json').read_text())
+assert audit['template_sha256'] == bg['template_sha256'] and ua['complex_template_sha256'] == ch['template_sha256']
+assert json.loads((upstream/'RECEIPT.json').read_text())['status']in ('PASS_FULL_RANK138_IDLE_HOSTING','PASS_FULL_HOSTING_SELECTED_KERNEL')
+# ---------------- bit: two moments and the parent's invoice formulas with the hosted stock
+P = {int(r): n for r, n in audit['profile'].items()}; m, W = 78, audit['live']; E = sum(P.values())
+geo = json.loads((bd / 'GEOMETRY.json').read_text());pg=bg
+T, L, R, V, K = 8, 11, 740, 120, 5
+assert pg["replicas"]==T and pg["R"]==R
+mass = sum(r * z for r, z in P.items()); assert m * W - mass == (2*K*V-L*72)*T
+physical = W + 9; d = m * m; N = 2 * m
+unit = L * T * pg['local_additions'] + pg['bridge_additions']
+J = 8 * T * L * (2 * V + R) + 8 * (2 * K * V * T) + 2 * L * T * R + 2 * pg['copy_erase_episodes']   # every helper route charged (bank or hosted)
+high = 16 * (d + 1) ** 2; good = 8 * m * m + 8; compiler = 128 * N ** 3
+selectors = 2 * L * T * ((W - 1) + R * m * (geo['max_route_factors'] + 144 + 2 + (m - 1) + m))   # 144: residual isometry; +2: hosted slot permutation and idle basis U_q
+prefix = int(pg['global_prefix_bound']); charged_prefix = 64 * ((prefix.bit_length() + 63) // 64)
+assert 1<<128 <= prefix < 1<<charged_prefix <= 1<<256
+coefficient = unit + J * high + J * physical + E * (good + compiler) + 16 * m ** 3 + pg['copy_erase_episodes'] + selectors + prefix + 1
+two = (coefficient + 1) ** 3 * (E + 1) ** 3; charged_two = 1024
+assert 1 << 512 <= two < 1 << charged_two and 2 * max(P) ** 3 < m ** 3
+rows = row_bound(m,physical,max(P),3);row=rows["complete_row_coefficient"]
+assert row==19431<20161
+row_rejected=row_controls()
+root = M.certify(P, m, W, True); c = Q(root['lower']); chi = Q(root['upper'])
+fb = 32 * m * m * E
+lo, hi = Other.moment(m, W, list(P.items()), c); bl, bh = Other.moment(m, W, [(1, fb)], c); assert hi + bh / 10 ** 16 < 1
+lo2, hi2 = Other.moment(m, W, list(P.items()), chi); bl2, bh2 = Other.moment(m, W, [(1, fb)], chi); assert lo2 + bl2 / 10 ** 16 > 1
+# ---------------- complex: two moments and the parent's invoice with the hosted stock
+PC = {int(r): n for r, n in ua['complex_profile'].items()}; mc, WC = 73, ua['complex_live']; EC = sum(PC.values())
+massc = sum(r * z for r, z in PC.items()); assert mc * WC - massc == 2496
+rc = M.certify(PC, mc, WC, True); b = Q(rc['lower'])
+assert b>=Q(ur['complex_lower'])
+fbc = 32 * mc * mc * EC
+l3, h3 = Other.moment(mc, WC, list(PC.items()), b); b3, bh3 = Other.moment(mc, WC, [(1, fbc)], b); assert h3 + bh3 / 10 ** 16 < 1
+integ = json.loads((par / 'split-centres/INTEGRATION.json').read_text()); inv = integ['finite_invoice']
+physc = ch['physical']; Rc = 560; v = 120
+compilerc = 64 * (mc + 1) ** 3
+pervertex = inv['pervertex'] - integ['physical'] * (64 + 1) + physc * (64 + 1) - integ['live'] + WC   # stock-dependent terms re-based
+r_ = mc // 2; group = 2 ** (r_ * r_) * math.prod(2 ** (2 * i) - 1 for i in range(1, r_ + 1)); stock = group * physc
+smass = group * massc; logical = group * max(pervertex, inv['pervertex']) + 64; router = compilerc * (logical + 1) * (stock + 1) ** 2
+GG, EE, C0 = 1 << 30000, 1 << 100000, 1 << 210000; BB = smass + EE
+literal = 2 * GG * stock ** 2 + 8 * smass + 4 * stock + 4 + 32 * mc
+assert logical < 1 << 6050 and router < GG and literal < EE and BB < 1 << 100001 and 32 * mc * BB * BB < C0 and 2 * BB + 18 < C0
+depth = 2; assert mc ** depth > 2 * max(PC) ** depth
+rowc = depth * stock.bit_length() + 9909 + 252; assert rowc < 20161
+# ---------------- outer assembly exactly as #434's combined.py
+eta = beta = Q(1, 10 ** 18); grid = Q(1, 10 ** 18); s = min(c, (1 - beta) * b) - Q(1, 10 ** 24)
+assert 0 < s < c and s < (1 - beta) * b
+chain = [Q(384599, 10 ** 10)]; cutoffs = []
+def ceil(x): return -((-x.numerator) // x.denominator)
+for j in range(6):
+    old = chain[-1]; a = (1 - s) * s + s * old
+    gap = min(s - a, 1 - a - s, 1 - a - s * (1 - old), 1 - s); assert old < a < s < 1 - a and gap > 0
+    cutoff = max(ceil(36 / gap ** 2), ceil(2 * (4 + charged_two) / gap)); assert cutoff * gap ** 2 >= 36 and cutoff * gap >= 2 * (4 + charged_two)
+    cutoffs.append(dict(gap=str(gap), cutoff_log2=str(cutoff))); chain.append(a)
+q = chain[-1] * (1 - 2 * eta); margin = (1 - eta) * q / (1 + q); ticks = margin / grid; k = grid * ((ticks.numerator - 1) // ticks.denominator)
+bridge = {'semantic': {'C0': {'base': 2, 'exponent': 210000}, 'strict_literal_gap': 1}, 'rows': {'degree_gap': Q(10 ** 6) - Q(51 * 20161, 25)}}
+a = Outer.assembly(chain[-1], b, bridge, k, eta=eta, beta=beta)
+assert len(a['strict_constraints']) == 47 and all(x > 0 for x in a['strict_constraints'].values())
+controls = []
+for name, kk, ee, bb in [('next_grid', k + grid, eta, beta), ('zero_eta', k, Q(0), beta), ('zero_beta', k, eta, Q(0)), ('unit_beta', k, eta, Q(1))]:
+    try: Outer.assembly(chain[-1], b, bridge, kk, eta=ee, beta=bb)
+    except AssertionError: controls.append(name)
+    else: raise AssertionError(name)
+parent_k = Q('315841366195289/250000000000000000')
+assert json.loads((parent444/'RECEIPT.json').read_text())['status']in ('PASS_FULL_RANK138_IDLE_HOSTING','PASS_FULL_HOSTING_SELECTED_KERNEL')
+res = dict(status='PASS_CONDITIONAL_ELEVEN_STAGE_HOSTING_ASSEMBLY', kappa=str(k), kappa_decimal=format(float(k), '.18f'),
+           bit_lower=str(c), complex_lower=str(b), binding_component='bit' if c < (1 - beta) * b else 'complex',
+           gain_over_pr445_percent=float(100 * (k / parent_k - 1)),
+           bit=dict(live=W, physical=physical, maxchild=max(P), rank_mass=mass, hosted_residuals=audit['hosted_residuals'],
+                    prefix_bits=prefix.bit_length(), charged_prefix_bits=charged_prefix, coefficient_bits=coefficient.bit_length(),
+                    three_level_coefficient_bits=two.bit_length(), charged_three_level_coefficient_bits=charged_two, row_coefficient=row),
+           complex=dict(live=WC, physical=physc, maxchild=max(PC), rank_mass=massc, hosted_residuals=ua['complex_hosted_residuals'],
+                        physical_stock_bits=stock.bit_length(), router_bits=router.bit_length(), literal_bits=literal.bit_length(), row_coefficient=rowc),
+           strict_outer_constraints={n: str(x) for n, x in a['strict_constraints'].items()}, outer_controls=controls, bootstrap=cutoffs,
+           bit_template_sha256=bg['template_sha256'], complex_template_sha256=ch['template_sha256'], emitted_program_sha256=bg['emitted_program_sha256'], bank_assignments=audit['bank_assignments'], bit_profile=audit['profile'], parent_kappa=str(parent_k), additional_interface='PR442 idle-data hosting during untouched windows',row_bound=rows,row_controls=row_rejected, halving_depth=3, finite_controls=['old 128-bit prefix charge insufficient','old 512-bit composite charge insufficient'])
+outp.write_text(json.dumps(res, indent=2) + '\n')
+print(res['status'], res['kappa_decimal'], 'binding', res['binding_component'], 'gain over #445 %.4f%%' % res['gain_over_pr445_percent'])
diff --git a/research/e8-eleven-hosting-selected/code/audit.py b/research/e8-eleven-hosting-selected/code/audit.py
new file mode 100644
index 0000000000..c8730e84dd
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/code/audit.py
@@ -0,0 +1,181 @@
+"""Independent eleven-stage schedule, geometry embedding and hosted ownership audit.
+Derived from PR386/436/443/444 and DaysSky PR442; all source notices retained.
+Eleven-stage integration by chafreaky with OpenAI Codex assistance, Apache-2.0.
+No emitter, schedule constructor, hosting solver or expander is imported.
+Usage: audit.py PARENT443_CANDIDATE OUT
+"""
+import copy,gzip,hashlib,json,sys
+from collections import Counter,defaultdict
+from pathlib import Path
+K,L,M,T,V,R=5,11,78,8,120,740
+DATA=2*K*V*T
+read=lambda p:json.loads(p.read_text())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+load_template=lambda p:json.loads(gzip.decompress(p.read_bytes()))
+
+def windows(schedule):
+    last={};seen=[];win={};ranks={};pairs={}
+    for position,event in enumerate(schedule):
+        kind=event['kind']
+        if kind=='local_cover_sweep':
+            seen.append((position,event['stage'],event['pair']));last[event['pair']]=position
+        elif kind=='bridge':
+            last[event['dst']]=position;last[event['src']]=position
+        elif kind=='idle':
+            i=event['idx'];assert i not in win
+            win[i]={s for pos,s,p in seen if last.get(event['pair'],-1)<pos<position and p!=event['pair']}
+            ranks[i]=event['rank'];pairs[i]=event['pair']
+        else:assert kind=='exchange' and position==len(schedule)-1
+    return win,ranks,pairs
+
+def schedule_check(schedule):
+    # Ten formal integer rows, keeping the signs lost by F2 reduction.
+    rows=[[int(i==j) for j in range(2*K)] for i in range(2*K)]
+    levels=[-1]*K;stages=[];bridges=0;exchanged=False;idles=[]
+    def add(dst,src,c):rows[dst]=[x+c*y for x,y in zip(rows[dst],rows[src])]
+    for e in schedule:
+        kind=e['kind'];assert not exchanged
+        if kind=='local_cover_sweep':
+            s,p,rev=e['stage'],e['pair'],e['reverse']
+            assert s==len(stages) and 0<=s<L and p==max(0,(s-1)//2) and rev==bool(s%2)
+            assert levels[p]==s-1
+            add(2*p,2*p+1,-1) if rev else add(2*p+1,2*p,1)
+            levels[p]=s;stages.append(s)
+        elif kind=='idle':
+            p,lo,hi=e['pair'],e['source_level'],e['target_level']
+            assert 0<=p<K and levels[p]==lo and lo<=hi<=L-1 and e['rank']==7*(hi-lo)
+            assert e['idx']==len(idles);idles.append((p,lo,hi,e['rank']));levels[p]=hi
+        elif kind=='bridge':
+            dst,src,c=e['dst'],e['src'],e['coefficient']
+            assert 0<=dst<K and 0<=src<K and dst!=src and c in (-1,1) and levels[dst]==levels[src]
+            add(2*dst,2*src,c);add(2*src+1,2*dst+1,-c);bridges+=1
+        else:
+            assert kind=='exchange' and levels==[L-1]*K
+            for p in range(K):rows[2*p],rows[2*p+1]=rows[2*p+1],[-x for x in rows[2*p]]
+            exchanged=True
+    assert exchanged and rows==[[int(i==j) for j in range(2*K)] for i in range(2*K)]
+    assert stages==list(range(L)) and bridges==3*(K-1)
+    return idles
+
+def audit(t,parent,widths):
+    assert (t['m'],t['h'],t['stages'],t['replicas'],t['live'],t['private_centre_reserve'])==(M,8,L,T,DATA,9)
+    assert t['banks_per_stage']==0 and t['bank_padding'] is None
+    for key in ('local_programs','residual_isometries','entrance_rank_total','source_record_sha256','bit_operator'):
+        assert t[key]==parent[key],key
+    schedule_check(t['schedule'])
+    win,rank,pair=windows(t['schedule']);hs=t['hosting'];used=defaultdict(set);hosted={}
+    assert hs['windows']=={str(i):[pair[i],rank[i],sorted(win[i])] for i in win if rank[i] and win[i]}
+    for i,cp,off,w,s,h in hs['slots']:
+        assert i in win and s in win[i] and 0<=s<L and 0<=h<R and 0<=cp<2*V
+        assert w==widths[h]>0 and 0<=off and off+w<=rank[i]
+        cells=set(range(off,off+w));assert not cells&used[i,cp];used[i,cp]|=cells
+        assert (s,h) not in hosted;hosted[s,h]=(i,cp,off,w)
+    assert set(hosted)=={(s,h) for s in range(L) for h in range(R)}
+    rem={};summaries={}
+    for i in rank:
+        if not rank[i]:continue
+        for cp in range(2*V):rem[i,cp]=rank[i]-len(used[i,cp])
+        if str(i) in hs['windows']:
+            summaries[str(i)]={str(r):n for r,n in sorted(Counter(rem[i,cp] for cp in range(2*V)).items())}
+    assert hs['remainders']==summaries
+    assert len(t['calls'])==L*T;seen=set();paid=Counter()
+    localhash={ori:hashlib.sha256(json.dumps(es,separators=(',',':')).encode()).hexdigest() for ori,es in t['local_programs'].items()}
+    for index,c in enumerate(t['calls']):
+        s,rep=c['stage'],c['replica'];p=max(0,(s-1)//2);rev=bool(s%2)
+        assert (s,rep)==divmod(index,T) and c['pair']==p and c['orientation']==('reverse' if rev else 'forward')
+        assert c['local_hash']==localhash[c['orientation']]
+        own=c['owners'];assert len(own)==2*V+R
+        assert len({(f,tuple(route)) for f,route in own})==2*V+R
+        for j,(f,route) in enumerate(own):
+            assert 0<=f<DATA
+            if j<2*V:
+                side=j//V;side=1-side if rev else side
+                assert f==rep*(2*K*V)+(2*p+side)*V+j%V and route==['data',s,j%V]
+            else:
+                h=j-2*V;i,cp,off,w=hosted[s,h];side,port=divmod(cp,V)
+                assert pair[i]!=p and f==rep*(2*K*V)+(2*pair[i]+side)*V+port
+                assert route==['hosted',i,off,w]
+                assert (s,rep,h) not in seen;seen.add((s,rep,h))
+        for z in t['local_programs'][c['orientation']]:
+            if z[0]==0 and z[4]:paid[z[4]]+=1
+            if z[0]==2:paid[z[5]]+=1
+    assert len(seen)==L*T*R
+    for r in rem.values():
+        if r:paid[r]+=T
+    assert M*DATA-sum(r*n for r,n in paid.items())==T*(2*K*V-72*L)
+    assert M**2<=2*max(paid)**2 and M**3>2*max(paid)**3
+    return paid
+
+def expanded_digest(t):
+    h=hashlib.sha256();count=0
+    for call in t['calls']:
+        for op in t['local_programs'][call['orientation']]:
+            row=[op[0],call['owners'][op[1]]]
+            if op[0]==0:row.extend(op[2:])
+            else:
+                row.append(call['owners'][op[2]] if op[2]<2*V+R else [t['live'],['private',0]])
+                row.extend(op[3:])
+            h.update(json.dumps(row,separators=(',',':')).encode());h.update(b'\n');count+=1
+    return h.hexdigest(),count
+
+def main():
+    par,out=map(Path,sys.argv[1:]);t=load_template(out/'GLOBAL-TEMPLATE.json.gz');pt=load_template(par/'nine/GLOBAL-TEMPLATE.json.gz')
+    g=read(out/'GLOBAL.json');geo=read(out/'GEOMETRY.json');pg=read(par/'nine/GEOMETRY.json')
+    state=read(par/'records/249-states.json');fs=read(par/'records/frames.json')['frames']
+    widths=[8-fs[str(state['initial'][str(h)])]['dim'] for h in range(240,980)]
+    P=audit(t,pt,widths)
+    assert geo['m']==78 and geo['stages']==11 and len(geo['ports'])==120 and not geo['bank_slots'] and not geo['bank_permutations']
+    for p,old in zip(geo['ports'],pg['ports']):
+        assert {k:v for k,v in p.items() if k!='routes'}=={k:v for k,v in old.items() if k!='routes'}
+        assert p['routes'][:9]==old['routes'] and len(p['routes'])==11
+        for s,route in enumerate(p['routes']):
+            if s==0:assert route==dict(stage=0,axes=list(range(8)),identity=True)
+            else:
+                assert route==dict(stage=s,axes=list(range(8))+list(range(8+7*(s-1),8+7*s)),elementary_inverse_replay=old['routes'][1]['elementary_inverse_replay'])
+                assert len(set(route['axes']))==15 and max(route['axes'])<M
+    idle=schedule_check(t['schedule'])
+    assert idle==[(e['pair'],e['source_level'],e['target_level'],e['rank']) for e in geo['idle_per_port_and_data_member']]
+    assert t['geometry_sha256']==sha(out/'GEOMETRY.json')==g['geometry_sha256']
+    assert t['source_record_sha256']==sha(par/'records/249-records.bin')==g['source_records_sha256']
+    th=hashlib.sha256(gzip.decompress((out/'GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest();assert th==g['template_sha256']
+    digest,count=expanded_digest(t);assert digest==g['emitted_program_sha256'] and count==g['emitted_events']
+    assert P==Counter({int(r):n for r,n in g['profile'].items()})
+    assert (g['live'],g['physical'],g['hosted_residuals'],g['bank_assignments'],g['deficit'])==(9600,9609,65120,0,3264)
+    assert g['rank_mass']==sum(r*n for r,n in P.items()) and g['paid_calls']==sum(P.values()) and g['maxchild']==max(P)
+    assert g['independent_unbanked_scalar_columns']==9340 and len(g['scalar_stages'])==11 and g['all_scalar_columns_restored']
+    assert g['omitted_bridge_shears_rejected']==list(range(24))
+    controls=[]
+    def reject(name,fn):
+        q=copy.deepcopy(t);fn(q)
+        try:audit(q,pt,widths)
+        except (AssertionError,KeyError,IndexError,TypeError):controls.append(name)
+        else:raise AssertionError('accepted '+name)
+    slot=lambda q:q['hosting']['slots'][0]
+    reject('slot outside window',lambda q:slot(q).__setitem__(4,10))
+    reject('copy outside family',lambda q:slot(q).__setitem__(1,240))
+    reject('negative slot offset',lambda q:slot(q).__setitem__(2,-1))
+    reject('wrong residual width',lambda q:slot(q).__setitem__(3,slot(q)[3]+1))
+    reject('duplicate helper',lambda q:q['hosting']['slots'].append(slot(q)))
+    reject('missing helper',lambda q:q['hosting']['slots'].pop())
+    reject('cross-replica host',lambda q:q['calls'][0]['owners'][240].__setitem__(0,q['calls'][0]['owners'][240][0]+1200))
+    reject('cross-replica data',lambda q:q['calls'][0]['owners'][0].__setitem__(0,1200))
+    reject('wrong hosted coordinate',lambda q:q['calls'][0]['owners'][240][1].__setitem__(2,99))
+    reject('helper changed to bank',lambda q:q['calls'][0]['owners'][240][1].__setitem__(0,'bank'))
+    reject('wrong call orientation',lambda q:q['calls'][0].__setitem__('orientation','reverse'))
+    reject('duplicate call',lambda q:q['calls'].__setitem__(1,q['calls'][0]))
+    reject('dropped final stage',lambda q:q.__setitem__('calls',[c for c in q['calls'] if c['stage']<10]))
+    reject('wrong idle rank',lambda q:next(e for e in q['schedule'] if e['kind']=='idle').__setitem__('rank',1))
+    reject('omitted bridge',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='bridge')))
+    reject('wrong bridge sign',lambda q:next(e for e in q['schedule'] if e['kind']=='bridge').__setitem__('coefficient',-1))
+    reject('omitted terminal exchange',lambda q:q['schedule'].pop())
+    reject('understated live stock',lambda q:q.__setitem__('live',q['live']-1))
+    reject('missing remainder summary',lambda q:q['hosting']['remainders'].pop(next(iter(q['hosting']['remainders']))))
+    reject('wrong residual isometry',lambda q:q['residual_isometries'][0]['orthogonal_rows_numerator'][0].__setitem__(0,99))
+    reject('omitted local instruction',lambda q:q['local_programs']['forward'].pop())
+    reject('wrong reflected copy rank',lambda q:next(z for z in q['local_programs']['reverse'] if z[0]==2).__setitem__(5,0))
+    res=dict(status='PASS_INDEPENDENT_ELEVEN_STAGE_HOSTING_AUDIT',template_sha256=th,emitted_program_sha256=digest,
+             emitted_events=count,profile={str(r):n for r,n in sorted(P.items())},live=9600,physical=9609,hosted_residuals=65120,
+             bank_assignments=0,rank_mass=sum(r*n for r,n in P.items()),deficit=3264,maxchild=max(P),geometry_routes=1320,
+             halving_depth=3,mutations_rejected=controls)
+    (out/'AUDIT.json').write_text(json.dumps(res,indent=2)+'\n');print(json.dumps(res))
+if __name__=='__main__':main()
diff --git a/research/e8-eleven-hosting-selected/code/bank_routes.py b/research/e8-eleven-hosting-selected/code/bank_routes.py
new file mode 100644
index 0000000000..9e43a87666
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/code/bank_routes.py
@@ -0,0 +1,65 @@
+"""Exact residual bank routes for the kernel word; chafreaky with OpenAI Codex.
+
+The stored integer rows divided by two are an orthonormal basis. Entrance
+rows span E; the remaining rows span E-perp. A coordinate permutation sends
+the latter to the assigned contiguous block in a width-64 bank. This gives
+an explicit rational isometry, with only powers of two in denominators.
+"""
+from collections import Counter, deque
+from tile_m import tile
+
+
+def placement(widths, replicas=32):
+    assert replicas > 0 and replicas % 8 == 0
+    by_width = {}
+    for rep in range(replicas):
+        for helper, width in enumerate(widths):
+            assert 0 < width <= 8
+            by_width.setdefault(width, deque()).append((rep, helper))
+    patterns = tile({w: len(q) for w, q in by_width.items()}, 64)
+    result = {}
+    bank = 0
+    for widths_in_bank, count in patterns:
+        for _ in range(count):
+            offset = 0
+            for width in widths_in_bank:
+                key = by_width[width].popleft()
+                result[key] = (bank, offset, width)
+                offset += width
+            assert offset == 64
+            bank += 1
+    assert all(not q for q in by_width.values())
+    assert len(result) == replicas * len(widths)
+    return result, bank
+
+
+def validate_isometries(rows, frames, roots, dimensions):
+    seen = set()
+    dot = lambda a, b: sum(x*y for x, y in zip(a, b))
+    for record in rows:
+        f = record['frame']
+        assert f not in seen
+        seen.add(f)
+        e = record['entrance_rank']
+        assert e == dimensions[f] and record['denominator'] == 2
+        basis = record['entrance_basis'] + record['residual_basis']
+        matrix = record['orthogonal_rows_numerator']
+        assert len(basis) == len(matrix) == 8
+        assert matrix == [roots[i] for i in basis]
+        assert all(len(r) == 8 and all(type(x) is int for x in r) for r in matrix)
+        assert all(dot(a,b) == 4*(i==j) for i,a in enumerate(matrix) for j,b in enumerate(matrix))
+        # The first e rows span precisely the frame, not only its dimension.
+        for i in frames[f]:
+            assert sum(dot(roots[i], q)**2 for q in matrix[:e]) == 4*dot(roots[i], roots[i])
+        assert len(record['entrance_basis']) == e
+        # This selected family needs coordinate permutations only. Checking the
+        # elementary reduction also bounds the literal route cost and primes.
+        reduced = [[x // 2 for x in row] for row in matrix]
+        assert all(x % 2 == 0 for row in matrix for x in row)
+        operations = record['gaussian_reduction']
+        assert len(operations) <= 7
+        for kind, i, j, scalar in operations:
+            assert kind == 'swap' and scalar is None and 0 <= i < 8 and 0 <= j < 8
+            reduced[i], reduced[j] = reduced[j], reduced[i]
+        assert reduced == [[int(i == j) for j in range(8)] for i in range(8)]
+    return seen
diff --git a/research/e8-eleven-hosting-selected/code/e8core.py b/research/e8-eleven-hosting-selected/code/e8core.py
new file mode 100644
index 0000000000..78983b3687
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/code/e8core.py
@@ -0,0 +1,203 @@
+"""Our own engine for bitE8/1 words (E8 root-line labels, h = 8): frame algebra over Q via root-line masks,
+legality/F2 replay, five-stage histogram, exact bit coarse saving and PR #315 outer assembly (our engine copies).
+Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0."""
+import gzip, json, os, importlib.util
+from fractions import Fraction as Q
+from collections import Counter
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+def _load(n):
+    s = importlib.util.spec_from_file_location('e8_' + n, os.path.join(HERE, "engines", n + ".py"))
+    m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+moment = _load('moment'); other = _load('base_two_moment'); outer = _load('outer')
+
+B2 = Q(876248285600677, 10**18)   # Sussman E8 five-stage (PR #352)
+B3 = Q(932783231884153, 10**18)   # DaysSky seven-stage B_3 (PR #363; no Lean proof)
+
+
+def load_word(p):
+    with (gzip.open(p, 'rt') if p.endswith('.gz') else open(p)) as f:
+        return json.load(f)
+
+
+def save_word(c, p):
+    with gzip.open(p, 'wt') as f:
+        json.dump(c, f, separators=(',', ':'))
+
+
+def rank(vecs):
+    rows = [[Q(x) for x in r] for r in vecs]; rk = 0
+    n = len(rows[0]) if rows else 0
+    for col in range(n):
+        p = next((i for i in range(rk, len(rows)) if rows[i][col] != 0), None)
+        if p is None: continue
+        rows[rk], rows[p] = rows[p], rows[rk]
+        for i in range(len(rows)):
+            if i != rk and rows[i][col] != 0:
+                f = rows[i][col] / rows[rk][col]; rows[i] = [a - f * b for a, b in zip(rows[i], rows[rk])]
+        rk += 1
+    return rk
+
+
+class Lat:
+    """Root-spanned subspaces of Q^8 represented by the mask of root lines they contain."""
+    def __init__(self, lines):
+        self.lines = [tuple(x) for x in lines]; self.v = len(lines)
+        self._dim = {0: 0}; self._close = {}
+        # Gram (form <x,y>/2) for orthogonality
+        self.ip = [[sum(a * b for a, b in zip(x, y)) // 2 for y in self.lines] for x in self.lines]
+
+    def close(self, mask):
+        """mask of all root lines in span(roots of mask)"""
+        if mask in self._close: return self._close[mask]
+        idx = [i for i in range(self.v) if mask >> i & 1]
+        basis = []
+        for i in idx:
+            if rank([self.lines[j] for j in basis] + [self.lines[i]]) > len(basis): basis.append(i)
+        d = len(basis); out = 0
+        if d == 8: out = (1 << self.v) - 1
+        elif d:
+            B = [self.lines[j] for j in basis]
+            for i in range(self.v):
+                if rank(B + [self.lines[i]]) == d: out |= 1 << i
+        self._close[mask] = out; self._close[out] = out; self._dim[out] = d
+        return out
+
+    def dim(self, mask):
+        if mask not in self._dim: self.close(mask)
+        return self._dim[mask]
+
+    def basis(self, mask):
+        b = []
+        for i in range(self.v):
+            if mask >> i & 1 and rank([self.lines[j] for j in b] + [self.lines[i]]) > len(b): b.append(i)
+        return b
+
+    def perp(self, t):
+        return self.close(sum(1 << j for j in range(self.v) if self.ip[t][j] == 0))
+
+
+def to_masks(c, L):
+    return [L.close(sum(1 << i for i in fr)) for fr in c['frames']]
+
+
+PHASES = ('D', 'A', 'B', 'C')
+
+
+def replay(c, L=None, masks=None, check_f2=True, span=True, span_mode='z'):
+    """Exact legality + F2 replay + histogram of a bitE8/1 word. Returns dict(H_local, steps, ...).
+    Legality: each register's frames nested (mask inclusion = exact Q-subspace inclusion for root-spanned frames) and
+    strictly increasing at each move; every gate at one common frame; D compensation at frame 0; y at frame 0 at the
+    scatter; COPY of retained totals; final frames (x, helpers FULL; y_t at its cap t-perp).
+    Source-span: every non-target operand's x-support lies in the gate frame."""
+    L = L or Lat(c['lines']); masks = masks or to_masks(c, L)
+    v, R, h = c['v'], c['R'], c['h']; n = 2 * v + R; FULL = (1 << v) - 1
+    cur = [masks[f] for f in c['start']]
+    for r in range(v): assert cur[r] == L.close(1 << r), 'x start'
+    for r in range(v, 2 * v): assert cur[r] == 0, 'y start at 0'
+    sig = [L.dim(cur[r]) for r in range(n)]
+    H = Counter(); steps = 0; viol = []
+    val = [1 << i for i in range(n)]
+    zsupp = [{i: 1} if i < v else {} for i in range(n)]  # integer support of each register over the x columns (all ADDs are +1)
+    def climb(r, m):
+        nonlocal steps
+        if cur[r] == m: return
+        assert cur[r] & ~m == 0 and cur[r] != m, ('not nested', r)
+        H[L.dim(m) - L.dim(cur[r])] += 1; steps += 1; cur[r] = m
+    def run(gates, ph):
+        for k, (f, d, srcs) in enumerate(gates):
+            m = masks[f]
+            assert d >= v and d not in srcs and len(set(srcs)) == len(srcs), (ph, k)
+            for x in [d] + srcs: climb(x, m)
+            for s in srcs:
+                val[d] ^= val[s]
+                if span:
+                    if s < v or s >= 2 * v:
+                        ms = sum(1 << i for i in zsupp[s])
+                        if ms & ~m: viol.append((ph, k, s))
+                    zd = zsupp[d]
+                    for i, a in zsupp[s].items():
+                        w = zd.get(i, 0) + a
+                        if w: zd[i] = w
+                        else: zd.pop(i, None)
+                    if span_mode == 'f2':
+                        zsupp[d] = {i: 1 for i in range(v) if val[d] >> i & 1}
+            if span and d >= 2 * v:
+                md = sum(1 << i for i in zsupp[d])
+                if md & ~m: viol.append((ph, k, d))
+    run(c['D'], 'D')
+    for r in range(v, n): assert cur[r] == masks[c['start'][r]], 'D compensation at frame 0 (helpers untouched otherwise)'
+    run(c['A'], 'A')
+    for t in range(v): assert cur[v + t] == 0, 'y at frame 0 at the scatter'
+    copies = [val[q] for q in c['ret']]
+    for q in c['ret']:
+        assert q >= 2 * v; H[L.dim(cur[q])] += 1
+    for t, row in enumerate(c['scatter']):
+        for k in row: val[v + t] ^= copies[k]
+    run(c['B'], 'B'); run(c['C'], 'C')
+    for r in range(n): climb(r, masks[c['final'][r]])
+    for r in range(v): assert cur[r] == FULL
+    for r in range(2 * v, n): assert cur[r] == FULL
+    for t in range(v): assert cur[v + t] == L.perp(t), 'y final at cap'
+    if check_f2:
+        for s in range(v): assert val[s] == 1 << s
+        for t in range(v): assert val[v + t] == (1 << (v + t)) | (1 << t), ('target', t)
+        for r in range(2 * v, n): assert val[r] == 1 << r, ('helper', r)
+    return dict(sig=sig, viol=viol, H=H, steps=steps, n=n, v=v, R=R, h=h, L=L, masks=masks, ncopy=len(c['ret']))
+
+
+def profile(H_local, v, h=8):
+    prof = Counter({j: 5 * c for j, c in H_local.items()})
+    for j in (2 * h - 2, h - 1, 2 * h + 2, 4): prof[j] += 2 * v
+    return prof
+
+
+def coarse(H, m, W):
+    grid = Q(1, 10**18)
+    root = moment.certify(dict(H), m, W, True); c = Q(int(Q(root['lower']) * 10**18), 10**18)
+    assert moment.moment(H, m, W, c, True)[1] < 1 < moment.moment(H, m, W, c + grid, True)[0]
+    fb = 32 * m * m * sum(H.values())
+    _, up = other.moment(m, W, list(H.items()), c); _, bad = other.moment(m, W, [(1, fb)], c)
+    lo, _ = other.moment(m, W, list(H.items()), c + grid); blo, _ = other.moment(m, W, [(1, fb)], c + grid)
+    assert up + Q(1, 10**16) * bad < 1 < lo + Q(1, 10**16) * blo
+    return c
+
+
+def kappa(c, b):
+    grid = Q(1, 10**18); eta = Q(1, 10**12); beta = Q(1, 10**9); cap = (1 - beta) * b
+    sv = min(c, Q(((cap - grid) * 10**18).__floor__(), 10**18)); binding = 'bit' if sv == c else 'complex'
+    chain = [Q(384599, 10**10)]
+    for _ in range(3):
+        a = (1 - sv) * sv + sv * chain[-1]; assert chain[-1] < a < sv < 1 - a; chain.append(a)
+    bit = chain[-1]
+    bridge = dict(proof='PROOF.md', representation='Exact powers with source-bound finite overcharges',
+                  semantic=dict(G=dict(base=2, exponent=30000), E=dict(base=2, exponent=100000), B_upper=dict(base=2, exponent=100001),
+                                C0=dict(base=2, exponent=210000), C1=1, strict_literal_gap=1, induction_gap_lower=1),
+                  rows=dict(coefficient=20161, degree=10**6, suffix_slope=4 * 10**6, degree_gap=Q(10**6) - Q(51 * 20161, 25)))
+    q = bit * (1 - 2 * eta); mn = (1 - eta) * q / (1 + q); t = mn * 10**18; k = Q((t.numerator - 1) // t.denominator, 10**18)
+    asm = outer.assembly(bit, b, bridge, k, eta=eta, beta=beta)
+    assert len(asm['strict_constraints']) == 47 and min(asm['strict_constraints'].values()) > 0
+    try:
+        outer.assembly(bit, b, bridge, k + grid, eta=eta, beta=beta); raise SystemExit('ADJACENT ADMITTED')
+    except AssertionError: pass
+    return k, binding
+
+
+def price_word(c, **kw):
+    r = replay(c, **kw)
+    v, h, R = r['v'], r['h'], r['R']; m = 5 * h
+    resid = sum(h - r['sig'][x] for x in range(2 * v, 2 * v + R))
+    T = 1 if resid % h == 0 else h
+    W = (4 * v * h + resid) * T // h; assert (4 * v * h + resid) * T % h == 0
+    prof = Counter({j: T * k for j, k in profile(r['H'], v, h).items()}); mass = sum(a * b for a, b in prof.items())
+    L_copy = h * r['ncopy']
+    assert m * W - mass == T * (4 * v - 5 * L_copy), ('deficit', m * W - mass)
+    assert 2 * max(prof) < m
+    cc = coarse(prof, m, W)
+    return dict(c=cc, H=r['H'], prof=prof, W=W, T=T, resid=resid, m=m, deficit=m * W - mass, replay=r)
+
+
+def phi_fn(m, W, a):
+    """linearized moment term per child of rank r (float), for search scoring"""
+    import math
+    return lambda r: r / (m * W) * math.exp(a * math.log(m / r))
diff --git a/research/e8-eleven-hosting-selected/code/emit.py b/research/e8-eleven-hosting-selected/code/emit.py
new file mode 100644
index 0000000000..e033a8ceec
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/code/emit.py
@@ -0,0 +1,259 @@
+# Kernel integration of PR436/PR386 by chafreaky, with OpenAI Codex assistance.
+# Original copyright and attribution retained below. This variant uses explicit
+# residual isometries and mixed-width banks; the original all-zero-start
+# requirement is replaced by the verified kernel entrance contract.
+"""Source-bound eleven-stage bit template with 8 independent replicas and no helper banks.
+PR386 global identity and PR436 generalization by Zhihao Chen and eumemic,
+with their disclosed OpenAI Codex and Anthropic Claude assistance, Apache-2.0.
+PR439 explicit residual routes and this replication extension by chafreaky,
+with OpenAI Codex assistance. All owner assignments and emitted calls are checked.
+Historical PR386 regression is performed by the unchanged parent wrapper.
+"""
+import argparse, gzip, hashlib, json, struct, time, sys
+from collections import Counter
+from pathlib import Path
+HERE=Path(__file__).resolve().parent
+sys.path.insert(0,str(HERE.parents[1]/"e8-r740-replica32/code"))
+sys.path.insert(0,str(HERE.parents[1]/"idle-axis-hosting"))
+from bank_routes import validate_isometries
+import hosting_core as HC
+
+H,L,K,T,M=8,11,5,8,78
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+def write(p,x): p.write_text(json.dumps(x,indent=2)+'\n')
+
+def recipe():
+    out=[dict(kind='local',stage=0,pair=0,reverse=False)]; stage=1
+    for j in range(K):
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=True)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=1))
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=False)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=-1))
+    for j in reversed(range(K-1)): out.append(dict(kind='bridge',dst=j+1,src=j,coefficient=1))
+    out.append(dict(kind='exchange'))
+    return out
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--word',type=Path,required=True)
+    ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    ap.add_argument('--isometries',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out; out.mkdir(parents=True,exist_ok=True)
+    wp=a.word; w=json.loads(gzip.decompress(wp.read_bytes()))
+    V,R=w['v'],w['R']; LOCAL=2*V+R; DATA=2*K*V*T; LIVE=DATA+L*R
+    assert (w['h'],V,w['form'])==(8,120,'<x,y>/2')
+    geo=json.loads((out/'GEOMETRY.json').read_text())
+    assert geo['status']=='PASS_COMPRESSED_ELEVEN_BIT_GEOMETRY'
+    # the port routes depend only on the labels: same 120 label vectors, in the same order
+    assert len(geo['ports'])==V and all(p['port']==t and p['q']==w['lines'][t] for t,p in enumerate(geo['ports']))
+    rp=a.local_check/'records/249-records.bin'; raw=rp.read_bytes(); rec=list(struct.iter_unpack('<6i',raw))
+    state=json.loads((a.local_check/'records/249-states.json').read_text())
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    dims={int(f):z['dim'] for f,z in fs.items()}
+    parent_global=json.loads((a.local_check/'nine/GLOBAL.json').read_text())
+    assert (state['v'],state['n'])==(V,LOCAL)
+    ADDS=sum(row[0]==1 for row in rec)
+    assert ADDS==parent_global['local_additions']
+    initial=[state['initial'][str(i)] for i in range(LOCAL)]
+    final=[state['final'][str(i)] for i in range(LOCAL)]
+    assert all(dims[final[i]]==H for i in range(2*V,LOCAL))
+    widths=[H-dims[initial[i]] for i in range(2*V,LOCAL)]
+    ENT=sum(H-z for z in widths)
+    NB=0;LIVE=DATA
+    assert T==8 and M==8+7*(L-1)
+    isometries=json.loads(a.isometries.read_text())
+    assert validate_isometries(isometries,w['frames'],w['lines'],dims)==set(initial[2*V:])
+    streams={}; checks={}; localH=None
+    for reverse in (False,True):
+        cur=(final if reverse else initial)[:]+[-1]; val=[1<<i for i in range(LOCAL)]+[0]
+        norm=[1]*LOCAL+[0]; maxnorm=1; center=None; hist=Counter(); events=[]; copies=0; adds=0
+        dim=lambda f:H-dims[f] if reverse else dims[f]
+        for op,x,y,c,f,z in (reversed(rec) if reverse else rec):
+            if op==0:
+                oldf,newf=(c,y) if reverse else (y,c)
+                assert cur[x]==oldf and dim(newf)-dim(oldf)==f>=0
+                cur[x]=newf
+                if f: hist[f]+=1
+                events.append([0,x,oldf,newf,f,int(reverse)])
+            elif op==1:
+                assert cur[x]==cur[y]==f and x!=y and x<LOCAL
+                if center is not None: assert x!=center
+                if y==LOCAL: assert center is not None
+                if c&1: val[x]^=val[y]
+                norm[x]+=abs(c)*norm[y]; maxnorm=max(maxnorm,norm[x]); adds+=1
+                events.append([1,x,y,-c if reverse else c,f,int(reverse)])
+            elif op==(3 if reverse else 2):
+                assert center is None and y==LOCAL and cur[x]==c and val[LOCAL]==0
+                copy_rank=abs(dim(c)-dim(f)); assert copy_rank==8
+                assert z==(0 if reverse else copy_rank)
+                center=x; cur[LOCAL]=f; val[LOCAL]=val[x]; norm[LOCAL]=norm[x]
+                hist[copy_rank]+=1; copies+=1; events.append([2,x,LOCAL,c,f,copy_rank,int(reverse)])
+            else:
+                assert op==(2 if reverse else 3)
+                assert center==x and y==LOCAL and cur[x]==c and cur[LOCAL]==f
+                assert val[LOCAL]==val[x]
+                val[LOCAL]=0; norm[LOCAL]=0; cur[LOCAL]=-1; center=None
+                events.append([3,x,LOCAL,c,f,z,int(reverse)])
+        assert center is None and copies==9 and adds==ADDS
+        assert cur[:LOCAL]==(initial if reverse else final)
+        for i in range(LOCAL):
+            want=(1<<i) ^ ((1<<(i-V)) if V<=i<2*V else 0)
+            assert val[i]==want
+        assert val[LOCAL]==0
+        if localH is None: localH=hist
+        else: assert localH==hist
+        key='reverse' if reverse else 'forward'; streams[key]=events
+        checks[key]=dict(copies=copies,adds=adds,records=len(events),all_columns=LOCAL,
+                         cancellation_free_row_l1=maxnorm,profile=dict(sorted(hist.items())),
+                         sha256=hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest())
+    assert sum(r*n for r,n in localH.items())==H*R-ENT+72+2*V*(H-1)
+    assert localH==Counter({int(r):n for r,n in parent_global['local_checks']['forward']['profile'].items()})
+
+    events=recipe(); levels=[-1]*K; schedule=[]; bridge_controls=[]
+    # Full scalar replay on separate dirty helpers for all eleven stages.
+    # Physical hosting then uses the separately checked injective cover owners.
+    n=2*K*V+L*R; vals=[1<<i for i in range(n)]+[0]; temp=n
+    stages=[]
+    for e in events:
+        if e['kind']=='local':
+            s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1
+            def mapper(i):
+                if i==LOCAL: return temp
+                if i<2*V:
+                    side=i//V; side=1-side if rev else side
+                    return (2*p+side)*V+i%V
+                return 2*K*V+s*R+i-2*V
+            before=vals[:]; opened=False
+            for z in streams['reverse' if rev else 'forward']:
+                if z[0]==0: continue
+                x,y=mapper(z[1]),mapper(z[2])
+                if z[0]==1:
+                    if z[3]&1: vals[x]^=vals[y]
+                elif z[0]==2:
+                    assert not opened; vals[temp]=vals[x]; opened=True
+                else:
+                    assert opened and vals[temp]==vals[x]; vals[temp]=0; opened=False
+            assert not opened
+            d=(2*p+(0 if rev else 1))*V; src=(2*p+(1 if rev else 0))*V
+            for t in range(V): before[d+t]^=before[src+t]
+            assert vals==before
+            levels[p]=s; schedule.append(dict(kind='local_cover_sweep',**{k:v for k,v in e.items() if k!='kind'}))
+            if s in range(1,2*K-1,2):
+                j=(s+1)//2; assert levels[j]==-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7*(s+1),source_level=-1,target_level=s))
+            elif s in range(2,2*K,2):
+                j=s//2; assert levels[j]==s-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7,source_level=s-1,target_level=s))
+            elif s==2*K:
+                for j in range(K):
+                    oldlevel=levels[j]; assert oldlevel==2*j+2
+                    schedule.append(dict(kind='idle',pair=j,rank=7*(2*K-oldlevel),source_level=oldlevel,target_level=2*K))
+                    levels[j]=2*K
+            stages.append(dict(stage=s,all_columns=n,helper_columns=L*R,reverse=rev))
+        elif e['kind']=='bridge':
+            d,s=e['dst'],e['src']; assert levels[d]==levels[s]
+            for t in range(V): vals[2*d*V+t]^=vals[2*s*V+t]; vals[(2*s+1)*V+t]^=vals[(2*d+1)*V+t]
+            schedule.append(e)
+        else:
+            assert levels==[2*K]*K
+            for j in range(K):
+                for t in range(V):
+                    x=2*j*V+t; y=(2*j+1)*V+t; vals[x],vals[y]=vals[y],vals[x]
+            schedule.append(e)
+    assert vals==[1<<i for i in range(n)]+[0]
+    # Integer scalar ten-wire matrix, with each individual bridge shear omitted.
+    def small(skip=-1):
+        z=[[int(i==j) for j in range(2*K)] for i in range(2*K)]; count=0
+        def add(d,s,c): z[d]=[x+c*y for x,y in zip(z[d],z[s])]
+        for e in events:
+            if e['kind']=='local':
+                p=e['pair']; add(2*p,2*p+1,-1) if e['reverse'] else add(2*p+1,2*p,1)
+            elif e['kind']=='bridge':
+                d,s,c=e['dst'],e['src'],e['coefficient']
+                for x,y,sgn in [(2*d,2*s,c),(2*s+1,2*d+1,-c)]:
+                    if count!=skip: add(x,y,sgn)
+                    count+=1
+            else:
+                for j in range(K): z[2*j],z[2*j+1]=z[2*j+1],[-x for x in z[2*j]]
+        return z,count
+    ident=[[int(i==j) for j in range(2*K)] for i in range(2*K)]
+    z,nb=small(); assert z==ident and nb==6*(K-1)
+    for skip in range(nb): assert small(skip)[0]!=ident; bridge_controls.append(skip)
+
+    # Freeze and expand the full-helper idle assignment for one replica.
+    indexed=[];idx=0
+    for e in schedule:
+        if e['kind']=='local_cover_sweep': indexed.append(dict(kind='local',stage=e['stage'],pair=e['pair']))
+        elif e['kind']=='bridge': indexed.append(dict(kind='bridge',dst=e['dst'],src=e['src']))
+        elif e['kind']=='idle':
+            e['idx']=idx;indexed.append(dict(kind='idle',idx=idx,pair=e['pair'],rank=e['rank']));idx+=1
+    win={i:w for i,w in HC.windows(indexed).items() if w[1] and w[2]}
+    ys,zs,proxy=HC.load_selection(HERE.parent/'data/selection.json','bit')
+    slots,rem=HC.expand(win,ys,zs,{s:list(enumerate(widths)) for s in range(L)},2*V)
+    hosted={(s,h):(i,cp,off,width) for i,cp,off,width,s,h in slots}
+    assert len(slots)==len(hosted)==L*R and set(hosted)=={(s,h) for s in range(L) for h in range(R)}
+    remainder={str(i):{str(r):n for r,n in sorted(Counter(rem[i,cp] for cp in range(2*V)).items())} for i in win}
+    paid=Counter(); calls=[]; assignment=set(); expanded=hashlib.sha256(); full_event_count=0
+    for e in events:
+        if e['kind']!='local': continue
+        s,p,rev=e['stage'],e['pair'],e['reverse']; ori='reverse' if rev else 'forward'
+        for rep in range(T):
+            owners=[]
+            for i in range(2*V):
+                side=i//V; side=1-side if rev else side
+                owners.append([rep*(2*K*V)+(2*p+side)*V+i%V, ['data',s,i%V]])
+            for r in range(R):
+                i,cp,off,width=hosted[s,r];pair=win[i][0];side,port=divmod(cp,V)
+                family=rep*(2*K*V)+(2*pair+side)*V+port
+                owners.append([family,['hosted',i,off,width]])
+                assignment.add((s,rep,r,family,off))
+            assert len({(f,tuple(route)) for f,route in owners})==LOCAL
+            assert all(0<=f<LIVE for f,route in owners)
+            # Stream one full renamed instruction program into a source-bound
+            # digest, including exact owner route descriptors and reflection.
+            for z in streams[ori]:
+                op=z[0]
+                if op==0: paid[z[4]]+=bool(z[4]); mapped=[op,owners[z[1]],*z[2:]]
+                else:
+                    ox=owners[z[1]]; oy=owners[z[2]] if z[2]<LOCAL else [LIVE,['private',0]]
+                    mapped=[op,ox,oy,*z[3:]]
+                    if op==2: paid[z[5]]+=1
+                expanded.update((json.dumps(mapped,separators=(',',':'))+'\n').encode()); full_event_count+=1
+            calls.append(dict(stage=s,replica=rep,pair=p,orientation=ori,owners=owners,local_hash=checks[ori]['sha256']))
+    paid.pop(0,None)
+    assert len(assignment)==L*T*R and len(calls)==L*T
+    for e in schedule:
+        if e['kind']=='idle' and e['rank']:
+            i=e['idx']
+            for cp in range(2*V):
+                r=rem[i,cp] if i in win else e['rank']
+                if r:paid[r]+=T
+    mass=sum(r*c for r,c in paid.items());assert M*LIVE-mass==(2*K*V-L*72)*T
+    cf=checks['forward']['cancellation_free_row_l1']; cb=checks['reverse']['cancellation_free_row_l1']
+    prefix=(1<<nb)*cf**(K+1)*cb**K; assert prefix<1<<192
+    template=dict(version='compressed-eleven-hosted-e8-bit-v1',m=M,h=H,stages=L,replicas=T,live=LIVE,private_centre_reserve=9,
+                  cover='O(I_78/2,F_q) for admitted odd address primes q',loop_order='Each recipe phase: replicas then all cover classes; finish every local invocation before the next.',
+                  schedule=schedule,local_programs=streams,calls=calls,bank_padding=None,
+                  helper_route='Exact residual isometry from the listed root basis, extended by identity and mapped onto the assigned pending idle coordinates using PR442 hosting.',
+                  residual_isometries=isometries,banks_per_stage=NB,entrance_rank_total=ENT,
+                  hosting=dict(windows={str(i):[w[0],w[1],sorted(w[2])] for i,w in win.items()},slots=[list(x) for x in slots],remainders=remainder),
+                  data_route='owner (replica*1200 + (2*pair+side)*120+port, d*rho_stage,port)',
+                  bit_operator='D_U exchanges the two address halves on projector U; D_I D_P = D_(I-P) exactly.',
+                  geometry_sha256=sha(out/'GEOMETRY.json'),source_record_sha256=sha(rp))
+    blob=json.dumps(template,separators=(',',':'),sort_keys=True).encode(); (out/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+    result=dict(status='PASS_SOURCE_BOUND_ELEVEN_STAGE_HOSTED_BIT_TEMPLATE',h=H,m=M,v=V,R=R,replicas=T,live=LIVE,physical=LIVE+9,
+                word_sha256=sha(wp),source_records_sha256=sha(rp),local_checks=checks,scalar_stages=stages,
+                independent_unbanked_scalar_columns=n,all_scalar_columns_restored=True,
+                geometry_sha256=sha(out/'GEOMETRY.json'),template_sha256=hashlib.sha256(blob).hexdigest(),
+                emitted_program_sha256=expanded.hexdigest(),emitted_events=full_event_count,local_invocations=len(calls),
+                bank_assignments=0,hosted_residuals=len(assignment),banks_per_stage=NB,entrance_rank_total=ENT,residual_bank_slots=False,padding_calls=0,
+                profile=dict(sorted(paid.items())),paid_calls=sum(paid.values()),rank_mass=mass,deficit=(2*K*V-L*72)*T,
+                maxchild=max(paid),halving_depth=3,halving_integer_inequality=[M**3,2*max(paid)**3],
+                local_additions=ADDS,bridge_additions=6*(K-1)*V*T,copy_erase_episodes=9*L*T,
+                global_prefix_bound=str(prefix),global_prefix_bits=prefix.bit_length(),charged_prefix_bits=192,
+                omitted_bridge_shears_rejected=bridge_controls,
+                scope='Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; idle-data hosting follows conditionally from PR442 plus injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.',
+                seconds=time.monotonic()-start)
+    write(out/'GLOBAL.json',result)
+    print(json.dumps({k:v for k,v in result.items() if k not in ('local_checks','scalar_stages','global_prefix_bound')}),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-eleven-hosting-selected/code/engines/base_two_moment.py b/research/e8-eleven-hosting-selected/code/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/code/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/e8-eleven-hosting-selected/code/engines/moment.py b/research/e8-eleven-hosting-selected/code/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/code/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/e8-eleven-hosting-selected/code/engines/outer.py b/research/e8-eleven-hosting-selected/code/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/code/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/e8-eleven-hosting-selected/code/geometry.py b/research/e8-eleven-hosting-selected/code/geometry.py
new file mode 100644
index 0000000000..b4ad507401
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/code/geometry.py
@@ -0,0 +1,111 @@
+"""Exact compressed eleven-stage E8 bit geometry; no external research fetches.
+
+Prepared by Zhihao Chen with OpenAI Codex assistance, Apache-2.0.
+Eleven-stage extension by chafreaky with OpenAI Codex assistance.
+Uses the E8 root data and port-reflection construction credited to PR #370.
+"""
+import argparse, gzip, hashlib, json, time
+from pathlib import Path
+import sympy as S
+
+def dump(p, x): p.write_text(json.dumps(x,indent=2,default=str)+'\n')
+def digest(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def factor(a):
+    """Exact elementary factorization, reconstructed from the identity."""
+    n=a.rows; z=a.copy(); ops=[]
+    for j in range(n):
+        p=next(i for i in range(j,n) if z[i,j])
+        if p!=j: z.row_swap(p,j); ops.append(['swap',p,j,None])
+        if z[j,j]!=1:
+            c=1/z[j,j]; z[j,:]=c*z[j,:]; ops.append(['scale',j,None,c])
+        for i in range(n):
+            if i!=j and z[i,j]:
+                c=-z[i,j]; z[i,:]=z[i,:]+c*z[j,:]; ops.append(['add',i,j,c])
+    assert z==S.eye(n)
+    def replay(skip=-1):
+        z=S.eye(n)
+        for k in reversed(range(len(ops))):
+            if k==skip: continue
+            typ,i,j,c=ops[k]
+            if typ=='swap': z.row_swap(i,j)
+            elif typ=='scale': z[i,:]=z[i,:]/c
+            else: z[i,:]=z[i,:]-c*z[j,:]
+        return z
+    assert replay()==a
+    assert ops and replay(0)!=a
+    return [[t,i,j,None if c is None else str(c)] for t,i,j,c in ops]
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--source',type=Path,required=True)
+    ap.add_argument('--out',type=Path,required=True); a=ap.parse_args(); t0=time.monotonic()
+    a.out.mkdir(parents=True,exist_ok=True)
+    p=a.source/'data/bit/bitE8-r865.json.gz'; w=json.loads(gzip.decompress(p.read_bytes()))
+    assert (w['h'],w['v'],w['R'],w['form'])==(8,120,865,'<x,y>/2')
+    lines=[S.Matrix(x) for x in w['lines']]; I=S.eye(8); Z=S.zeros(8)
+    assert lines[0]==S.Matrix([2,0,0,0,0,0,0,0])
+    ip=lambda u,v:(u.T*v)[0]/2
+    gs={0:I}; todo=[0]
+    while todo:
+        more=[]
+        for i in todo:
+            for j in range(120):
+                if j in gs or abs(ip(lines[i],lines[j]))!=1: continue
+                d=lines[i]-lines[j] if ip(lines[i],lines[j])==1 else lines[i]+lines[j]
+                r=I-d*d.T/(d.T*d)[0]*2
+                gs[j]=r*gs[i]; more.append(j)
+        todo=more
+    assert len(gs)==120
+    recipes=[]; denoms=set(); max_factors=0
+    for t,q in enumerate(lines):
+        g=gs[t]; assert g.T*g==I and g*lines[0] in (q,-q)
+        P=q*q.T/4; K=I-P; A=g[:,1:]
+        assert A.T*A==S.eye(7) and A*A.T==K and P*A==S.zeros(8,7)
+        rho=P.row_join(A).col_join(A.T.row_join(S.zeros(7)))
+        assert rho.T==rho and rho*rho==S.eye(15)
+        expected={'P':S.diag(I,S.zeros(7)), 'H':S.eye(15),
+                  '0':S.diag(K,S.zeros(7)), 'K':S.diag(K,S.eye(7))}
+        for name,U in [('P',P),('H',I),('0',Z),('K',K)]:
+            assert rho*S.diag(U,S.eye(7))*rho==expected[name]
+        # Exact bit address operators D_U: head/tail exchange on U.
+        # Unlike complex C_U, they carry no omitted scalar/translation phase.
+        def D(U): return (I-U).row_join(U).col_join(U.row_join(I-U))
+        assert D(I)*D(P)==D(K) and D(P)*D(P)==S.eye(16)
+        ops=factor(rho); max_factors=max(max_factors,len(ops))
+        for typ,i,j,c in ops:
+            if c is not None: denoms.add(int(S.Rational(c).q))
+        # Compact exact global matrices: these 15 axes are the first eight
+        # local coordinates and exterior block s. All other axes are fixed.
+        routes=[dict(stage=0,axes=list(range(8)),identity=True)]
+        for s in range(1,11):
+            axes=list(range(8))+list(range(8+7*(s-1),8+7*s))
+            assert len(set(axes))==15 and max(axes)<78
+            routes.append(dict(stage=s,axes=axes,elementary_inverse_replay=ops))
+        recipes.append(dict(port=t,q=list(map(int,q)),complement_columns=[[str(x) for x in row] for row in A.tolist()],
+                            rho15=[[str(x) for x in row] for row in rho.tolist()],routes=routes))
+        if t%30==0: print('compressed geometry',t+1,flush=True)
+    # Exact nested data levels: local I (or K_q) plus s exterior rank-7
+    # blocks. Width 78=8+10*7; each bridge sees identical complete operators.
+    idle=[]
+    for j in range(1,5):
+        idle += [dict(pair=j,source_level=-1,target_level=2*j-1,rank=14*j,phase='before_positive_bridge'),
+                 dict(pair=j,source_level=2*j-1,target_level=2*j,rank=7,phase='before_negative_bridge')]
+    for j in range(5):
+        idle.append(dict(pair=j,source_level=2*j+2,target_level=10,rank=14*(4-j),phase='terminal'))
+    assert sum(z['rank'] for z in idle)==308
+    # Every residual is hosted in a data family; no helper bank exists.
+    slots=[];perms=[]
+    out=dict(status='PASS_COMPRESSED_ELEVEN_BIT_GEOMETRY',h=8,m=78,stages=11,
+             word_sha256=digest(p),ports=recipes,idle_per_port_and_data_member=idle,
+             local_window='U direct_sum E_s, with E_s the first s exterior coordinate 7-blocks',
+             ambient_form='I_78/2',bank_slots=slots,bank_permutations=perms,
+             route_checks=1320,exact_bit_endpoint_operator_checks=240,
+             max_route_factors=max_factors,route_denominators=sorted(denoms),
+             bad_prime_factors=sorted({int(q) for d in denoms for q in S.factorint(d)}),
+             missing_route_factor_controls=120,bank_free=True,
+             scope='All port isometries, stage boundary identities, nested idle ranks, exact bit endpoint operators and coordinate embeddings. No residual banks are used. Full local-word scalar and chronological lowering are checked separately.',
+             seconds=time.monotonic()-t0)
+    dump(a.out/'GEOMETRY.json',out)
+    print(json.dumps({k:v for k,v in out.items() if k not in ('ports','bank_permutations','idle_per_port_and_data_member')}),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-eleven-hosting-selected/code/hosting_core.py b/research/e8-eleven-hosting-selected/code/hosting_core.py
new file mode 100644
index 0000000000..68b536daa9
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/code/hosting_core.py
@@ -0,0 +1,138 @@
+"""Idle-axis hosting: place whole dirty-helper residuals on the pending coordinates of an idle data family.
+
+A data family that is advanced by an idle child from level a to level b receives the commuting coordinate factors of
+that child.  If the family is untouched (no local invocation on its pair and no bridge naming its pair) during an
+interval of local invocations ending at the child, a helper residual of width w from an invocation inside that
+interval may own w of those pending coordinates instead of a bank slot.  The child keeps only the remaining
+coordinates.  This module computes the windows from the recipe and chooses, per replica, how many residuals of each
+width each child hosts (exact integer programme), then expands that choice into explicit slot assignments.
+Standard library plus scipy for the integer programme; the emitted assignment is re-checked without scipy."""
+import math
+from collections import Counter, defaultdict
+
+def windows(schedule):
+    """schedule: ordered events dict(kind='local',stage,pair) | dict(kind='bridge',dst,src) | dict(kind='idle',pair,rank,idx).
+    Returns {idx: (pair, rank, frozenset(stages))} - stages whose invocation lies strictly between the last touch of
+    the pair and the idle child."""
+    last = {}; out = {}; locals_ = []
+    for pos, e in enumerate(schedule):
+        k = e['kind']
+        if k == 'local':
+            locals_.append((pos, e['stage'], e['pair'])); last[e['pair']] = pos
+        elif k == 'bridge':
+            last[e['dst']] = pos; last[e['src']] = pos
+        elif k == 'idle':
+            p = e['pair']; lo = last.get(p, -1)
+            st = frozenset(s for q, s, pp in locals_ if lo < q < pos and pp != p)
+            out[e['idx']] = (p, e['rank'], st)      # an idle child acts on other coordinates (or the other member): not a touch
+    return out
+
+def patterns(rank, widths, maxk=12):
+    """multisets of widths with sum <= rank (as sorted tuples)"""
+    ws = sorted(set(widths), reverse=True); res = []
+    def rec(i, cur, s):
+        if i == len(ws): res.append(tuple(cur)); return
+        w = ws[i]; k = 0
+        while s + k * w <= rank and len(cur) + k <= maxk:
+            rec(i + 1, cur + [w] * k, s + k * w); k += 1
+    rec(0, [], 0)
+    return res
+
+def cost(r, m):
+    return r * math.log(m / r) if r else 0.0
+
+def solve(win, copies, avail, m, pad_value=0.0, group=None):
+    """win: {idx: (pair, rank, stages)}; copies: piece copies per replica of each idx (2V);
+    avail: {(stage, width): count per replica}; maximise saved idle cost (+ pad_value per hosted residual).
+    group: optional {width: g} - remaining count of that width per stage must be a multiple of g (exact bank tiling).
+    Returns {(idx, pattern): copies} and {(idx, width, stage): count}."""
+    import numpy as np
+    from scipy.optimize import milp, LinearConstraint, Bounds
+    widths = sorted({w for (_, w) in avail})
+    var = []; index = {}
+    for idx, (p, r, st) in win.items():
+        for pat in patterns(r, widths):
+            index[('y', idx, pat)] = len(var); var.append(('y', idx, pat))
+        for w in widths:
+            for s in st:
+                if avail.get((s, w), 0):
+                    index[('z', idx, w, s)] = len(var); var.append(('z', idx, w, s))
+    stages = sorted({s for (s, _) in avail})
+    if group:
+        for w, g in group.items():
+            for s in stages:
+                index[('g', w, s)] = len(var); var.append(('g', w, s))
+    n = len(var); c = np.zeros(n); integ = np.ones(n); lb = np.zeros(n); ub = np.full(n, np.inf)
+    for key, j in index.items():
+        if key[0] == 'y':
+            _, idx, pat = key; r = win[idx][1]; c[j] = -(cost(r, m) - cost(r - sum(pat), m) + pad_value * len(pat))
+    rows, lo, hi = [], [], []
+    for idx in win:
+        row = np.zeros(n)
+        for key, j in index.items():
+            if key[0] == 'y' and key[1] == idx: row[j] = 1
+        rows.append(row); lo.append(copies); hi.append(copies)
+        for w in widths:
+            row = np.zeros(n)
+            for key, j in index.items():
+                if key[0] == 'y' and key[1] == idx: row[j] = key[2].count(w)
+                if key[0] == 'z' and key[1] == idx and key[2] == w: row[j] = -1
+            rows.append(row); lo.append(0); hi.append(0)
+    for (s, w), a in avail.items():
+        row = np.zeros(n)
+        for key, j in index.items():
+            if key[0] == 'z' and key[2] == w and key[3] == s: row[j] = 1
+        if group and w in group:
+            row[index[('g', w, s)]] = group[w]; rows.append(row); lo.append(a); hi.append(a)   # used + g*k = avail
+        else:
+            rows.append(row); lo.append(0); hi.append(a)
+    res = milp(c, constraints=LinearConstraint(np.array(rows), lo, hi), integrality=integ, bounds=Bounds(lb, ub),
+               options=dict(time_limit=600, disp=False))
+    assert res.x is not None, res.message
+    x = [int(round(t)) for t in res.x]
+    ys = {(k[1], k[2]): x[j] for k, j in index.items() if k[0] == 'y' and x[j]}
+    zs = {(k[1], k[2], k[3]): x[j] for k, j in index.items() if k[0] == 'z' and x[j]}
+    return ys, zs, -res.fun
+
+def expand(win, ys, zs, helpers, V2):
+    """helpers: {stage: [(helper, width), ...]} for ONE replica; returns list of
+    (idx, copy, offset, width, stage, helper) and the remainder rank of every (idx, copy).
+    Copies of a piece are the 2V (side, port) data families; residuals packed from offset 0 in decreasing width."""
+    pool = defaultdict(list)                    # (stage, width) -> helpers
+    for s, hs in helpers.items():
+        for h, w in hs: pool[s, w].append(h)
+    for k in pool: pool[k].sort()
+    need = defaultdict(list)                    # (idx, width) -> stages multiset in deterministic order
+    for (idx, w, s), cnt in sorted(zs.items()): need[idx, w] += [s] * cnt
+    out = []; rem = {}
+    for idx in sorted(win):
+        pats = sorted([(pat, cnt) for (i, pat), cnt in ys.items() if i == idx], key=lambda t: (-sum(t[0]), t[0]))
+        copy = 0; ptr = Counter()
+        r = win[idx][1]
+        for pat, cnt in pats:
+            for _ in range(cnt):
+                off = 0
+                for w in sorted(pat, reverse=True):
+                    s = need[idx, w][ptr[idx, w]]; ptr[idx, w] += 1
+                    h = pool[s, w].pop(0)
+                    out.append((idx, copy, off, w, s, h)); off += w
+                rem[idx, copy] = r - off; copy += 1
+        while copy < V2: rem[idx, copy] = r; copy += 1
+    return out, rem
+
+def save_selection(path, key, ys, zs, val):
+    """freeze the integer-programme choice (patterns per child, residual stages per child) for stdlib-only replay"""
+    import json
+    from pathlib import Path
+    p = Path(path); d = json.loads(p.read_text()) if p.exists() else {}
+    d[key] = dict(patterns=sorted([[i, list(pat), n] for (i, pat), n in ys.items()]),
+                  stages=sorted([[i, w, s, n] for (i, w, s), n in zs.items()]), proxy_saving=val)
+    p.write_text(json.dumps(d, indent=1, sort_keys=True) + '\n')
+
+def load_selection(path, key):
+    import json
+    from pathlib import Path
+    d = json.loads(Path(path).read_text())[key]
+    ys = {(i, tuple(pat)): n for i, pat, n in d['patterns']}
+    zs = {(i, w, s): n for i, w, s, n in d['stages']}
+    return ys, zs, d['proxy_saving']
diff --git a/research/e8-eleven-hosting-selected/code/row_bound.py b/research/e8-eleven-hosting-selected/code/row_bound.py
new file mode 100644
index 0000000000..11d3c0d48e
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/code/row_bound.py
@@ -0,0 +1,47 @@
+"""Elementary orthogonal-cover row count; no exact group-order formula is needed.
+
+Over an odd finite field, diagonalize a nondegenerate d-dimensional symmetric
+form. Fixing d-1 coordinates of a vector leaves a nonzero-coefficient quadratic
+in the last coordinate; hence a prescribed nonzero norm has at most 2*q^(d-1)
+solutions. The orthogonal complement of such a vector is nondegenerate.
+Induction while choosing the images of a diagonal orthogonal basis gives
+|O_m(q)| <= product(d=1..m, 2*q^(d-1)) = 2^m*q^(m*(m-1)/2).
+Since q>=3, this is strictly below q^(m*(m+1)/2). Physical family stock adds
+ceil(log_3(physical)) to this uniform exponent. The restored-row divisor
+argument in PR234/PR386 multiplies it by the halving depth, then adds the
+unchanged 9909 and 252 allowances. Routing-time bills still use m^2.
+
+This arithmetic checker verifies the exponent calculation and strict margins;
+the preceding elementary induction is the all-q proof, not a finite q sample.
+chafreaky with OpenAI Codex assistance, Apache-2.0.
+"""
+from fractions import Fraction
+
+def bound(m,physical,child,depth):
+    assert m>1 and physical>0 and 0<child<m and depth>0
+    assert m**depth>2*child**depth
+    overhead=0
+    while 3**overhead<=physical:overhead+=1
+    column_exponent=sum(d-1 for d in range(1,m+1))
+    assert column_exponent==m*(m-1)//2 and 2**m<3**m
+    cover_exponent=column_exponent+m
+    stock_exponent=cover_exponent+overhead
+    assert physical<3**overhead and 2**m*physical<3**(m+overhead)
+    row=depth*stock_exponent+9909+252
+    assert row<20161 and Fraction(10**6)-Fraction(51*20161,25)>0
+    return dict(method='successive nonzero-norm vectors in nondegenerate complements',
+                minimum_q=3,column_exponent=column_exponent,factor_two_power=m,
+                cover_exponent=cover_exponent,physical_families=physical,
+                physical_exponent=overhead,stock_exponent=stock_exponent,
+                halving_depth=depth,complete_row_coefficient=row,retained_row_coefficient=20161)
+
+def controls():
+    rejected=[]
+    for name,args in [('false two-level halving',(78,9609,56,2)),
+                      ('understated row reserve',(100,9609,90,7))]:
+        try:bound(*args)
+        except AssertionError:rejected.append(name)
+        else:raise AssertionError('accepted '+name)
+    # The original coarse enumeration bound does NOT fit this retained row cap.
+    assert 3*(78**2+1)+9909+252==28416>20161
+    return rejected
diff --git a/research/e8-eleven-hosting-selected/code/tile_m.py b/research/e8-eleven-hosting-selected/code/tile_m.py
new file mode 100644
index 0000000000..cd5fd9b539
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/code/tile_m.py
@@ -0,0 +1,93 @@
+"""Residual census (8 - sigma per helper) and an exact zero-padding bank tiling of width m = (2K+1)h with T replicas:
+tile() and economy_tile() verbatim from our PR #329 bank_template.py (via code/tile.py of our dtst3 package).
+usage: tile_m.py WORD.json.gz M [replicas]  (replicas default: the least T with T x residual sum = 0 mod M that tiles)"""
+import sys,os,collections
+from collections import Counter
+sys.path.insert(0,os.path.dirname(os.path.abspath(__file__)))
+from e8core import *
+def economy_tile(blocks, m):
+    """Exact zero-padding tiling used when the filler search of tile() runs out of filler blocks (the kernel pivots
+    and early restorations of the stage stack add many residual widths that do not divide m; the PR #299 analogue at
+    p = 12 was the (r^4, 24, 4^(24-r)) re-tiling). The fillers are the two most numerous widths dividing m (here the
+    full helper width h and the rank-4 entrance residual). Each other width w, in decreasing order, gets the bank
+    w^a F^c f^b (w*a + F*c + f*b = m) that spends the fewest narrow fillers f per w block (then the largest a), plus
+    at most one bank w^r F^c' f^b' for the remainder r = n mod a. The leftover fillers fill pure banks F^(m/F),
+    f^(m/f) and y residue banks F^j f^k. Every bank sums to m and every block is used exactly once (no padding)."""
+    from fractions import Fraction
+    blocks = {w: n for w, n in blocks.items() if n}
+    div = sorted((w for w in blocks if m % w == 0), key=lambda w: (-blocks[w], w))
+    assert len(div) >= 2, ('economy tiling needs two filler widths', blocks)
+    F, f = sorted(div[:2], reverse=True)
+
+    def fill(rest):
+        """(c, b) with F*c + f*b = rest, c maximal (fewest narrow fillers); None if impossible."""
+        return next(((c, (rest - F*c)//f) for c in range(rest//F, -1, -1) if (rest - F*c) % f == 0), None)
+
+    left = {F: blocks[F], f: blocks[f]}; out = []
+    for w in sorted((x for x in blocks if x not in (F, f)), reverse=True):
+        n = blocks[w]
+        opts = [(Fraction(cb[1], a), -a, a, cb) for a in range(m//w, 0, -1) for cb in [fill(m - w*a)] if cb]
+        assert opts, ('no bank for width', w)
+        _, _, a, (c, b) = min(opts); q, r = divmod(n, a)
+        if q: out.append(((w,)*a + (F,)*c + (f,)*b, q)); left[F] -= q*c; left[f] -= q*b
+        if r:
+            cb = fill(m - w*r); assert cb, ('no remainder bank', w, r)
+            out.append(((w,)*r + (F,)*cb[0] + (f,)*cb[1], 1)); left[F] -= cb[0]; left[f] -= cb[1]
+    assert left[F] >= 0 and left[f] >= 0, ('fillers exhausted', left)
+    pF, pf = m//F, m//f
+    for y in range((pF*pf) + 1):
+        for j in range(1 if y else 0, pF if y else 1):
+            if (m - F*j) % f: continue
+            k = (m - F*j)//f; aF, af = left[F] - y*j, left[f] - y*k
+            if aF >= 0 and af >= 0 and aF % pF == 0 and af % pf == 0:
+                out += ([((F,)*j + (f,)*k, y)] if y else []) + ([((F,)*pF, aF//pF)] if aF else []) + ([((f,)*pf, af//pf)] if af else [])
+                return out
+    raise AssertionError(('no exact zero-padding tiling', blocks, m))
+
+
+def tile(blocks, m):
+    """Exact tiling of {width: number of blocks} into banks of total width m, as ((widths, banks), ...).
+
+    A width dividing m fills pure banks. A width w not dividing m is mixed with a filler width f dividing m:
+    banks w^a f^b with a maximal (w*a + f*b = m), then at most one bank w^r f^t for the remainder r. Fillers
+    are tried in a fixed order (most blocks first) with backtracking until every pure width also divides out.
+    Fails (AssertionError) unless every block is used and every bank is full; there is no padding."""
+    blocks = {w: n for w, n in blocks.items() if n}
+    assert all(0 < w <= m for w in blocks)
+    mixed = sorted(x for x in blocks if m % x)
+
+    def search(i, left, out):
+        if i == len(mixed):
+            if any(left[w] % (m // w) for w in left): return None
+            return out + [(tuple([w]*(m // w)), left[w]//(m // w)) for w in sorted(left) if left[w]]
+        w = mixed[i]; n = blocks[w]
+        for f in sorted(left, key=lambda x: (-left[x], x)):
+            a = next((a for a in range(m // w, 0, -1) if (m - w*a) % f == 0), None)
+            if a is None: continue
+            b = (m - w*a)//f; q, r = divmod(n, a)
+            if r and (m - w*r) % f: continue
+            t = (m - w*r)//f if r else 0
+            if q*b + t > left[f]: continue
+            rest = dict(left); rest[f] -= q*b + t
+            found = search(i + 1, rest, out + ([(tuple([w]*a + [f]*b), q)] if q else []) + ([(tuple([w]*r + [f]*t), 1)] if r else []))
+            if found is not None: return found
+        return None
+    out = search(0, {w: n for w, n in blocks.items() if not m % w}, [])
+    if out is None: out = economy_tile(blocks, m)
+    assert all(sum(widths) == m and count > 0 for widths, count in out)
+    used = Counter()
+    for widths, count in out:
+        for x in widths: used[x] += count
+    assert used == Counter(blocks), 'every block used exactly once'
+    return tuple(out)
+if __name__ == '__main__':
+    c = load_word(sys.argv[1]); m = int(sys.argv[2])
+    L = Lat(c['lines']); M = to_masks(c, L); v = c['v']; n = 2 * v + c['R']
+    res = Counter(8 - L.dim(M[c['start'][r]]) for r in range(2 * v, n)); tot = sum(k * x for k, x in res.items())
+    reps = [int(sys.argv[3])] if len(sys.argv) > 3 else [t for t in range(1, 200) if t * tot % m == 0]
+    for T in reps:
+        try: pat = tile({r: T * k for r, k in res.items() if r > 0}, m); break
+        except AssertionError: pat = None
+    assert pat, 'no tiling'
+    print('   residual census', dict(sorted(res.items())), 'sum', tot)
+    print('   PASS exact width-%d tiling with %d replicas: %d banks' % (m, T, sum(k for _, k in pat)), pat)
diff --git a/research/e8-eleven-hosting-selected/data/selection.json b/research/e8-eleven-hosting-selected/data/selection.json
new file mode 100644
index 0000000000..7e36f3f270
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/data/selection.json
@@ -0,0 +1,513 @@
+{
+ "bit": {
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+  ]
+ }
+}
diff --git a/research/e8-eleven-hosting-selected/evidence/assembly.log b/research/e8-eleven-hosting-selected/evidence/assembly.log
new file mode 100644
index 0000000000..9f548bcb3b
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/evidence/assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_ELEVEN_STAGE_HOSTING_ASSEMBLY 0.001265848755025709 binding complex gain over #445 0.1966%
diff --git a/research/e8-eleven-hosting-selected/evidence/audit.log b/research/e8-eleven-hosting-selected/evidence/audit.log
new file mode 100644
index 0000000000..5e06462347
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/evidence/audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_ELEVEN_STAGE_HOSTING_AUDIT", "template_sha256": "8d3580817dc305ec62d4a9bc2f3ceec6f571be1da91db464a9050b47e9036bbe", "emitted_program_sha256": "4ab6c4a1cecef52521cff258e2722f8755e65f5c9f8d87344ee78a1388bc57ec", "emitted_events": 1740288, "profile": {"1": 223960, "2": 93568, "3": 23528, "4": 34296, "5": 9504, "6": 2000, "7": 5112, "8": 792, "49": 8, "56": 440}, "live": 9600, "physical": 9609, "hosted_residuals": 65120, "bank_assignments": 0, "rank_mass": 745536, "deficit": 3264, "maxchild": 56, "geometry_routes": 1320, "halving_depth": 3, "mutations_rejected": ["slot outside window", "copy outside family", "negative slot offset", "wrong residual width", "duplicate helper", "missing helper", "cross-replica host", "cross-replica data", "wrong hosted coordinate", "helper changed to bank", "wrong call orientation", "duplicate call", "dropped final stage", "wrong idle rank", "omitted bridge", "wrong bridge sign", "omitted terminal exchange", "understated live stock", "missing remainder summary", "wrong residual isometry", "omitted local instruction", "wrong reflected copy rank"]}
diff --git a/research/e8-eleven-hosting-selected/evidence/draft-assembly.log b/research/e8-eleven-hosting-selected/evidence/draft-assembly.log
new file mode 100644
index 0000000000..ee608c69b0
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/evidence/draft-assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_ELEVEN_STAGE_HOSTING_ASSEMBLY 0.001265848755025708 binding complex gain over #445 0.1966%
diff --git a/research/e8-eleven-hosting-selected/evidence/eleven-kernel-screen-first-failure.log b/research/e8-eleven-hosting-selected/evidence/eleven-kernel-screen-first-failure.log
new file mode 100644
index 0000000000..5301172d3a
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/evidence/eleven-kernel-screen-first-failure.log
@@ -0,0 +1,8 @@
+rank138 widths Counter({8: 626, 7: 106, 4: 8})
+rank138 {'lower': '0.001264963576077378514188', 'upper': '0.001264963576077378514189', 'lower_endpoint_residual_upper': '-2.875480767539835571081718228727337621804110483269027000584762030996056E-24', 'upper_endpoint_residual_lower': '5.784170821291645329236105450415928776519175109291695949734503517906767E-25', 'strict_rational_signs': True, 'moment_minus_one_at_current_k_required_rate': ['-0.001965631554361473106301609572550609329705087054587936612065100225750303', '-0.001965631554361473106301609572550609329705087054587936612065100225676119'], 'nominal_k_ceiling_interval': ['0.001263365464781156283335875383949443788201099818183217979492195563283368', '0.001263365464781156283336872858814606523490240182752727874312570542318136']}
+rank147 widths Counter({8: 617, 7: 115, 4: 8})
+Traceback (most recent call last):
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/screen_eleven_kernels.py", line 38, in <module>
+    assert len(slots)==L*w['R'],('not all hosted',len(slots))
+           ^^^^^^^^^^^^^^^^^^^^
+AssertionError: ('not all hosted', 8139)
diff --git a/research/e8-eleven-hosting-selected/evidence/eleven-kernel-screen.log b/research/e8-eleven-hosting-selected/evidence/eleven-kernel-screen.log
new file mode 100644
index 0000000000..9a17269104
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/evidence/eleven-kernel-screen.log
@@ -0,0 +1,4 @@
+rank138 widths Counter({8: 626, 7: 106, 4: 8})
+rank138 {'lower': '0.001264963576077378514188', 'upper': '0.001264963576077378514189', 'lower_endpoint_residual_upper': '-2.875480767539835571081718228727337621804110483269027000584762030996056E-24', 'upper_endpoint_residual_lower': '5.784170821291645329236105450415928776519175109291695949734503517906767E-25', 'strict_rational_signs': True, 'moment_minus_one_at_current_k_required_rate': ['-0.001965631554361473106301609572550609329705087054587936612065100225750303', '-0.001965631554361473106301609572550609329705087054587936612065100225676119'], 'nominal_k_ceiling_interval': ['0.001263365464781156283335875383949443788201099818183217979492195563283368', '0.001263365464781156283336872858814606523490240182752727874312570542318136']}
+rank147 widths Counter({8: 617, 7: 115, 4: 8})
+rank147 {'lower': '0.001267514693114214441041', 'upper': '0.001267514693114214441042', 'lower_endpoint_residual_upper': '-2.782889730763200527593184403209346195401932589974601157479256446826582E-24', 'upper_endpoint_residual_lower': '6.640877076530205660573601780922367447521464703492231892297175440490870E-25', 'strict_rational_signs': True, 'moment_minus_one_at_current_k_required_rate': ['-0.001970464511653381971522895259680762831293435990600548790093478065563860', '-0.001970464511653381971522895259680762831293435990600548790093478065489676'], 'nominal_k_ceiling_interval': ['0.001265910133419942488379467346913241111194380468906392190363936825991158', '0.001265910133419942488380464816695502737204700300785447909471769059641653']}
diff --git a/research/e8-eleven-hosting-selected/evidence/emit-missing-engines.log b/research/e8-eleven-hosting-selected/evidence/emit-missing-engines.log
new file mode 100644
index 0000000000..782a7cb54c
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/evidence/emit-missing-engines.log
@@ -0,0 +1,16 @@
+Traceback (most recent call last):
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/eleven147-screen/code/emit.py", line 18, in <module>
+    from bank_routes import validate_isometries
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/eleven147-screen/code/bank_routes.py", line 9, in <module>
+    from tile_m import tile
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/eleven147-screen/code/tile_m.py", line 7, in <module>
+    from e8core import *
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/eleven147-screen/code/e8core.py", line 12, in <module>
+    moment = _load('moment'); other = _load('base_two_moment'); outer = _load('outer')
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/eleven147-screen/code/e8core.py", line 11, in _load
+    m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+                                            ~~~~~~~~~~~~~~~~~~~~^^^
+  File "<frozen importlib._bootstrap_external>", line 759, in exec_module
+  File "<frozen importlib._bootstrap_external>", line 896, in get_code
+  File "<frozen importlib._bootstrap_external>", line 954, in get_data
+FileNotFoundError: [Errno 2] No such file or directory: '/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/eleven147-screen/code/engines/moment.py'
diff --git a/research/e8-eleven-hosting-selected/evidence/emit-missing-vendor.log b/research/e8-eleven-hosting-selected/evidence/emit-missing-vendor.log
new file mode 100644
index 0000000000..6b83f07b23
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/evidence/emit-missing-vendor.log
@@ -0,0 +1,6 @@
+Traceback (most recent call last):
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/eleven147-screen/code/emit.py", line 18, in <module>
+    from bank_routes import validate_isometries
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/eleven147-screen/code/bank_routes.py", line 9, in <module>
+    from tile_m import tile
+ModuleNotFoundError: No module named 'tile_m'
diff --git a/research/e8-eleven-hosting-selected/evidence/emit.log b/research/e8-eleven-hosting-selected/evidence/emit.log
new file mode 100644
index 0000000000..63a7ed28fb
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/evidence/emit.log
@@ -0,0 +1 @@
+{"status": "PASS_SOURCE_BOUND_ELEVEN_STAGE_HOSTED_BIT_TEMPLATE", "h": 8, "m": 78, "v": 120, "R": 740, "replicas": 8, "live": 9600, "physical": 9609, "word_sha256": "ee4cda817d5220fdbba1d116556e3dacb3da553ed81af43e74f19365e1393a5c", "source_records_sha256": "f9e0f3cdbc6a4eb5bfaf3fd843731a79c26740a6c4715079f2228e94b8706403", "independent_unbanked_scalar_columns": 9340, "all_scalar_columns_restored": true, "geometry_sha256": "49bc07c36f27dc960c8c14e15b4eec75251dc845209809bc3ef677c8a271a7bc", "template_sha256": "8d3580817dc305ec62d4a9bc2f3ceec6f571be1da91db464a9050b47e9036bbe", "emitted_program_sha256": "4ab6c4a1cecef52521cff258e2722f8755e65f5c9f8d87344ee78a1388bc57ec", "emitted_events": 1740288, "local_invocations": 88, "bank_assignments": 0, "hosted_residuals": 65120, "banks_per_stage": 0, "entrance_rank_total": 147, "residual_bank_slots": false, "padding_calls": 0, "profile": {"1": 223960, "2": 93568, "3": 23528, "4": 34296, "5": 9504, "6": 2000, "7": 5112, "8": 792, "49": 8, "56": 440}, "paid_calls": 393208, "rank_mass": 745536, "deficit": 3264, "maxchild": 56, "halving_depth": 3, "halving_integer_inequality": [474552, 351232], "local_additions": 15446, "bridge_additions": 23040, "copy_erase_episodes": 792, "global_prefix_bits": 153, "charged_prefix_bits": 192, "omitted_bridge_shears_rejected": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], "scope": "Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; idle-data hosting follows conditionally from PR442 plus injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.", "seconds": 3.2126199159538373}
diff --git a/research/e8-eleven-hosting-selected/evidence/geometry.log b/research/e8-eleven-hosting-selected/evidence/geometry.log
new file mode 100644
index 0000000000..0b096e1ca5
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/evidence/geometry.log
@@ -0,0 +1,5 @@
+compressed geometry 1
+compressed geometry 31
+compressed geometry 61
+compressed geometry 91
+{"status": "PASS_COMPRESSED_ELEVEN_BIT_GEOMETRY", "h": 8, "m": 78, "stages": 11, "word_sha256": "1fb726ea3818fe0837cceb0dd22a71a0814f064e5e781628104610d6468e0e55", "local_window": "U direct_sum E_s, with E_s the first s exterior coordinate 7-blocks", "ambient_form": "I_78/2", "bank_slots": [], "route_checks": 1320, "exact_bit_endpoint_operator_checks": 240, "max_route_factors": 77, "route_denominators": [1, 2, 4], "bad_prime_factors": [2], "missing_route_factor_controls": 120, "bank_free": true, "scope": "All port isometries, stage boundary identities, nested idle ranks, exact bit endpoint operators and coordinate embeddings. No residual banks are used. Full local-word scalar and chronological lowering are checked separately.", "seconds": 2.211304625030607}
diff --git a/research/e8-eleven-hosting-selected/evidence/hosted147-full314.log b/research/e8-eleven-hosting-selected/evidence/hosted147-full314.log
new file mode 100644
index 0000000000..d4a5aa12c1
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/evidence/hosted147-full314.log
@@ -0,0 +1,27 @@
+RUN parent-full
+PASS parent-full
+RUN kernel-rebuild
+PASS kernel-rebuild
+RUN export-records
+Traceback (most recent call last):
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/early-reuse-publication/research/e8-hosting-selected-kernel/verify.py", line 37, in <module>
+    run('export-records',ORIGINAL/'vendor/export_records.py',b/'bit-source-centres.json',b/'records')
+    ~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/early-reuse-publication/research/e8-hosting-selected-kernel/verify.py", line 27, in run
+    assert q.returncode==0,(name,log.read_text()[-3000:])
+           ^^^^^^^^^^^^^^^
+AssertionError: ('export-records', '')
+
+During handling of the above exception, another exception occurred:
+
+Traceback (most recent call last):
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/early-reuse-publication/research/e8-hosting-selected-kernel/verify.py", line 50, in <module>
+    (OUT/'FAILURE.json').write_text(json.dumps(dict(error=repr(e),completed=steps),indent=2)+'\n');raise
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+  File "/opt/homebrew/Cellar/python@3.14/3.14.8/Frameworks/Python.framework/Versions/3.14/lib/python3.14/pathlib/__init__.py", line 809, in write_text
+    with self.open(mode='w', encoding=encoding, errors=errors, newline=newline) as f:
+         ~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+  File "/opt/homebrew/Cellar/python@3.14/3.14.8/Frameworks/Python.framework/Versions/3.14/lib/python3.14/pathlib/__init__.py", line 771, in open
+    return io.open(self, mode, buffering, encoding, errors, newline)
+           ~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+OSError: [Errno 28] No space left on device: '/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/hosted147-full314/FAILURE.json'
diff --git a/research/e8-eleven-hosting-selected/evidence/screen_eleven_kernels.py b/research/e8-eleven-hosting-selected/evidence/screen_eleven_kernels.py
new file mode 100644
index 0000000000..0f98229daf
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/evidence/screen_eleven_kernels.py
@@ -0,0 +1,49 @@
+"""Nominate eleven-stage hosting of exact local words; no global claim."""
+from pathlib import Path
+import sys,json,math
+from collections import Counter
+from fractions import Fraction as Q
+r=Path.cwd();sys.path.insert(0,str(r/'early-reuse-publication/research/e8-r740-idle-hosting'));import hosting_core as HC
+sys.path.insert(0,str(r/'source443-review/code/engines'));import moment as M
+out=r/'eleven-kernel-screen';out.mkdir(exist_ok=True)
+K=5;L=2*K+1;m=8+7*(L-1);T=8;c=.0012649635760773785
+HC.cost=lambda rank,m:rank*math.expm1(c*math.log(m/rank))/c if rank else 0.
+events=[dict(kind='local',stage=0,pair=0)];stage=1
+for j in range(K):
+ events.append(dict(kind='local',stage=stage,pair=j));stage+=1
+ if j<K-1:events.append(dict(kind='bridge',dst=j,src=j+1))
+ events.append(dict(kind='local',stage=stage,pair=j));stage+=1
+ if j<K-1:events.append(dict(kind='bridge',dst=j,src=j+1))
+for j in reversed(range(K-1)):events.append(dict(kind='bridge',dst=j+1,src=j))
+levels=[-1]*K;indexed=[];idx=0
+for e in events:
+ indexed.append(e)
+ if e['kind']!='local':continue
+ s=e['stage'];levels[e['pair']]=s
+ idles=[]
+ if s in range(1,2*K-1,2):
+  j=(s+1)//2;idles.append((j,7*(s+1)));levels[j]=s
+ elif s in range(2,2*K,2):
+  j=s//2;idles.append((j,7));levels[j]=s
+ elif s==2*K:
+  for j in range(K):idles.append((j,7*(2*K-levels[j])));levels[j]=2*K
+ for j,rank in idles:indexed.append(dict(kind='idle',idx=idx,pair=j,rank=rank));idx+=1
+win={i:w for i,w in HC.windows(indexed).items() if w[1] and w[2]}
+dims=[x['dim'] for k,x in sorted(json.loads((r/'research439-screen/records/frames.json').read_text())['frames'].items(),key=lambda kv:int(kv[0]))]
+for tag,path,hpath in [('rank138',r/'hosted138-screen/bit426-source-centres/bit-source-centres.json',r/'hosting443-kernel138-screen/RESULT.json'),('rank147',r/'hosting-kernel-growth/WORD.json',r/'hosting-kernel-growth/EXACT-LOCAL.json')]:
+ w=json.loads(path.read_text());counts=Counter(8-dims[w['start'][h]] for h in range(240,980));H={int(k):v for k,v in json.loads(hpath.read_text())['local_profile'].items()}
+ print(tag,'widths',counts,flush=True)
+ y,z,val=HC.solve(win,240,{(s,width):n for s in range(L) for width,n in counts.items()},m,pad_value=1000.0)
+ slots,rem=HC.expand(win,y,z,{s:list(enumerate([8-dims[w['start'][h]] for h in range(240,980)])) for s in range(L)},240)
+ assert len(slots)==L*w['R'],('not all hosted',len(slots))
+ paid=Counter({k:v*L*T for k,v in H.items()})
+ for e in indexed:
+  if e['kind']!='idle' or not e['rank']:continue
+  for cp in range(240):
+   q=rem[e['idx'],cp] if e['idx'] in win else e['rank']
+   if q:paid[q]+=T
+ assert m*(2*K*120*T)-sum(k*n for k,n in paid.items())==(2*K*120-L*72)*T
+ cert=M.certify(paid,m,2*K*120*T,True)
+ HC.save_selection(out/(tag+'-selection.json'),'bit',y,z,val)
+ result=dict(status='EXACT_AGGREGATE_ONLY_GLOBAL_PENDING',tag=tag,profile=dict(paid),widths=dict(counts),moment=cert)
+ (out/(tag+'.json')).write_text(json.dumps(result,indent=2)+'\n');print(tag,cert,flush=True)
diff --git a/research/e8-eleven-hosting-selected/upstream445/EXPECTED.json b/research/e8-eleven-hosting-selected/upstream445/EXPECTED.json
new file mode 100644
index 0000000000..8d13a297ec
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/EXPECTED.json
@@ -0,0 +1,67 @@
+{
+  "status": "PASS_CONDITIONAL_ELEVEN_STAGE_HOSTING_ASSEMBLY",
+  "kappa": "315841366195289/250000000000000000",
+  "bit_lower": "316240894019344628547/250000000000000000000000",
+  "complex_lower": "1267453159029119/1000000000000000000",
+  "binding_component": "bit",
+  "bit": {
+    "live": 9600,
+    "physical": 9609,
+    "maxchild": 56,
+    "rank_mass": 745536,
+    "hosted_residuals": 65120,
+    "prefix_bits": 153,
+    "charged_prefix_bits": 192,
+    "coefficient_bits": 153,
+    "three_level_coefficient_bits": 513,
+    "charged_three_level_coefficient_bits": 1024,
+    "row_coefficient": 19431
+  },
+  "complex": {
+    "live": 8400,
+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
+  },
+  "bit_profile": {
+    "1": 222640,
+    "2": 92312,
+    "3": 24704,
+    "4": 33448,
+    "5": 10384,
+    "6": 2144,
+    "7": 5456,
+    "8": 792,
+    "56": 376
+  },
+  "emitted_program_sha256": "274b8599ee2165f0b46ab068c435b7322c4e0f494f4392701536b4655986ab56",
+  "bank_assignments": 0,
+  "parent_kappa": "623036752743971/500000000000000000",
+  "row_bound": {
+    "method": "successive nonzero-norm vectors in nondegenerate complements",
+    "minimum_q": 3,
+    "column_exponent": 3003,
+    "factor_two_power": 78,
+    "cover_exponent": 3081,
+    "physical_families": 9609,
+    "physical_exponent": 9,
+    "stock_exponent": 3090,
+    "halving_depth": 3,
+    "complete_row_coefficient": 19431,
+    "retained_row_coefficient": 20161
+  },
+  "row_controls": [
+    "false two-level halving",
+    "understated row reserve"
+  ],
+  "halving_depth": 3,
+  "finite_controls": [
+    "old 128-bit prefix charge insufficient",
+    "old 512-bit composite charge insufficient"
+  ]
+}
diff --git a/research/e8-eleven-hosting-selected/upstream445/LICENSE b/research/e8-eleven-hosting-selected/upstream445/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
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+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
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+      "Contribution" shall mean any work of authorship, including
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+      designated in writing by the copyright owner as "Not a Contribution."
+
+      "Contributor" shall mean Licensor and any individual or Legal Entity
+      on behalf of whom a Contribution has been received by Licensor and
+      subsequently incorporated within the Work.
+
+   2. Grant of Copyright License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      copyright license to reproduce, prepare Derivative Works of,
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+      Work and such Derivative Works in Source or Object form.
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+   3. Grant of Patent License. Subject to the terms and conditions of
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+      institute patent litigation against any entity (including a
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+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
+      granted to You under this License for that Work shall terminate
+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
+      Work or Derivative Works thereof in any medium, with or without
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+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
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+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
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+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
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+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
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+          within a display generated by the Derivative Works, if and
+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+      implied, including, without limitation, any warranties or conditions
+      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+      PARTICULAR PURPOSE. You are solely responsible for determining the
+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
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+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
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+      on Your own behalf and on Your sole responsibility, not on behalf
+      of any other Contributor, and only if You agree to indemnify,
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diff --git a/research/e8-eleven-hosting-selected/upstream445/MANIFEST.json b/research/e8-eleven-hosting-selected/upstream445/MANIFEST.json
new file mode 100644
index 0000000000..f77cb0617f
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/MANIFEST.json
@@ -0,0 +1,17 @@
+{
+  "PROOF.md": "4aede2a05d9570cc5d8a19032513c973137ee9083f079ae845b04f3f362e2ca0",
+  "EXPECTED.json": "1a2e35da8c586be03201a8d102c72f681b0b6698bbcb3a2ea286d8b0d9c0c1e4",
+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "SOURCE.json": "976eebfec20d467f3384194fc03bd6f5b289a615e3b2deb70a7be910aaee8579",
+  "README.md": "15e76f8a2200af0f871b04d410ebd7fac059b800b5ec4a1f376a333c9f5638bf",
+  "verify.py": "4a161d35c65fa1d35e655c3957c05a8164a003ca05c3effe9fee7dc8d0f38090",
+  "NOTICE.md": "b80411c1db53d12bf43d6cbb8bf2804102f2e57be2a2f55dd7820c6c2f2b9570",
+  "proof/UPSTREAM-PR234-NOTICE.md": "ce978c8dfc8a2b36eed7a53014b1a792248b22ef4cee3edd8adab825a571c429",
+  "proof/INHERITED-ROW-DIVISOR.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8",
+  "code/audit.py": "9900a1b2f1f314f2b93ca8f99b5516ed2e1a7295d668ea51df2df89cef84e381",
+  "code/assemble.py": "42dbfaddd284088474a80f0b6e894332b6737b8e9f9b5c45260e21c5df139792",
+  "code/geometry.py": "9554182d67e434ea84b4430f909a2c400abc755d8487b51454a8e6968e62859d",
+  "code/emit.py": "ac63ee481f3d75cb9f0658faaa2412db81d55bc44d9f1ff1c0329ce1e75aa0d4",
+  "code/row_bound.py": "de4a9b9cd797e1a05da56f62cfe725c8728cea3a4aa031b7d1b0a68f869760d6",
+  "data/selection.json": "52dbbb68e8c147690d15eaa1d952df05d074b0c121885a4159d9f6732f391872"
+}
diff --git a/research/e8-eleven-hosting-selected/upstream445/NOTICE.md b/research/e8-eleven-hosting-selected/upstream445/NOTICE.md
new file mode 100644
index 0000000000..a9b3a02a45
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/NOTICE.md
@@ -0,0 +1,26 @@
+# Attribution and licence
+
+Eleven-stage R740 hosting, dimension78 geometry extension, complete construction,
+independent audit, elementary orthogonal-cover row count, enlarged finite invoice
+and release wrapper: chafreaky with substantial OpenAI Codex assistance.
+Apache-2.0. Credits do not imply review or endorsement.
+
+The complete PR444 and PR443 packages are unchanged and pinned. Their notices
+retain all earlier authorship and AI-assistance disclosures.
+
+- DaysSky, PR442 (Anthropic Claude assistance): idle-data hosting lemma,
+  selection expander, hosted complex supplier and finite assembly.
+- chafreaky, PR444/443/439 (OpenAI Codex assistance): replicated R740 kernel,
+  explicit residual isometries, hosted composition and independent audits.
+- Zhihao Chen / jacklightChen, PR386 (OpenAI Codex assistance): compressed
+  bit geometry, stage recipe and exact global scalar and projector audits.
+- eumemic, PR436 (Anthropic Claude assistance), and PR440/441 (OpenAI Codex
+  assistance): R740 local word and composed retiming witnesses.
+- Henry Grant / hcg890, PR234: restored-row divisor and ordinary-conversion
+  interface. Its inherited proof excerpt is preserved byte-identically with
+  the full upstream notice in `proof/`.
+- icekylinx PR433, rohanarun PR434, Dylan Crow PR370, Jacob Sussman and all
+  earlier contributors: see `../r740-idle-hosted-replicas/NOTICE.md`,
+  `../e8-r740-replica32/NOTICE.md` and the unchanged source-specific notices.
+
+No unconditional theorem or new Lean proof is claimed.
diff --git a/research/e8-eleven-hosting-selected/upstream445/PROOF.md b/research/e8-eleven-hosting-selected/upstream445/PROOF.md
new file mode 100644
index 0000000000..e63bf47269
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/PROOF.md
@@ -0,0 +1,126 @@
+# Eleven-stage composition
+
+## Compressed windows and complete calls
+
+Let h=8, K=5, L=2K+1=11, m=h+(L−1)(h−1)=78, v=120 and T=8.
+Use the unchanged R740 word of PR443, including its rank138 kernel and B-frame
+retiming. The local forward and reflected instruction lists, residual isometries,
+source spans and all-column identity are regenerated by the unchanged parent
+verifier before this construction runs.
+
+The compressed route of PR386 acts on the eight local axes and one exterior
+rank-seven block. Its exact 15×15 orthogonal matrix extends by identity on every
+other axis. Add exterior blocks nine and ten to the parent's eight blocks.
+`geometry.py` recomputes all 120 port matrices, elementary factorizations and
+endpoint equations and emits all 1,320 port/stage routes. The independent audit
+compares the local matrices to the freshly verified parent and checks every
+new coordinate embedding and all idle ranks. Adding an identical orthogonal
+exterior summand leaves each local projector difference unchanged, including
+its reflected counterpart, so the parent's checked nested local frames lift
+without new denominators or bad primes.
+
+The recipe begins with a forward invocation on pair zero. On each of five pairs
+it then performs a reflected invocation, a positive bridge to the next pair
+when present, a forward invocation, and the corresponding negative bridge.
+Required idle advances precede each bridge. After the final invocation, idle
+advances bring all pairs to level ten; reverse-order bridges and terminal
+exchanges complete the identity. The emitter replays all 9,340 independent F2
+columns with distinct stage helpers. A separate ten-wire integer matrix replay
+retains bridge signs; omitting any of the 24 bridge shears breaks the identity.
+The audit independently checks stage chronology, level matching, integer
+matrix identity and data ownership.
+
+## All helpers hosted
+
+Use exactly the idle-data hosting lemma stated in PR442 and retained by PR444.
+A complete local invocation applies the factor of a helper's residual projector
+on its owning stream, with arbitrary correlated input. During an untouched
+window on another data pair, place this whole residual on pending coordinates
+of that pair's next idle advance. Its factor commutes to the advance; leave only
+the complementary coordinates in the advance. The complete operator is unchanged.
+
+The frozen assignment hosts all 11×740 helpers in each replica. The audit checks
+last-touch windows directly from the emitted schedule; exact residual widths;
+helper and copy bounds; unique helpers; disjoint coordinate intervals; all eight
+replicas' physical owners; exclusion of the active pair; complete call coverage;
+and exact remainder children. There is no helper bank, partial bank or padding.
+The conditional correlated-data hosting interface remains a separate proof
+assumption; combinatorial checks are not a numerical address-space replay.
+
+The complete eight-replica paid profile is:
+
+```
+rank:       1      2      3      4      5     6     7    8   56
+count: 222640  92312  24704  33448  10384  2144  5456  792  376
+```
+
+Its rank mass is 745,536, and 78×9,600 − 745,536 = 3,264.
+The 65,120 hosted residuals and every unchanged local instruction appear in the
+88 emitted calls. The renamed stream contains 1,736,152 instructions. Its digest
+is recomputed independently. Twenty-two mutations reject changes to calls,
+bridges, signs, geometry-dependent ranks, local programs, residual isometries,
+replica owners, hosting windows, slots and remainder counts.
+
+## Three-level halving and row stock
+
+Two levels fail: 78²=6,084 ≤ 2×56²=6,272. Three levels succeed:
+78³=474,552 > 2×56³=351,232. The one-level moment is strictly below one; its
+third power is also below one. Floors can only reduce descendant widths.
+
+The coarse q^(m²+1) enumeration estimate would give complete row coefficient
+3×6,085+9,909+252=28,416, exceeding 20,161. We instead count actual orthogonal
+cover elements using the following elementary bound, valid for every odd q.
+
+Diagonalize a nondegenerate symmetric form in dimension d. For a specified
+nonzero norm, fixing d−1 coordinates leaves a nonzero-coefficient quadratic in
+the last coordinate, with at most two roots. Thus there are at most 2q^(d−1)
+choices for a vector of that norm. Its orthogonal complement is nondegenerate.
+Successively choosing the images of a diagonal orthogonal basis therefore gives
+
+```
+|O_m(q)| ≤ ∏(d=1..m) 2q^(d−1) = 2^m q^(m(m−1)/2) < q^(m(m+1)/2),  q ≥ 3.
+```
+
+For m=78 the cover exponent is 3,081. Physical stock is 9,609 families, including
+nine private-centre reserves, and 9,609 < 3^9 ≤ q^9. Thus the physical row divisor
+is strictly below q^3090. The inherited restored-row argument uses this divisor
+once per recursion depth, reusing restored rows for sequential operations; its
+statement is preserved verbatim in `proof/INHERITED-ROW-DIVISOR.tex`. Three-level
+halving gives complete coefficient
+
+```
+3×3,090 + 9,909 + 252 = 19,431 < 20,161.
+```
+
+This changes only the bound on actual stock. Finite routing-time charges still
+use the larger m² parameter. No faster group enumeration or new compiler
+interface is assumed. `row_bound.py` checks the exponents and strict margins and
+rejects false two-level halving and an overflowing row reserve. Its finite checks
+support the arithmetic; the induction above proves the bound uniformly in q.
+The complex row coefficient remains 15,443. Both fit the retained 20,161 bound,
+so the existing outer degree gap 10^6 − (51/25)×20,161 remains unchanged.
+
+## Finite invoice and exact assembly
+
+The global prefix bound is 2^24 times six forward and five reflected local
+cancellation-free row bounds. It uses 153 bits, charged at 192. All 65,120 helper
+routes, 23,040 bridge additions, 792 copy/erase episodes, private centres and
+paid children enter the coefficient. Each residual route retains the 144-factor
+isometry overcharge plus the two PR442 hosting factors. The three-level envelope
+(C+1)^3(E+1)^3 has 513 bits, so the inherited 512-bit cap is explicitly rejected
+and the new cutoff charges 1,024 bits. This only increases finite cutoffs.
+
+Two independent rational moment engines with the inherited bad-branch allowance
+certify c=1264963576077378514188/10^24 and bracket its next 10^-24 point.
+The full PR442 complex geometry, phases, hosted audit and finite invoice are
+freshly rerun through PR444; b=1267453159029119/10^18 is recomputed, not cited.
+The six bootstrap levels use the enlarged finite cutoff; all 47 strict outer
+inequalities pass. The next 10^-18 grid point and zero-η, zero-β and unit-β
+controls are rejected. The result is
+
+```
+κ = 315841366195289 / 250000000000000000 = 0.001263365464781156.
+```
+
+All all-size and hosting interfaces listed in the README remain explicit
+assumptions. The finite certificate does not discharge those hypotheses.
diff --git a/research/e8-eleven-hosting-selected/upstream445/README.md b/research/e8-eleven-hosting-selected/upstream445/README.md
new file mode 100644
index 0000000000..ffc20470ae
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/README.md
@@ -0,0 +1,49 @@
+# Eleven-stage hosted R740 supplier
+
+Conditional **κ = 0.001263365464781156**, **1.3877% above PR444**.
+The bit saving is `1264963576077378514188 / 10^24`. The freshly rebuilt
+PR442 complex supplier remains `1267453159029119 / 10^18`; the bit side binds.
+
+This uses PR443's unchanged R740 rank138 local word in **eleven compressed
+stages**, dimension **78**, and **eight replicas**. PR442 idle-data hosting
+places **all 65,120 helper occurrences** on pending idle coordinates. There
+are no helper banks or padding children. The emitted template has 88 local
+calls, 9,600 live families, 9,609 physical families and rank deficit 3,264.
+
+The largest child has rank 56, so halving needs three levels. The new finite
+invoice charges the 153-bit prefix at 192 bits and the 513-bit three-level
+coefficient at 1,024 bits. An elementary orthogonal-cover count gives complete
+row coefficient 19,431, within the unchanged 20,161 allowance. The old coarse
+matrix-count estimate would not fit; `PROOF.md` proves the sharper bound.
+
+## Reproduce
+
+Python 3.11+, SymPy, a C++17 compiler and Boost headers are required:
+
+```sh
+python -m pip install -r research/e8-r740-replica32/parent436/requirements.txt
+python -B research/r740-hosted-eleven/verify.py /tmp/r740-eleven-new
+```
+
+The output directory must not exist. Set `BOOST_INCLUDE` if needed. `--quick`
+skips only PR443's inherited exhaustive mutation suite; all new checks and the
+full hosted complex reconstruction remain enabled. No optimizer is required.
+
+The wrapper reconstructs PR444, generates the 78-dimensional geometry and all
+88 calls, replays all 9,340 unbanked scalar columns, rejects each of the 24
+missing bridge shears, and independently audits the changed schedule, owners,
+idle windows, residual routes and remainder children. It rejects 22 template
+mutations and checks the complete renamed instruction digest. Two rational
+moment engines, both finite invoices, three-level halving, six bootstrap levels,
+47 strict outer inequalities and adjacent-grid/parameter controls must pass.
+Source bytes and exact results are frozen by `SOURCE.json`, `MANIFEST.json`
+and `EXPECTED.json`. `RECEIPT.json` records each completed run.
+
+## Scope
+
+This is a conditional finite certificate. PR442's idle-data hosting extension,
+the inherited all-size compiler, correlated dirty-helper, restored-work,
+common-grid, precision and analytic interfaces remain assumptions. The new
+finite geometry, column identity, stock count and numerical inequalities are
+explicitly checked. No unconditional multiplication theorem, κ = 1 result or
+new Lean proof is claimed.
diff --git a/research/e8-eleven-hosting-selected/upstream445/SOURCE.json b/research/e8-eleven-hosting-selected/upstream445/SOURCE.json
new file mode 100644
index 0000000000..1ff86fa334
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/SOURCE.json
@@ -0,0 +1,297 @@
+{
+  "upstream443": "5a514e94f156edcc5fd827b87494d962f79d0f6c",
+  "upstream442": "4e16d001d505d4f21dd2bcfc44591f9be4c279bd",
+  "packages": {
+    "e8-r740-replica32": {
+      "commit": "5a514e94f156edcc5fd827b87494d962f79d0f6c",
+      "files": {
+        "PROOF.md": "380a5269e012cb7d54cdf13289b7187aa82c16d23ed1689c5986485398f5cdca",
+        "EXPECTED.json": "02f3fd3ac40f17f25822fa49d01ae6e84c2e02e2fafbf24f02845f24e02ec931",
+        "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+        "SOURCE.json": "20b4bc7418b62a7126fc476b0e8757f713f09dbe03b430048e9f66326688ea88",
+        "verify.sh": "3720f542e9cf1ec35b052dec130b9cb6eefa37798f73ba5a4026b400c78d0697",
+        "README.md": "86030e96e06e0df02cc775ed1e41122854bc8dba2d1f90eb30b646436028ae5f",
+        "MANIFEST.json": "11f8fc7eb52127b078c1d29029ba71a2e1bd3340e9f4d76c92fae1e22511d550",
+        "NOTICE.md": "cb5bb6520addd9517672136c5519df4a2c06ed17b8afa1ce24e63855689c114d",
+        "parent436/MANIFEST.sha256": "7c6d4bd2ac74710d8a8a68fd637b31df9028a2376b569732374a739092c34310",
+        "parent436/EXPECTED.json": "a9655e303cb2c40ce024443b27c0a810ffc24f1ee1e5b07eb19241fad399b5e2",
+        "parent436/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+        "parent436/requirements.txt": "b9f87c1ec529679c19b8421a7a69b377b54b89949cfc5e1b1ed8c134bfab8917",
+        "parent436/SOURCE-pr381.json": "c457c422d54645ad841c8528bf2efa6c253d1c134ee86c875b9b7d76d4f9520c",
+        "parent436/SOURCE-pr417.json": "d9b7e606f09b840ed9fe10dc8c8250b4cab9bbe5d0cacb62864ca8366a28b2b1",
+        "parent436/SOURCE-pr426.json": "f884cc42793a3afd249ebee20985f61422e7b5baf7c1fcab5b990e1959f31697",
+        "parent436/SOURCE-pr386.json": "bba849ed0a1af4d45a76ec734d5f0d07806da2b161f1b5ad8ea63cf2d64b5aa4",
+        "parent436/verify.sh": "19bf483b109163b0ccc941f459e70c2e37d20c9c04e69e7c8eb98f329577b26c",
+        "parent436/SOURCE-pr431.json": "71cd86e64217fc4db0199ae8e5ef65cb0cc2ed593e15f03bc1501d4b32fdeb66",
+        "parent436/README.md": "d737a3b77de97bdf67d2a140465be5b8886af6aa57516f78ad8f2839f3dae8cc",
+        "parent436/SOURCE-pr370.json": "352a68f0898535311c63cac879a52b686246ba80844f1a3cc2f3c3f6b1046b4d",
+        "parent436/SOURCE-pr425.json": "a2c5e2f0e03b0dbcba4ca18282a4ff390a6a395f14411410cfff42d5281d0289",
+        "parent436/SOURCE-pr433.json": "f1181aa9f30dcc2e5df7e94738fa0c0cabe5f56b31c8eb843fa0a257da79ed91",
+        "parent436/SOURCE-pr376.json": "1608c15638f874243c3ad00bd6a08b30f0e9608de83002273819365ab300b0e7",
+        "parent436/NOTICE.md": "eb9cb7eab03977930484fee70d0aea066803917a6304b1ad2644cfcc6bf2acd4",
+        "code/iface386.py": "1b7c998513759195dee3e82a34c1a46dc3310236530a7f1dfbeefe00f108fc4f",
+        "code/config.py": "283d7fad45155ee91e704d63ec947cf4a60aeff5cc43510bc0e835f7da7d8767",
+        "code/global_kernel.py": "01cf4be0ab9affe48598062c4ae3610882aa77a9e18e75c4e596e2f08d8b2173",
+        "code/e8core.py": "1cb286196c1530d06f50f0997febc5993b388f33464e295611b920ba30a24eeb",
+        "code/replica_kernel.py": "780e08ad63983d0256271e8c7803c74bb1623d15cc202d98177c440ff3726aad",
+        "code/stages.py": "e73ab7836519510ed30dd7e3022dae557fa50fc513d723197929bff741859668",
+        "code/bank_routes.py": "7c6997c455bd55acca3a1603797c34e7733d557c27a7694a1429ff15773a505d",
+        "code/audit_kernel.py": "e49f9b499f98dc2938b10e32db28da3e4f38291dc345c0b5e7b906ca2b0cfb9c",
+        "code/export249.py": "6d9817f7c431573aff695e1eacfa7c2ca6d3a2a10baa3a2ea814ab9b9f7b13ab",
+        "code/compose_kernel.py": "010e081821f20bcf6e097306289031804b2609e5160dba1c743272126ef7472a",
+        "code/tile_m.py": "d6ae4a556472d403773cd2117c992bfc10e1187112da1b3893f3fae628a131dd",
+        "code/rebuild.py": "3efb6c81a247ac6d5cab87c47030a332292c2c46d482ff996588858f41cdad4d",
+        "data/word.json.gz": "d8d6d3d3f336720302bc40b3c1504fe3c3583a7a8d707bb9bd7b21f85e5e69c6",
+        "data/residual-isometries.json": "e12ed7ddd13cee101ba74a083b54665fd64d0b122b0bad5b83d817dcc8bae9d8",
+        "data/post-retiming.json": "d25a636bcebf97b46b01cd39259e8c4f59ab92a188f4cb4bd0b0b34936cf3b56",
+        "data/selection.json": "1a96e47f1889bc690316f95a3858b0062ce212ea876dd15e5123ed89d09a9c39",
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+        "data/upstream441/window-retime-selection.json": "170a2190b6bae36de3a18a8b4c1a152cebd95b839ae889da3049f9d9b0109e30",
+        "data/upstream441/pair-retime-selection.json": "201d8cbc8ac1df10ee74246815f3ce8507b94395af69835e8098a8274bca5651",
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+        "parent436/discovery/search_params.py": "57de04a8ea7e2df8b783e02c454bb102edab48206db0a41a1f28d50e7f164441",
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+        "parent436/data/complex-b-nine.json": "2815ca568c88edde758c31e756d0d07aa08233243f365bc111383d7f0c1c757a",
+        "parent436/data/bit/bitE8-r740.json.gz": "f8daa4982d865748fa9a3095b2cf4290f34e2c085d6d35673fd7171cab95623c",
+        "parent436/data/bit/reuse-ledger.json": "e7bb324150a5342076c9a268f69b83c65f817a7cfc1d14fda9558a9f7e486f0b",
+        "parent436/data/bit/bitE8-r865.json.gz": "1fb726ea3818fe0837cceb0dd22a71a0814f064e5e781628104610d6468e0e55",
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+        "parent436/data/controls/pr386/AUDIT.json": "59625785de14c3df03abe009cdc67c7918b8fcfa8dc5f468c3d363af0494cbb7",
+        "parent436/data/controls/pr386/GLOBAL.json": "55af2a11552c04f5a87268bc2d1798246297874e9e87b50e49773e91cc495c2d",
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+        "parent436/code/tail/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
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+        "parent436/code/bit/producer/fullword.py": "0daf87599e9e48646b985ad87351c56c1b73cfc99cdf9eca081483846ddbfa90",
+        "parent436/code/bit/producer/price.py": "46c858e60ba0a117bf8227b864abf55e85ebee2d56a0dce64472b706499ac405",
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+      "git_blob": "590da4b892a08b9d5182fb3d8a983c6239dd27db"
+    },
+    "UPSTREAM-PR234-NOTICE.md": {
+      "repository_path": "research/five-stage-source527-banks/UPSTREAM-PR234-NOTICE.md",
+      "snapshot_commit": "8c4242ea61c67827fe62b07b2edc093d7ddfa631",
+      "sha256": "ce978c8dfc8a2b36eed7a53014b1a792248b22ef4cee3edd8adab825a571c429",
+      "git_blob": "5f8fbb25c12781420284bc220a041592619e27c0"
+    }
+  }
+}
diff --git a/research/e8-eleven-hosting-selected/upstream445/code/assemble.py b/research/e8-eleven-hosting-selected/upstream445/code/assemble.py
new file mode 100644
index 0000000000..870b027ffa
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/code/assemble.py
@@ -0,0 +1,94 @@
+# Adapted from DaysSky PR442 with Claude assistance; Eleven-stage R740 integration by chafreaky with OpenAI Codex. Apache-2.0.
+"""Two exact moments for both hosted suppliers, fresh finite invoices with the hosted stock, and the strict outer
+assembly of #434 (six bootstrap levels, 47 inequalities, next-grid and parameter controls).
+usage: assemble.py VERIFIED444_DIR BIT_DIR"""
+import gzip, hashlib, importlib.util, json, math, sys
+from fractions import Fraction as Q
+from pathlib import Path
+parent444, bd = map(Path, sys.argv[1:3])
+upstream=parent444/"upstream442"
+ap=bd/"AUDIT.json";outp=bd/"RESULT.json"
+from row_bound import bound as row_bound, controls as row_controls
+par=upstream / "parent/changed"
+cd=upstream / "complex"
+def load(name):
+    sp = importlib.util.spec_from_file_location('hosted_' + name, par / 'work/pr361/code/engines' / (name + '.py'))
+    mod = importlib.util.module_from_spec(sp); sp.loader.exec_module(mod); return mod
+M, Other, Outer = load('moment'), load('base_two_moment'), load('outer')
+audit = json.loads(ap.read_text()); ua=json.loads((upstream/'AUDIT.json').read_text()); ur=json.loads((upstream/'RESULT.json').read_text()); bg = json.loads((bd / 'GLOBAL.json').read_text()); ch = json.loads((cd / 'HOSTED.json').read_text())
+assert audit['template_sha256'] == bg['template_sha256'] and ua['complex_template_sha256'] == ch['template_sha256']
+assert json.loads((upstream/'RECEIPT.json').read_text())['status']=='PASS_FULL_IDLE_AXIS_HOSTING_COMPOSITION'
+# ---------------- bit: two moments and the parent's invoice formulas with the hosted stock
+P = {int(r): n for r, n in audit['profile'].items()}; m, W = 78, audit['live']; E = sum(P.values())
+geo = json.loads((bd / 'GEOMETRY.json').read_text());pg=bg
+T, L, R, V, K = 8, 11, 740, 120, 5
+assert pg["replicas"]==T and pg["R"]==R
+mass = sum(r * z for r, z in P.items()); assert m * W - mass == (2*K*V-L*72)*T
+physical = W + 9; d = m * m; N = 2 * m
+unit = L * T * pg['local_additions'] + pg['bridge_additions']
+J = 8 * T * L * (2 * V + R) + 8 * (2 * K * V * T) + 2 * L * T * R + 2 * pg['copy_erase_episodes']   # every helper route charged (bank or hosted)
+high = 16 * (d + 1) ** 2; good = 8 * m * m + 8; compiler = 128 * N ** 3
+selectors = 2 * L * T * ((W - 1) + R * m * (geo['max_route_factors'] + 144 + 2 + (m - 1) + m))   # 144: residual isometry; +2: hosted slot permutation and idle basis U_q
+prefix = int(pg['global_prefix_bound']); charged_prefix = 64 * ((prefix.bit_length() + 63) // 64)
+assert 1<<128 <= prefix < 1<<charged_prefix <= 1<<256
+coefficient = unit + J * high + J * physical + E * (good + compiler) + 16 * m ** 3 + pg['copy_erase_episodes'] + selectors + prefix + 1
+two = (coefficient + 1) ** 3 * (E + 1) ** 3; charged_two = 1024
+assert 1 << 512 <= two < 1 << charged_two and 2 * max(P) ** 3 < m ** 3
+rows = row_bound(m,physical,max(P),3);row=rows["complete_row_coefficient"]
+assert row==19431<20161
+row_rejected=row_controls()
+root = M.certify(P, m, W, True); c = Q(root['lower']); chi = Q(root['upper'])
+fb = 32 * m * m * E
+lo, hi = Other.moment(m, W, list(P.items()), c); bl, bh = Other.moment(m, W, [(1, fb)], c); assert hi + bh / 10 ** 16 < 1
+lo2, hi2 = Other.moment(m, W, list(P.items()), chi); bl2, bh2 = Other.moment(m, W, [(1, fb)], chi); assert lo2 + bl2 / 10 ** 16 > 1
+# ---------------- complex: two moments and the parent's invoice with the hosted stock
+PC = {int(r): n for r, n in ua['complex_profile'].items()}; mc, WC = 73, ua['complex_live']; EC = sum(PC.values())
+massc = sum(r * z for r, z in PC.items()); assert mc * WC - massc == 2496
+rc = M.certify(PC, mc, WC, True); b = Q(int(Q(rc['lower']) * 10 ** 18), 10 ** 18)
+assert b==Q(ur['complex_lower'])
+fbc = 32 * mc * mc * EC
+l3, h3 = Other.moment(mc, WC, list(PC.items()), b); b3, bh3 = Other.moment(mc, WC, [(1, fbc)], b); assert h3 + bh3 / 10 ** 16 < 1
+integ = json.loads((par / 'split-centres/INTEGRATION.json').read_text()); inv = integ['finite_invoice']
+physc = ch['physical']; Rc = 560; v = 120
+compilerc = 64 * (mc + 1) ** 3
+pervertex = inv['pervertex'] - integ['physical'] * (64 + 1) + physc * (64 + 1) - integ['live'] + WC   # stock-dependent terms re-based
+r_ = mc // 2; group = 2 ** (r_ * r_) * math.prod(2 ** (2 * i) - 1 for i in range(1, r_ + 1)); stock = group * physc
+smass = group * massc; logical = group * max(pervertex, inv['pervertex']) + 64; router = compilerc * (logical + 1) * (stock + 1) ** 2
+GG, EE, C0 = 1 << 30000, 1 << 100000, 1 << 210000; BB = smass + EE
+literal = 2 * GG * stock ** 2 + 8 * smass + 4 * stock + 4 + 32 * mc
+assert logical < 1 << 6050 and router < GG and literal < EE and BB < 1 << 100001 and 32 * mc * BB * BB < C0 and 2 * BB + 18 < C0
+depth = 2; assert mc ** depth > 2 * max(PC) ** depth
+rowc = depth * stock.bit_length() + 9909 + 252; assert rowc < 20161
+# ---------------- outer assembly exactly as #434's combined.py
+eta = beta = Q(1, 10 ** 18); grid = Q(1, 10 ** 18); s = min(c, (1 - beta) * b) - Q(1, 10 ** 24)
+assert 0 < s < c and s < (1 - beta) * b
+chain = [Q(384599, 10 ** 10)]; cutoffs = []
+def ceil(x): return -((-x.numerator) // x.denominator)
+for j in range(6):
+    old = chain[-1]; a = (1 - s) * s + s * old
+    gap = min(s - a, 1 - a - s, 1 - a - s * (1 - old), 1 - s); assert old < a < s < 1 - a and gap > 0
+    cutoff = max(ceil(36 / gap ** 2), ceil(2 * (4 + charged_two) / gap)); assert cutoff * gap ** 2 >= 36 and cutoff * gap >= 2 * (4 + charged_two)
+    cutoffs.append(dict(gap=str(gap), cutoff_log2=str(cutoff))); chain.append(a)
+q = chain[-1] * (1 - 2 * eta); margin = (1 - eta) * q / (1 + q); ticks = margin / grid; k = grid * ((ticks.numerator - 1) // ticks.denominator)
+bridge = {'semantic': {'C0': {'base': 2, 'exponent': 210000}, 'strict_literal_gap': 1}, 'rows': {'degree_gap': Q(10 ** 6) - Q(51 * 20161, 25)}}
+a = Outer.assembly(chain[-1], b, bridge, k, eta=eta, beta=beta)
+assert len(a['strict_constraints']) == 47 and all(x > 0 for x in a['strict_constraints'].values())
+controls = []
+for name, kk, ee, bb in [('next_grid', k + grid, eta, beta), ('zero_eta', k, Q(0), beta), ('zero_beta', k, eta, Q(0)), ('unit_beta', k, eta, Q(1))]:
+    try: Outer.assembly(chain[-1], b, bridge, kk, eta=ee, beta=bb)
+    except AssertionError: controls.append(name)
+    else: raise AssertionError(name)
+parent_k = Q(json.loads((parent444/'RESULT.json').read_text())['kappa'])
+assert json.loads((parent444/'RECEIPT.json').read_text())['status']=='PASS_R740_REPLICATED_HOSTING'
+res = dict(status='PASS_CONDITIONAL_ELEVEN_STAGE_HOSTING_ASSEMBLY', kappa=str(k), kappa_decimal=format(float(k), '.18f'),
+           bit_lower=str(c), complex_lower=str(b), binding_component='bit' if c < (1 - beta) * b else 'complex',
+           gain_over_pr444_percent=float(100 * (k / parent_k - 1)),
+           bit=dict(live=W, physical=physical, maxchild=max(P), rank_mass=mass, hosted_residuals=audit['hosted_residuals'],
+                    prefix_bits=prefix.bit_length(), charged_prefix_bits=charged_prefix, coefficient_bits=coefficient.bit_length(),
+                    three_level_coefficient_bits=two.bit_length(), charged_three_level_coefficient_bits=charged_two, row_coefficient=row),
+           complex=dict(live=WC, physical=physc, maxchild=max(PC), rank_mass=massc, hosted_residuals=ua['complex_hosted_residuals'],
+                        physical_stock_bits=stock.bit_length(), router_bits=router.bit_length(), literal_bits=literal.bit_length(), row_coefficient=rowc),
+           strict_outer_constraints={n: str(x) for n, x in a['strict_constraints'].items()}, outer_controls=controls, bootstrap=cutoffs,
+           bit_template_sha256=bg['template_sha256'], complex_template_sha256=ch['template_sha256'], emitted_program_sha256=bg['emitted_program_sha256'], bank_assignments=audit['bank_assignments'], bit_profile=audit['profile'], parent_kappa=str(parent_k), additional_interface='PR442 idle-data hosting during untouched windows',row_bound=rows,row_controls=row_rejected, halving_depth=3, finite_controls=['old 128-bit prefix charge insufficient','old 512-bit composite charge insufficient'])
+outp.write_text(json.dumps(res, indent=2) + '\n')
+print(res['status'], res['kappa_decimal'], 'binding', res['binding_component'], 'gain over #444 %.4f%%' % res['gain_over_pr444_percent'])
diff --git a/research/e8-eleven-hosting-selected/upstream445/code/audit.py b/research/e8-eleven-hosting-selected/upstream445/code/audit.py
new file mode 100644
index 0000000000..c8730e84dd
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/code/audit.py
@@ -0,0 +1,181 @@
+"""Independent eleven-stage schedule, geometry embedding and hosted ownership audit.
+Derived from PR386/436/443/444 and DaysSky PR442; all source notices retained.
+Eleven-stage integration by chafreaky with OpenAI Codex assistance, Apache-2.0.
+No emitter, schedule constructor, hosting solver or expander is imported.
+Usage: audit.py PARENT443_CANDIDATE OUT
+"""
+import copy,gzip,hashlib,json,sys
+from collections import Counter,defaultdict
+from pathlib import Path
+K,L,M,T,V,R=5,11,78,8,120,740
+DATA=2*K*V*T
+read=lambda p:json.loads(p.read_text())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+load_template=lambda p:json.loads(gzip.decompress(p.read_bytes()))
+
+def windows(schedule):
+    last={};seen=[];win={};ranks={};pairs={}
+    for position,event in enumerate(schedule):
+        kind=event['kind']
+        if kind=='local_cover_sweep':
+            seen.append((position,event['stage'],event['pair']));last[event['pair']]=position
+        elif kind=='bridge':
+            last[event['dst']]=position;last[event['src']]=position
+        elif kind=='idle':
+            i=event['idx'];assert i not in win
+            win[i]={s for pos,s,p in seen if last.get(event['pair'],-1)<pos<position and p!=event['pair']}
+            ranks[i]=event['rank'];pairs[i]=event['pair']
+        else:assert kind=='exchange' and position==len(schedule)-1
+    return win,ranks,pairs
+
+def schedule_check(schedule):
+    # Ten formal integer rows, keeping the signs lost by F2 reduction.
+    rows=[[int(i==j) for j in range(2*K)] for i in range(2*K)]
+    levels=[-1]*K;stages=[];bridges=0;exchanged=False;idles=[]
+    def add(dst,src,c):rows[dst]=[x+c*y for x,y in zip(rows[dst],rows[src])]
+    for e in schedule:
+        kind=e['kind'];assert not exchanged
+        if kind=='local_cover_sweep':
+            s,p,rev=e['stage'],e['pair'],e['reverse']
+            assert s==len(stages) and 0<=s<L and p==max(0,(s-1)//2) and rev==bool(s%2)
+            assert levels[p]==s-1
+            add(2*p,2*p+1,-1) if rev else add(2*p+1,2*p,1)
+            levels[p]=s;stages.append(s)
+        elif kind=='idle':
+            p,lo,hi=e['pair'],e['source_level'],e['target_level']
+            assert 0<=p<K and levels[p]==lo and lo<=hi<=L-1 and e['rank']==7*(hi-lo)
+            assert e['idx']==len(idles);idles.append((p,lo,hi,e['rank']));levels[p]=hi
+        elif kind=='bridge':
+            dst,src,c=e['dst'],e['src'],e['coefficient']
+            assert 0<=dst<K and 0<=src<K and dst!=src and c in (-1,1) and levels[dst]==levels[src]
+            add(2*dst,2*src,c);add(2*src+1,2*dst+1,-c);bridges+=1
+        else:
+            assert kind=='exchange' and levels==[L-1]*K
+            for p in range(K):rows[2*p],rows[2*p+1]=rows[2*p+1],[-x for x in rows[2*p]]
+            exchanged=True
+    assert exchanged and rows==[[int(i==j) for j in range(2*K)] for i in range(2*K)]
+    assert stages==list(range(L)) and bridges==3*(K-1)
+    return idles
+
+def audit(t,parent,widths):
+    assert (t['m'],t['h'],t['stages'],t['replicas'],t['live'],t['private_centre_reserve'])==(M,8,L,T,DATA,9)
+    assert t['banks_per_stage']==0 and t['bank_padding'] is None
+    for key in ('local_programs','residual_isometries','entrance_rank_total','source_record_sha256','bit_operator'):
+        assert t[key]==parent[key],key
+    schedule_check(t['schedule'])
+    win,rank,pair=windows(t['schedule']);hs=t['hosting'];used=defaultdict(set);hosted={}
+    assert hs['windows']=={str(i):[pair[i],rank[i],sorted(win[i])] for i in win if rank[i] and win[i]}
+    for i,cp,off,w,s,h in hs['slots']:
+        assert i in win and s in win[i] and 0<=s<L and 0<=h<R and 0<=cp<2*V
+        assert w==widths[h]>0 and 0<=off and off+w<=rank[i]
+        cells=set(range(off,off+w));assert not cells&used[i,cp];used[i,cp]|=cells
+        assert (s,h) not in hosted;hosted[s,h]=(i,cp,off,w)
+    assert set(hosted)=={(s,h) for s in range(L) for h in range(R)}
+    rem={};summaries={}
+    for i in rank:
+        if not rank[i]:continue
+        for cp in range(2*V):rem[i,cp]=rank[i]-len(used[i,cp])
+        if str(i) in hs['windows']:
+            summaries[str(i)]={str(r):n for r,n in sorted(Counter(rem[i,cp] for cp in range(2*V)).items())}
+    assert hs['remainders']==summaries
+    assert len(t['calls'])==L*T;seen=set();paid=Counter()
+    localhash={ori:hashlib.sha256(json.dumps(es,separators=(',',':')).encode()).hexdigest() for ori,es in t['local_programs'].items()}
+    for index,c in enumerate(t['calls']):
+        s,rep=c['stage'],c['replica'];p=max(0,(s-1)//2);rev=bool(s%2)
+        assert (s,rep)==divmod(index,T) and c['pair']==p and c['orientation']==('reverse' if rev else 'forward')
+        assert c['local_hash']==localhash[c['orientation']]
+        own=c['owners'];assert len(own)==2*V+R
+        assert len({(f,tuple(route)) for f,route in own})==2*V+R
+        for j,(f,route) in enumerate(own):
+            assert 0<=f<DATA
+            if j<2*V:
+                side=j//V;side=1-side if rev else side
+                assert f==rep*(2*K*V)+(2*p+side)*V+j%V and route==['data',s,j%V]
+            else:
+                h=j-2*V;i,cp,off,w=hosted[s,h];side,port=divmod(cp,V)
+                assert pair[i]!=p and f==rep*(2*K*V)+(2*pair[i]+side)*V+port
+                assert route==['hosted',i,off,w]
+                assert (s,rep,h) not in seen;seen.add((s,rep,h))
+        for z in t['local_programs'][c['orientation']]:
+            if z[0]==0 and z[4]:paid[z[4]]+=1
+            if z[0]==2:paid[z[5]]+=1
+    assert len(seen)==L*T*R
+    for r in rem.values():
+        if r:paid[r]+=T
+    assert M*DATA-sum(r*n for r,n in paid.items())==T*(2*K*V-72*L)
+    assert M**2<=2*max(paid)**2 and M**3>2*max(paid)**3
+    return paid
+
+def expanded_digest(t):
+    h=hashlib.sha256();count=0
+    for call in t['calls']:
+        for op in t['local_programs'][call['orientation']]:
+            row=[op[0],call['owners'][op[1]]]
+            if op[0]==0:row.extend(op[2:])
+            else:
+                row.append(call['owners'][op[2]] if op[2]<2*V+R else [t['live'],['private',0]])
+                row.extend(op[3:])
+            h.update(json.dumps(row,separators=(',',':')).encode());h.update(b'\n');count+=1
+    return h.hexdigest(),count
+
+def main():
+    par,out=map(Path,sys.argv[1:]);t=load_template(out/'GLOBAL-TEMPLATE.json.gz');pt=load_template(par/'nine/GLOBAL-TEMPLATE.json.gz')
+    g=read(out/'GLOBAL.json');geo=read(out/'GEOMETRY.json');pg=read(par/'nine/GEOMETRY.json')
+    state=read(par/'records/249-states.json');fs=read(par/'records/frames.json')['frames']
+    widths=[8-fs[str(state['initial'][str(h)])]['dim'] for h in range(240,980)]
+    P=audit(t,pt,widths)
+    assert geo['m']==78 and geo['stages']==11 and len(geo['ports'])==120 and not geo['bank_slots'] and not geo['bank_permutations']
+    for p,old in zip(geo['ports'],pg['ports']):
+        assert {k:v for k,v in p.items() if k!='routes'}=={k:v for k,v in old.items() if k!='routes'}
+        assert p['routes'][:9]==old['routes'] and len(p['routes'])==11
+        for s,route in enumerate(p['routes']):
+            if s==0:assert route==dict(stage=0,axes=list(range(8)),identity=True)
+            else:
+                assert route==dict(stage=s,axes=list(range(8))+list(range(8+7*(s-1),8+7*s)),elementary_inverse_replay=old['routes'][1]['elementary_inverse_replay'])
+                assert len(set(route['axes']))==15 and max(route['axes'])<M
+    idle=schedule_check(t['schedule'])
+    assert idle==[(e['pair'],e['source_level'],e['target_level'],e['rank']) for e in geo['idle_per_port_and_data_member']]
+    assert t['geometry_sha256']==sha(out/'GEOMETRY.json')==g['geometry_sha256']
+    assert t['source_record_sha256']==sha(par/'records/249-records.bin')==g['source_records_sha256']
+    th=hashlib.sha256(gzip.decompress((out/'GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest();assert th==g['template_sha256']
+    digest,count=expanded_digest(t);assert digest==g['emitted_program_sha256'] and count==g['emitted_events']
+    assert P==Counter({int(r):n for r,n in g['profile'].items()})
+    assert (g['live'],g['physical'],g['hosted_residuals'],g['bank_assignments'],g['deficit'])==(9600,9609,65120,0,3264)
+    assert g['rank_mass']==sum(r*n for r,n in P.items()) and g['paid_calls']==sum(P.values()) and g['maxchild']==max(P)
+    assert g['independent_unbanked_scalar_columns']==9340 and len(g['scalar_stages'])==11 and g['all_scalar_columns_restored']
+    assert g['omitted_bridge_shears_rejected']==list(range(24))
+    controls=[]
+    def reject(name,fn):
+        q=copy.deepcopy(t);fn(q)
+        try:audit(q,pt,widths)
+        except (AssertionError,KeyError,IndexError,TypeError):controls.append(name)
+        else:raise AssertionError('accepted '+name)
+    slot=lambda q:q['hosting']['slots'][0]
+    reject('slot outside window',lambda q:slot(q).__setitem__(4,10))
+    reject('copy outside family',lambda q:slot(q).__setitem__(1,240))
+    reject('negative slot offset',lambda q:slot(q).__setitem__(2,-1))
+    reject('wrong residual width',lambda q:slot(q).__setitem__(3,slot(q)[3]+1))
+    reject('duplicate helper',lambda q:q['hosting']['slots'].append(slot(q)))
+    reject('missing helper',lambda q:q['hosting']['slots'].pop())
+    reject('cross-replica host',lambda q:q['calls'][0]['owners'][240].__setitem__(0,q['calls'][0]['owners'][240][0]+1200))
+    reject('cross-replica data',lambda q:q['calls'][0]['owners'][0].__setitem__(0,1200))
+    reject('wrong hosted coordinate',lambda q:q['calls'][0]['owners'][240][1].__setitem__(2,99))
+    reject('helper changed to bank',lambda q:q['calls'][0]['owners'][240][1].__setitem__(0,'bank'))
+    reject('wrong call orientation',lambda q:q['calls'][0].__setitem__('orientation','reverse'))
+    reject('duplicate call',lambda q:q['calls'].__setitem__(1,q['calls'][0]))
+    reject('dropped final stage',lambda q:q.__setitem__('calls',[c for c in q['calls'] if c['stage']<10]))
+    reject('wrong idle rank',lambda q:next(e for e in q['schedule'] if e['kind']=='idle').__setitem__('rank',1))
+    reject('omitted bridge',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='bridge')))
+    reject('wrong bridge sign',lambda q:next(e for e in q['schedule'] if e['kind']=='bridge').__setitem__('coefficient',-1))
+    reject('omitted terminal exchange',lambda q:q['schedule'].pop())
+    reject('understated live stock',lambda q:q.__setitem__('live',q['live']-1))
+    reject('missing remainder summary',lambda q:q['hosting']['remainders'].pop(next(iter(q['hosting']['remainders']))))
+    reject('wrong residual isometry',lambda q:q['residual_isometries'][0]['orthogonal_rows_numerator'][0].__setitem__(0,99))
+    reject('omitted local instruction',lambda q:q['local_programs']['forward'].pop())
+    reject('wrong reflected copy rank',lambda q:next(z for z in q['local_programs']['reverse'] if z[0]==2).__setitem__(5,0))
+    res=dict(status='PASS_INDEPENDENT_ELEVEN_STAGE_HOSTING_AUDIT',template_sha256=th,emitted_program_sha256=digest,
+             emitted_events=count,profile={str(r):n for r,n in sorted(P.items())},live=9600,physical=9609,hosted_residuals=65120,
+             bank_assignments=0,rank_mass=sum(r*n for r,n in P.items()),deficit=3264,maxchild=max(P),geometry_routes=1320,
+             halving_depth=3,mutations_rejected=controls)
+    (out/'AUDIT.json').write_text(json.dumps(res,indent=2)+'\n');print(json.dumps(res))
+if __name__=='__main__':main()
diff --git a/research/e8-eleven-hosting-selected/upstream445/code/emit.py b/research/e8-eleven-hosting-selected/upstream445/code/emit.py
new file mode 100644
index 0000000000..5ff0de0d6f
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/code/emit.py
@@ -0,0 +1,261 @@
+# Kernel integration of PR436/PR386 by chafreaky, with OpenAI Codex assistance.
+# Original copyright and attribution retained below. This variant uses explicit
+# residual isometries and mixed-width banks; the original all-zero-start
+# requirement is replaced by the verified kernel entrance contract.
+"""Source-bound eleven-stage bit template with 8 independent replicas and no helper banks.
+PR386 global identity and PR436 generalization by Zhihao Chen and eumemic,
+with their disclosed OpenAI Codex and Anthropic Claude assistance, Apache-2.0.
+PR439 explicit residual routes and this replication extension by chafreaky,
+with OpenAI Codex assistance. All owner assignments and emitted calls are checked.
+Historical PR386 regression is performed by the unchanged parent wrapper.
+"""
+import argparse, gzip, hashlib, json, struct, time, sys
+from collections import Counter
+from pathlib import Path
+HERE=Path(__file__).resolve().parent
+sys.path.insert(0,str(HERE.parents[1]/"e8-r740-replica32/code"))
+sys.path.insert(0,str(HERE.parents[1]/"idle-axis-hosting"))
+from bank_routes import validate_isometries
+import hosting_core as HC
+
+H,L,K,T,M=8,11,5,8,78
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+def write(p,x): p.write_text(json.dumps(x,indent=2)+'\n')
+
+def recipe():
+    out=[dict(kind='local',stage=0,pair=0,reverse=False)]; stage=1
+    for j in range(K):
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=True)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=1))
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=False)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=-1))
+    for j in reversed(range(K-1)): out.append(dict(kind='bridge',dst=j+1,src=j,coefficient=1))
+    out.append(dict(kind='exchange'))
+    return out
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--word',type=Path,required=True)
+    ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    ap.add_argument('--isometries',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out; out.mkdir(parents=True,exist_ok=True)
+    wp=a.word; w=json.loads(gzip.decompress(wp.read_bytes()))
+    V,R=w['v'],w['R']; LOCAL=2*V+R; DATA=2*K*V*T; LIVE=DATA+L*R
+    assert (w['h'],V,w['form'])==(8,120,'<x,y>/2')
+    geo=json.loads((out/'GEOMETRY.json').read_text())
+    assert geo['status']=='PASS_COMPRESSED_ELEVEN_BIT_GEOMETRY'
+    # the port routes depend only on the labels: same 120 label vectors, in the same order
+    assert len(geo['ports'])==V and all(p['port']==t and p['q']==w['lines'][t] for t,p in enumerate(geo['ports']))
+    rp=a.local_check/'records/249-records.bin'; raw=rp.read_bytes(); rec=list(struct.iter_unpack('<6i',raw))
+    state=json.loads((a.local_check/'records/249-states.json').read_text())
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    dims={int(f):z['dim'] for f,z in fs.items()}
+    lg=json.loads((a.local_check/'cout/legality.json').read_text())
+    cc=json.loads((a.local_check/'cout/columns.json').read_text())
+    assert lg['status'].startswith('PASS') and cc['status'].startswith('PASS')
+    assert (state['v'],state['n'])==(V,LOCAL) and lg['copies']==lg['erasures']==9
+    ADDS=lg['common_frame_ADDs']
+    assert cc['formal_columns_checked']==4*V+R and cc['local_scalar_additions']==ADDS
+    initial=[state['initial'][str(i)] for i in range(LOCAL)]
+    final=[state['final'][str(i)] for i in range(LOCAL)]
+    assert all(dims[final[i]]==H for i in range(2*V,LOCAL))
+    widths=[H-dims[initial[i]] for i in range(2*V,LOCAL)]
+    ENT=sum(H-z for z in widths)
+    NB=0;LIVE=DATA
+    assert T==8 and M==8+7*(L-1)
+    isometries=json.loads(a.isometries.read_text())
+    assert validate_isometries(isometries,w['frames'],w['lines'],dims)==set(initial[2*V:])
+    streams={}; checks={}; localH=None
+    for reverse in (False,True):
+        cur=(final if reverse else initial)[:]+[-1]; val=[1<<i for i in range(LOCAL)]+[0]
+        norm=[1]*LOCAL+[0]; maxnorm=1; center=None; hist=Counter(); events=[]; copies=0; adds=0
+        dim=lambda f:H-dims[f] if reverse else dims[f]
+        for op,x,y,c,f,z in (reversed(rec) if reverse else rec):
+            if op==0:
+                oldf,newf=(c,y) if reverse else (y,c)
+                assert cur[x]==oldf and dim(newf)-dim(oldf)==f>=0
+                cur[x]=newf
+                if f: hist[f]+=1
+                events.append([0,x,oldf,newf,f,int(reverse)])
+            elif op==1:
+                assert cur[x]==cur[y]==f and x!=y and x<LOCAL
+                if center is not None: assert x!=center
+                if y==LOCAL: assert center is not None
+                if c&1: val[x]^=val[y]
+                norm[x]+=abs(c)*norm[y]; maxnorm=max(maxnorm,norm[x]); adds+=1
+                events.append([1,x,y,-c if reverse else c,f,int(reverse)])
+            elif op==(3 if reverse else 2):
+                assert center is None and y==LOCAL and cur[x]==c and val[LOCAL]==0
+                copy_rank=abs(dim(c)-dim(f)); assert copy_rank==8
+                assert z==(0 if reverse else copy_rank)
+                center=x; cur[LOCAL]=f; val[LOCAL]=val[x]; norm[LOCAL]=norm[x]
+                hist[copy_rank]+=1; copies+=1; events.append([2,x,LOCAL,c,f,copy_rank,int(reverse)])
+            else:
+                assert op==(2 if reverse else 3)
+                assert center==x and y==LOCAL and cur[x]==c and cur[LOCAL]==f
+                assert val[LOCAL]==val[x]
+                val[LOCAL]=0; norm[LOCAL]=0; cur[LOCAL]=-1; center=None
+                events.append([3,x,LOCAL,c,f,z,int(reverse)])
+        assert center is None and copies==9 and adds==ADDS
+        assert cur[:LOCAL]==(initial if reverse else final)
+        for i in range(LOCAL):
+            want=(1<<i) ^ ((1<<(i-V)) if V<=i<2*V else 0)
+            assert val[i]==want
+        assert val[LOCAL]==0
+        if localH is None: localH=hist
+        else: assert localH==hist
+        key='reverse' if reverse else 'forward'; streams[key]=events
+        checks[key]=dict(copies=copies,adds=adds,records=len(events),all_columns=LOCAL,
+                         cancellation_free_row_l1=maxnorm,profile=dict(sorted(hist.items())),
+                         sha256=hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest())
+    assert sum(r*n for r,n in localH.items())==H*R-ENT+72+2*V*(H-1)
+    assert localH==Counter({int(r):n for r,n in cc['local_raw_H']})
+
+    events=recipe(); levels=[-1]*K; schedule=[]; bridge_controls=[]
+    # Full scalar replay on separate dirty helpers for all eleven stages.
+    # Physical hosting then uses the separately checked injective cover owners.
+    n=2*K*V+L*R; vals=[1<<i for i in range(n)]+[0]; temp=n
+    stages=[]
+    for e in events:
+        if e['kind']=='local':
+            s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1
+            def mapper(i):
+                if i==LOCAL: return temp
+                if i<2*V:
+                    side=i//V; side=1-side if rev else side
+                    return (2*p+side)*V+i%V
+                return 2*K*V+s*R+i-2*V
+            before=vals[:]; opened=False
+            for z in streams['reverse' if rev else 'forward']:
+                if z[0]==0: continue
+                x,y=mapper(z[1]),mapper(z[2])
+                if z[0]==1:
+                    if z[3]&1: vals[x]^=vals[y]
+                elif z[0]==2:
+                    assert not opened; vals[temp]=vals[x]; opened=True
+                else:
+                    assert opened and vals[temp]==vals[x]; vals[temp]=0; opened=False
+            assert not opened
+            d=(2*p+(0 if rev else 1))*V; src=(2*p+(1 if rev else 0))*V
+            for t in range(V): before[d+t]^=before[src+t]
+            assert vals==before
+            levels[p]=s; schedule.append(dict(kind='local_cover_sweep',**{k:v for k,v in e.items() if k!='kind'}))
+            if s in range(1,2*K-1,2):
+                j=(s+1)//2; assert levels[j]==-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7*(s+1),source_level=-1,target_level=s))
+            elif s in range(2,2*K,2):
+                j=s//2; assert levels[j]==s-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7,source_level=s-1,target_level=s))
+            elif s==2*K:
+                for j in range(K):
+                    oldlevel=levels[j]; assert oldlevel==2*j+2
+                    schedule.append(dict(kind='idle',pair=j,rank=7*(2*K-oldlevel),source_level=oldlevel,target_level=2*K))
+                    levels[j]=2*K
+            stages.append(dict(stage=s,all_columns=n,helper_columns=L*R,reverse=rev))
+        elif e['kind']=='bridge':
+            d,s=e['dst'],e['src']; assert levels[d]==levels[s]
+            for t in range(V): vals[2*d*V+t]^=vals[2*s*V+t]; vals[(2*s+1)*V+t]^=vals[(2*d+1)*V+t]
+            schedule.append(e)
+        else:
+            assert levels==[2*K]*K
+            for j in range(K):
+                for t in range(V):
+                    x=2*j*V+t; y=(2*j+1)*V+t; vals[x],vals[y]=vals[y],vals[x]
+            schedule.append(e)
+    assert vals==[1<<i for i in range(n)]+[0]
+    # Integer scalar ten-wire matrix, with each individual bridge shear omitted.
+    def small(skip=-1):
+        z=[[int(i==j) for j in range(2*K)] for i in range(2*K)]; count=0
+        def add(d,s,c): z[d]=[x+c*y for x,y in zip(z[d],z[s])]
+        for e in events:
+            if e['kind']=='local':
+                p=e['pair']; add(2*p,2*p+1,-1) if e['reverse'] else add(2*p+1,2*p,1)
+            elif e['kind']=='bridge':
+                d,s,c=e['dst'],e['src'],e['coefficient']
+                for x,y,sgn in [(2*d,2*s,c),(2*s+1,2*d+1,-c)]:
+                    if count!=skip: add(x,y,sgn)
+                    count+=1
+            else:
+                for j in range(K): z[2*j],z[2*j+1]=z[2*j+1],[-x for x in z[2*j]]
+        return z,count
+    ident=[[int(i==j) for j in range(2*K)] for i in range(2*K)]
+    z,nb=small(); assert z==ident and nb==6*(K-1)
+    for skip in range(nb): assert small(skip)[0]!=ident; bridge_controls.append(skip)
+
+    # Freeze and expand the full-helper idle assignment for one replica.
+    indexed=[];idx=0
+    for e in schedule:
+        if e['kind']=='local_cover_sweep': indexed.append(dict(kind='local',stage=e['stage'],pair=e['pair']))
+        elif e['kind']=='bridge': indexed.append(dict(kind='bridge',dst=e['dst'],src=e['src']))
+        elif e['kind']=='idle':
+            e['idx']=idx;indexed.append(dict(kind='idle',idx=idx,pair=e['pair'],rank=e['rank']));idx+=1
+    win={i:w for i,w in HC.windows(indexed).items() if w[1] and w[2]}
+    ys,zs,proxy=HC.load_selection(HERE.parent/'data/selection.json','bit')
+    slots,rem=HC.expand(win,ys,zs,{s:list(enumerate(widths)) for s in range(L)},2*V)
+    hosted={(s,h):(i,cp,off,width) for i,cp,off,width,s,h in slots}
+    assert len(slots)==len(hosted)==L*R and set(hosted)=={(s,h) for s in range(L) for h in range(R)}
+    remainder={str(i):{str(r):n for r,n in sorted(Counter(rem[i,cp] for cp in range(2*V)).items())} for i in win}
+    paid=Counter(); calls=[]; assignment=set(); expanded=hashlib.sha256(); full_event_count=0
+    for e in events:
+        if e['kind']!='local': continue
+        s,p,rev=e['stage'],e['pair'],e['reverse']; ori='reverse' if rev else 'forward'
+        for rep in range(T):
+            owners=[]
+            for i in range(2*V):
+                side=i//V; side=1-side if rev else side
+                owners.append([rep*(2*K*V)+(2*p+side)*V+i%V, ['data',s,i%V]])
+            for r in range(R):
+                i,cp,off,width=hosted[s,r];pair=win[i][0];side,port=divmod(cp,V)
+                family=rep*(2*K*V)+(2*pair+side)*V+port
+                owners.append([family,['hosted',i,off,width]])
+                assignment.add((s,rep,r,family,off))
+            assert len({(f,tuple(route)) for f,route in owners})==LOCAL
+            assert all(0<=f<LIVE for f,route in owners)
+            # Stream one full renamed instruction program into a source-bound
+            # digest, including exact owner route descriptors and reflection.
+            for z in streams[ori]:
+                op=z[0]
+                if op==0: paid[z[4]]+=bool(z[4]); mapped=[op,owners[z[1]],*z[2:]]
+                else:
+                    ox=owners[z[1]]; oy=owners[z[2]] if z[2]<LOCAL else [LIVE,['private',0]]
+                    mapped=[op,ox,oy,*z[3:]]
+                    if op==2: paid[z[5]]+=1
+                expanded.update((json.dumps(mapped,separators=(',',':'))+'\n').encode()); full_event_count+=1
+            calls.append(dict(stage=s,replica=rep,pair=p,orientation=ori,owners=owners,local_hash=checks[ori]['sha256']))
+    paid.pop(0,None)
+    assert len(assignment)==L*T*R and len(calls)==L*T
+    for e in schedule:
+        if e['kind']=='idle' and e['rank']:
+            i=e['idx']
+            for cp in range(2*V):
+                r=rem[i,cp] if i in win else e['rank']
+                if r:paid[r]+=T
+    mass=sum(r*c for r,c in paid.items());assert M*LIVE-mass==(2*K*V-L*72)*T
+    cf=checks['forward']['cancellation_free_row_l1']; cb=checks['reverse']['cancellation_free_row_l1']
+    prefix=(1<<nb)*cf**(K+1)*cb**K; assert prefix<1<<192
+    template=dict(version='compressed-eleven-hosted-e8-bit-v1',m=M,h=H,stages=L,replicas=T,live=LIVE,private_centre_reserve=9,
+                  cover='O(I_78/2,F_q) for admitted odd address primes q',loop_order='Each recipe phase: replicas then all cover classes; finish every local invocation before the next.',
+                  schedule=schedule,local_programs=streams,calls=calls,bank_padding=None,
+                  helper_route='Exact residual isometry from the listed root basis, extended by identity and mapped onto the assigned pending idle coordinates using PR442 hosting.',
+                  residual_isometries=isometries,banks_per_stage=NB,entrance_rank_total=ENT,
+                  hosting=dict(windows={str(i):[w[0],w[1],sorted(w[2])] for i,w in win.items()},slots=[list(x) for x in slots],remainders=remainder),
+                  data_route='owner (replica*1200 + (2*pair+side)*120+port, d*rho_stage,port)',
+                  bit_operator='D_U exchanges the two address halves on projector U; D_I D_P = D_(I-P) exactly.',
+                  geometry_sha256=sha(out/'GEOMETRY.json'),source_record_sha256=sha(rp))
+    blob=json.dumps(template,separators=(',',':'),sort_keys=True).encode(); (out/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+    result=dict(status='PASS_SOURCE_BOUND_ELEVEN_STAGE_HOSTED_BIT_TEMPLATE',h=H,m=M,v=V,R=R,replicas=T,live=LIVE,physical=LIVE+9,
+                word_sha256=sha(wp),source_records_sha256=sha(rp),local_checks=checks,scalar_stages=stages,
+                independent_unbanked_scalar_columns=n,all_scalar_columns_restored=True,
+                geometry_sha256=sha(out/'GEOMETRY.json'),template_sha256=hashlib.sha256(blob).hexdigest(),
+                emitted_program_sha256=expanded.hexdigest(),emitted_events=full_event_count,local_invocations=len(calls),
+                bank_assignments=0,hosted_residuals=len(assignment),banks_per_stage=NB,entrance_rank_total=ENT,residual_bank_slots=False,padding_calls=0,
+                profile=dict(sorted(paid.items())),paid_calls=sum(paid.values()),rank_mass=mass,deficit=(2*K*V-L*72)*T,
+                maxchild=max(paid),halving_depth=3,halving_integer_inequality=[M**3,2*max(paid)**3],
+                local_additions=ADDS,bridge_additions=6*(K-1)*V*T,copy_erase_episodes=9*L*T,
+                global_prefix_bound=str(prefix),global_prefix_bits=prefix.bit_length(),charged_prefix_bits=192,
+                omitted_bridge_shears_rejected=bridge_controls,
+                scope='Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; idle-data hosting follows conditionally from PR442 plus injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.',
+                seconds=time.monotonic()-start)
+    write(out/'GLOBAL.json',result)
+    print(json.dumps({k:v for k,v in result.items() if k not in ('local_checks','scalar_stages','global_prefix_bound')}),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-eleven-hosting-selected/upstream445/code/geometry.py b/research/e8-eleven-hosting-selected/upstream445/code/geometry.py
new file mode 100644
index 0000000000..b4ad507401
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/code/geometry.py
@@ -0,0 +1,111 @@
+"""Exact compressed eleven-stage E8 bit geometry; no external research fetches.
+
+Prepared by Zhihao Chen with OpenAI Codex assistance, Apache-2.0.
+Eleven-stage extension by chafreaky with OpenAI Codex assistance.
+Uses the E8 root data and port-reflection construction credited to PR #370.
+"""
+import argparse, gzip, hashlib, json, time
+from pathlib import Path
+import sympy as S
+
+def dump(p, x): p.write_text(json.dumps(x,indent=2,default=str)+'\n')
+def digest(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def factor(a):
+    """Exact elementary factorization, reconstructed from the identity."""
+    n=a.rows; z=a.copy(); ops=[]
+    for j in range(n):
+        p=next(i for i in range(j,n) if z[i,j])
+        if p!=j: z.row_swap(p,j); ops.append(['swap',p,j,None])
+        if z[j,j]!=1:
+            c=1/z[j,j]; z[j,:]=c*z[j,:]; ops.append(['scale',j,None,c])
+        for i in range(n):
+            if i!=j and z[i,j]:
+                c=-z[i,j]; z[i,:]=z[i,:]+c*z[j,:]; ops.append(['add',i,j,c])
+    assert z==S.eye(n)
+    def replay(skip=-1):
+        z=S.eye(n)
+        for k in reversed(range(len(ops))):
+            if k==skip: continue
+            typ,i,j,c=ops[k]
+            if typ=='swap': z.row_swap(i,j)
+            elif typ=='scale': z[i,:]=z[i,:]/c
+            else: z[i,:]=z[i,:]-c*z[j,:]
+        return z
+    assert replay()==a
+    assert ops and replay(0)!=a
+    return [[t,i,j,None if c is None else str(c)] for t,i,j,c in ops]
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--source',type=Path,required=True)
+    ap.add_argument('--out',type=Path,required=True); a=ap.parse_args(); t0=time.monotonic()
+    a.out.mkdir(parents=True,exist_ok=True)
+    p=a.source/'data/bit/bitE8-r865.json.gz'; w=json.loads(gzip.decompress(p.read_bytes()))
+    assert (w['h'],w['v'],w['R'],w['form'])==(8,120,865,'<x,y>/2')
+    lines=[S.Matrix(x) for x in w['lines']]; I=S.eye(8); Z=S.zeros(8)
+    assert lines[0]==S.Matrix([2,0,0,0,0,0,0,0])
+    ip=lambda u,v:(u.T*v)[0]/2
+    gs={0:I}; todo=[0]
+    while todo:
+        more=[]
+        for i in todo:
+            for j in range(120):
+                if j in gs or abs(ip(lines[i],lines[j]))!=1: continue
+                d=lines[i]-lines[j] if ip(lines[i],lines[j])==1 else lines[i]+lines[j]
+                r=I-d*d.T/(d.T*d)[0]*2
+                gs[j]=r*gs[i]; more.append(j)
+        todo=more
+    assert len(gs)==120
+    recipes=[]; denoms=set(); max_factors=0
+    for t,q in enumerate(lines):
+        g=gs[t]; assert g.T*g==I and g*lines[0] in (q,-q)
+        P=q*q.T/4; K=I-P; A=g[:,1:]
+        assert A.T*A==S.eye(7) and A*A.T==K and P*A==S.zeros(8,7)
+        rho=P.row_join(A).col_join(A.T.row_join(S.zeros(7)))
+        assert rho.T==rho and rho*rho==S.eye(15)
+        expected={'P':S.diag(I,S.zeros(7)), 'H':S.eye(15),
+                  '0':S.diag(K,S.zeros(7)), 'K':S.diag(K,S.eye(7))}
+        for name,U in [('P',P),('H',I),('0',Z),('K',K)]:
+            assert rho*S.diag(U,S.eye(7))*rho==expected[name]
+        # Exact bit address operators D_U: head/tail exchange on U.
+        # Unlike complex C_U, they carry no omitted scalar/translation phase.
+        def D(U): return (I-U).row_join(U).col_join(U.row_join(I-U))
+        assert D(I)*D(P)==D(K) and D(P)*D(P)==S.eye(16)
+        ops=factor(rho); max_factors=max(max_factors,len(ops))
+        for typ,i,j,c in ops:
+            if c is not None: denoms.add(int(S.Rational(c).q))
+        # Compact exact global matrices: these 15 axes are the first eight
+        # local coordinates and exterior block s. All other axes are fixed.
+        routes=[dict(stage=0,axes=list(range(8)),identity=True)]
+        for s in range(1,11):
+            axes=list(range(8))+list(range(8+7*(s-1),8+7*s))
+            assert len(set(axes))==15 and max(axes)<78
+            routes.append(dict(stage=s,axes=axes,elementary_inverse_replay=ops))
+        recipes.append(dict(port=t,q=list(map(int,q)),complement_columns=[[str(x) for x in row] for row in A.tolist()],
+                            rho15=[[str(x) for x in row] for row in rho.tolist()],routes=routes))
+        if t%30==0: print('compressed geometry',t+1,flush=True)
+    # Exact nested data levels: local I (or K_q) plus s exterior rank-7
+    # blocks. Width 78=8+10*7; each bridge sees identical complete operators.
+    idle=[]
+    for j in range(1,5):
+        idle += [dict(pair=j,source_level=-1,target_level=2*j-1,rank=14*j,phase='before_positive_bridge'),
+                 dict(pair=j,source_level=2*j-1,target_level=2*j,rank=7,phase='before_negative_bridge')]
+    for j in range(5):
+        idle.append(dict(pair=j,source_level=2*j+2,target_level=10,rank=14*(4-j),phase='terminal'))
+    assert sum(z['rank'] for z in idle)==308
+    # Every residual is hosted in a data family; no helper bank exists.
+    slots=[];perms=[]
+    out=dict(status='PASS_COMPRESSED_ELEVEN_BIT_GEOMETRY',h=8,m=78,stages=11,
+             word_sha256=digest(p),ports=recipes,idle_per_port_and_data_member=idle,
+             local_window='U direct_sum E_s, with E_s the first s exterior coordinate 7-blocks',
+             ambient_form='I_78/2',bank_slots=slots,bank_permutations=perms,
+             route_checks=1320,exact_bit_endpoint_operator_checks=240,
+             max_route_factors=max_factors,route_denominators=sorted(denoms),
+             bad_prime_factors=sorted({int(q) for d in denoms for q in S.factorint(d)}),
+             missing_route_factor_controls=120,bank_free=True,
+             scope='All port isometries, stage boundary identities, nested idle ranks, exact bit endpoint operators and coordinate embeddings. No residual banks are used. Full local-word scalar and chronological lowering are checked separately.',
+             seconds=time.monotonic()-t0)
+    dump(a.out/'GEOMETRY.json',out)
+    print(json.dumps({k:v for k,v in out.items() if k not in ('ports','bank_permutations','idle_per_port_and_data_member')}),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-eleven-hosting-selected/upstream445/code/row_bound.py b/research/e8-eleven-hosting-selected/upstream445/code/row_bound.py
new file mode 100644
index 0000000000..11d3c0d48e
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/code/row_bound.py
@@ -0,0 +1,47 @@
+"""Elementary orthogonal-cover row count; no exact group-order formula is needed.
+
+Over an odd finite field, diagonalize a nondegenerate d-dimensional symmetric
+form. Fixing d-1 coordinates of a vector leaves a nonzero-coefficient quadratic
+in the last coordinate; hence a prescribed nonzero norm has at most 2*q^(d-1)
+solutions. The orthogonal complement of such a vector is nondegenerate.
+Induction while choosing the images of a diagonal orthogonal basis gives
+|O_m(q)| <= product(d=1..m, 2*q^(d-1)) = 2^m*q^(m*(m-1)/2).
+Since q>=3, this is strictly below q^(m*(m+1)/2). Physical family stock adds
+ceil(log_3(physical)) to this uniform exponent. The restored-row divisor
+argument in PR234/PR386 multiplies it by the halving depth, then adds the
+unchanged 9909 and 252 allowances. Routing-time bills still use m^2.
+
+This arithmetic checker verifies the exponent calculation and strict margins;
+the preceding elementary induction is the all-q proof, not a finite q sample.
+chafreaky with OpenAI Codex assistance, Apache-2.0.
+"""
+from fractions import Fraction
+
+def bound(m,physical,child,depth):
+    assert m>1 and physical>0 and 0<child<m and depth>0
+    assert m**depth>2*child**depth
+    overhead=0
+    while 3**overhead<=physical:overhead+=1
+    column_exponent=sum(d-1 for d in range(1,m+1))
+    assert column_exponent==m*(m-1)//2 and 2**m<3**m
+    cover_exponent=column_exponent+m
+    stock_exponent=cover_exponent+overhead
+    assert physical<3**overhead and 2**m*physical<3**(m+overhead)
+    row=depth*stock_exponent+9909+252
+    assert row<20161 and Fraction(10**6)-Fraction(51*20161,25)>0
+    return dict(method='successive nonzero-norm vectors in nondegenerate complements',
+                minimum_q=3,column_exponent=column_exponent,factor_two_power=m,
+                cover_exponent=cover_exponent,physical_families=physical,
+                physical_exponent=overhead,stock_exponent=stock_exponent,
+                halving_depth=depth,complete_row_coefficient=row,retained_row_coefficient=20161)
+
+def controls():
+    rejected=[]
+    for name,args in [('false two-level halving',(78,9609,56,2)),
+                      ('understated row reserve',(100,9609,90,7))]:
+        try:bound(*args)
+        except AssertionError:rejected.append(name)
+        else:raise AssertionError('accepted '+name)
+    # The original coarse enumeration bound does NOT fit this retained row cap.
+    assert 3*(78**2+1)+9909+252==28416>20161
+    return rejected
diff --git a/research/e8-eleven-hosting-selected/upstream445/data/selection.json b/research/e8-eleven-hosting-selected/upstream445/data/selection.json
new file mode 100644
index 0000000000..8e548e5a92
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/data/selection.json
@@ -0,0 +1,499 @@
+{
+ "bit": {
+  "patterns": [
+   [
+    0,
+    [
+     7,
+     7
+    ],
+    106
+   ],
+   [
+    0,
+    [
+     8
+    ],
+    134
+   ],
+   [
+    1,
+    [],
+    134
+   ],
+   [
+    1,
+    [
+     7
+    ],
+    106
+   ],
+   [
+    2,
+    [
+     7,
+     7,
+     7,
+     7
+    ],
+    26
+   ],
+   [
+    2,
+    [
+     8,
+     8,
+     8
+    ],
+    182
+   ],
+   [
+    2,
+    [
+     8,
+     8,
+     8,
+     4
+    ],
+    32
+   ],
+   [
+    3,
+    [],
+    134
+   ],
+   [
+    3,
+    [
+     7
+    ],
+    106
+   ],
+   [
+    4,
+    [
+     7,
+     7,
+     7,
+     7,
+     7,
+     7
+    ],
+    13
+   ],
+   [
+    4,
+    [
+     8,
+     8,
+     8,
+     7,
+     7,
+     4
+    ],
+    15
+   ],
+   [
+    4,
+    [
+     8,
+     8,
+     8,
+     8,
+     8
+    ],
+    212
+   ],
+   [
+    5,
+    [],
+    126
+   ],
+   [
+    5,
+    [
+     4
+    ],
+    8
+   ],
+   [
+    5,
+    [
+     7
+    ],
+    106
+   ],
+   [
+    6,
+    [],
+    47
+   ],
+   [
+    6,
+    [
+     8,
+     8,
+     8,
+     8,
+     8,
+     8,
+     8
+    ],
+    193
+   ],
+   [
+    7,
+    [],
+    134
+   ],
+   [
+    7,
+    [
+     7
+    ],
+    106
+   ],
+   [
+    8,
+    [
+     8,
+     8,
+     8,
+     8,
+     8,
+     8,
+     8
+    ],
+    240
+   ],
+   [
+    9,
+    [
+     8,
+     8,
+     8,
+     7,
+     7,
+     4
+    ],
+    1
+   ],
+   [
+    9,
+    [
+     8,
+     8,
+     8,
+     8,
+     8
+    ],
+    239
+   ],
+   [
+    10,
+    [
+     7,
+     7,
+     7,
+     7
+    ],
+    26
+   ],
+   [
+    10,
+    [
+     8,
+     8,
+     8
+    ],
+    182
+   ],
+   [
+    10,
+    [
+     8,
+     8,
+     8,
+     4
+    ],
+    32
+   ],
+   [
+    11,
+    [
+     7,
+     7
+    ],
+    106
+   ],
+   [
+    11,
+    [
+     8
+    ],
+    134
+   ]
+  ],
+  "proxy_saving": 41284.70059916264,
+  "stages": [
+   [
+    0,
+    7,
+    0,
+    106
+   ],
+   [
+    0,
+    7,
+    1,
+    106
+   ],
+   [
+    0,
+    8,
+    1,
+    134
+   ],
+   [
+    1,
+    7,
+    2,
+    106
+   ],
+   [
+    2,
+    4,
+    0,
+    8
+   ],
+   [
+    2,
+    4,
+    1,
+    8
+   ],
+   [
+    2,
+    4,
+    2,
+    8
+   ],
+   [
+    2,
+    4,
+    3,
+    8
+   ],
+   [
+    2,
+    7,
+    3,
+    104
+   ],
+   [
+    2,
+    8,
+    1,
+    492
+   ],
+   [
+    2,
+    8,
+    3,
+    150
+   ],
+   [
+    3,
+    7,
+    4,
+    106
+   ],
+   [
+    4,
+    4,
+    4,
+    8
+   ],
+   [
+    4,
+    4,
+    5,
+    7
+   ],
+   [
+    4,
+    7,
+    3,
+    2
+   ],
+   [
+    4,
+    7,
+    5,
+    106
+   ],
+   [
+    4,
+    8,
+    2,
+    626
+   ],
+   [
+    4,
+    8,
+    4,
+    479
+   ],
+   [
+    5,
+    4,
+    6,
+    8
+   ],
+   [
+    5,
+    7,
+    6,
+    106
+   ],
+   [
+    6,
+    8,
+    0,
+    626
+   ],
+   [
+    6,
+    8,
+    4,
+    45
+   ],
+   [
+    6,
+    8,
+    5,
+    626
+   ],
+   [
+    6,
+    8,
+    6,
+    54
+   ],
+   [
+    7,
+    7,
+    8,
+    106
+   ],
+   [
+    8,
+    8,
+    3,
+    476
+   ],
+   [
+    8,
+    8,
+    4,
+    102
+   ],
+   [
+    8,
+    8,
+    9,
+    610
+   ],
+   [
+    8,
+    8,
+    10,
+    492
+   ],
+   [
+    9,
+    4,
+    5,
+    1
+   ],
+   [
+    9,
+    7,
+    7,
+    2
+   ],
+   [
+    9,
+    8,
+    6,
+    572
+   ],
+   [
+    9,
+    8,
+    7,
+    626
+   ],
+   [
+    10,
+    4,
+    7,
+    8
+   ],
+   [
+    10,
+    4,
+    8,
+    8
+   ],
+   [
+    10,
+    4,
+    9,
+    8
+   ],
+   [
+    10,
+    4,
+    10,
+    8
+   ],
+   [
+    10,
+    7,
+    7,
+    104
+   ],
+   [
+    10,
+    8,
+    8,
+    626
+   ],
+   [
+    10,
+    8,
+    9,
+    16
+   ],
+   [
+    11,
+    7,
+    9,
+    106
+   ],
+   [
+    11,
+    7,
+    10,
+    106
+   ],
+   [
+    11,
+    8,
+    10,
+    134
+   ]
+  ]
+ }
+}
diff --git a/research/e8-eleven-hosting-selected/upstream445/proof/INHERITED-ROW-DIVISOR.tex b/research/e8-eleven-hosting-selected/upstream445/proof/INHERITED-ROW-DIVISOR.tex
new file mode 100644
index 0000000000..590da4b892
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/proof/INHERITED-ROW-DIVISOR.tex
@@ -0,0 +1,95 @@
+\subsection{Internal row reserve and ordinary conversion}
+The finite cover requires a row divisor $W(w)$ at each coarse level.
+All children have ratio at most $66/67$ and depth
+$D(n)\le47\lceil\log_2\max(2,n)\rceil+O(1)$.
+A sufficient common divisor is $W(w)^{D(n)}$ times the inherited old-leaf
+reserve. The old supplier has its retained complete-row contract and
+logarithmic reserve. Therefore a sufficient integer $S(e,w)$ satisfies
+\[
+ \log_qS(e,w)=O(w\log e).
+\]
+Unused stock is divided only into fresh descendant role fields; exposed
+parent low/high fields are spectator prefixes. Their weights cannot depend
+on those fresh roles. Every completed call restores its row coordinate,
+so successive residuals and the outer wrapper reuse one reserve instead
+of multiplying reserves for sequential calls.
+
+The unweighted reversed endpoint $F_n(H,D)=(C_nD,C_nH)$ converts to an
+ordinary interchange by the chronological sequence
+\[
+ D\leftarrow D-H;\quad F_n;\quad D\leftarrow D+H;\quad
+ F_n;\quad D\leftarrow H-D.
+\]
+Indeed the successive values are $(H,D-H)$, $(C_n(D-H),C_nH)$,
+$(C_n(D-H),C_nD)$, $(D,D-H)$, and $(D,H)$.
+The three additive maps cost $O(Vn)$ in the atom model. The two calls
+reuse restored rows; their constant multiplicity is outside the recursion
+and does not multiply its characteristic moment.
+
+\subsection{Borrowing and restoring the stock}
+Set $\beta=1/1000$, $w=\lceil e^\beta\rceil$, and
+$k=\lceil\log_qS(e,w)\rceil=O(w\log e)$, using the depth bound for the
+original width $e$. For sufficiently large $e$, $k<e/2$. Write the two
+original complete radix-$q$ chunks as $H=(H_{\rm hi},H_{\rm body})$ and
+$D=(D_{\rm hi},D_{\rm body})$, both high parts having $k$ digits. The
+physical order, including arbitrary original complete spectators $Z$, is
+\[
+ H_{\rm hi},\ H_{\rm body},\ Z,\ D_{\rm hi},\ D_{\rm body}.
+\]
+The complete $q^k$ range of $H_{\rm hi}$ already precedes both bodies.
+Reinterpret it as a preceding row field; $D_{\rm hi}$ remains an intervening
+spectator. Pad only this row range to $\lceil q^k/S\rceil S$. As $q^k\ge S$,
+the padding factor is less than two.
+
+Execute the completed \emph{ordinary} body wrapper with this row reserve,
+then remove the padding. Each row is restored, so the genuine row range
+is invariant at the completed endpoint. The order of values is now
+\[
+ H_{\rm hi},\ D_{\rm body},\ Z,\ D_{\rm hi},\ H_{\rm body}.
+\]
+One inherited ordinary width-$k$ interchange of the two high parts,
+with the bodies and $Z$ as spectators, gives
+\[
+ D_{\rm hi},\ D_{\rm body},\ Z,\ H_{\rm hi},\ H_{\rm body}.
+\]
+This is precisely the original full-chunk interchange. Its extra cost is
+$O(Vk^{1-a_{\rm old}})\le O(Vw\log e)$, conservatively. No full body is
+moved once per borrowed digit. Padding occurs only in this outer wrapper;
+it contributes one volume constant, not a recursive branching factor.
+The wrapper does not rely on a raw reversed call preserving borrowed high
+positions. Small widths use the retained supplier directly.
+
+\subsection{Uniform saving and return to binary addresses}
+Select atom width from the original $e$. Since $k=o(e)$, the body width
+$e-k$ has the same asymptotic powers as $e$. Apply the ordinary wrapper to
+its complete atom body and the old ordinary supplier to fewer than $w$
+remaining digits. The stopped recurrence and the borrowing cost give
+\[
+ O\!\left(V\left[e^{1-\beta}+
+ e^{(1-\beta)(1-a)+\beta(1-a_{\rm old})}+e^\beta\log e\right]\right).
+\]
+Here $a=747/2000000$ and $a_{\rm old}=384599/10^{10}$. Set
+\[
+ a_{\rm bit}=(1-\beta)a+\beta a_{\rm old}
+ =\frac{3731649599}{10^{13}}=0.0003731649599.
+\]
+The inequalities $\beta>a_{\rm bit}$ and $\beta<1-a_{\rm bit}$ make both
+the atom-adapter and borrowing terms lower order. The remainder cost
+$O(Vw^{1-a_{\rm old}})$ is also covered. Thus the ordinary radix-$q$
+interchange has cost $O(Ve^{1-a_{\rm bit}})$, without an externally supplied
+superpolynomial stock of rows.
+
+For an original binary chunk range $[2^e]$, let
+$t=\lceil e/\log_2q\rceil$ and embed it numerically into $[q^t]$.
+Pad both exchanged ranges while retaining every spectator. The total
+logical-volume increase is below $q^2$. Execute the completed ordinary
+radix-$q$ interchange, then remove the padding. Its endpoint preserves the
+rectangular genuine set $[2^e]\times[2^e]$; intermediate maps may mix genuine
+and padded addresses, which does not affect this endpoint justification.
+As $q$ is fixed and $t=\Theta(e)$, the binary interchange has the same
+saving exponent. All schedules use a fixed number of finite-alphabet
+tapes; low residue tables and port types are fixed independently of $w$.
+
+The conclusion retains the original local-producer, ordered-affine,
+ordinary-leaf and multiplication-framework hypotheses. It adds no free
+unit-scaling, dense chart transformation, or external row-stock primitive.
diff --git a/research/e8-eleven-hosting-selected/upstream445/proof/UPSTREAM-PR234-NOTICE.md b/research/e8-eleven-hosting-selected/upstream445/proof/UPSTREAM-PR234-NOTICE.md
new file mode 100644
index 0000000000..5f8fbb25c1
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/proof/UPSTREAM-PR234-NOTICE.md
@@ -0,0 +1,13 @@
+# Attribution and licence
+
+This contribution uses Apache-2.0. Original source headers, licences and notices are preserved. These credits do not imply review or endorsement by the named contributors or OpenAI.
+
+- Jacob Sussman: five-stage complex geometry and published gcert/1 export in wht-power-saving-lean at f010392c923279e3dd59ef3aa5fedad23affc5fd. Original Claude assistance disclosure retained in inputs/complex/NOTICE.
+- Avi Eisenberg / ikeboy: retained PR193 source-assisted complex helper and donor selection at 187e1010ac8b259af8e9b5166f68b64bc27b4b47.
+- eumemic: current PR210 frames, gauges, source borrowing and retimed bit helper at df95878d11190518e45ef9717c9ee05011f88ace.
+- Chafik Boukhalfa / chafreaky: PR200 physical bit construction carried by PR202 at 8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d.
+- Rohan Arun, Dugongue, evmckinney9, icekylinx, James Chang, Douglas Colkitt, OpenAI and earlier contributors retain the attribution and original assistance disclosures in the supplied source notices. The exact outer assembly also credits Zhihao Chen and the RaD / hipotures balanced reduction in its original header.
+
+The paired-cube helper design predates Sussman’s certificate export. The new contribution here is the explicit source-bound five-stage composition, adapters, paid accounting and reproducible finite verification. No exclusive priority is claimed for the inherited designs or theorem interfaces.
+
+Assisted with ChatGPT.
diff --git a/research/e8-eleven-hosting-selected/upstream445/verify.py b/research/e8-eleven-hosting-selected/upstream445/verify.py
new file mode 100644
index 0000000000..b0b82d5dd7
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/upstream445/verify.py
@@ -0,0 +1,50 @@
+"""Fresh PR444 reconstruction, eleven-stage geometry, hosted ownership and exact composition.
+Usage: python -B research/r740-hosted-eleven/verify.py /absolute/new/output [--quick]
+--quick skips only PR443's already-inherited exhaustive negative controls.
+Apache-2.0; chafreaky with OpenAI Codex assistance.
+"""
+from pathlib import Path
+import hashlib,json,os,subprocess,sys,time
+assert __debug__
+ROOT=Path(__file__).resolve().parent
+out=Path(sys.argv[1]).resolve();quick='--quick' in sys.argv[2:]
+assert not out.exists() and not out.is_relative_to(ROOT.parent)
+read=lambda p:json.loads(p.read_text())
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+def inventory(p):
+    return {f.relative_to(p).as_posix():sha(f) for f in p.rglob('*') if f.is_file() and '__pycache__' not in f.parts}
+def integrity():
+    actual=inventory(ROOT);actual.pop('MANIFEST.json')
+    assert actual==read(ROOT/'MANIFEST.json'),'package manifest differs'
+    for name,expected in read(ROOT/'SOURCE.json')['packages'].items():
+        assert inventory(ROOT.parent/name)==expected['files'],('upstream package differs',name)
+integrity();out.mkdir(parents=True)
+env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONINTMAXSTRDIGITS='0',PYTHON=sys.executable)
+env.pop('PYTHONOPTIMIZE',None);steps=[]
+def run(name,cmd):
+    log=out/(name+'.log');t=time.monotonic();print('RUN',name,flush=True)
+    with log.open('w') as f:q=subprocess.run(list(map(str,cmd)),env=env,stdout=f,stderr=subprocess.STDOUT)
+    if q.returncode:raise RuntimeError((name,q.returncode,log.read_text()[-4000:]))
+    steps.append(dict(name=name,seconds=round(time.monotonic()-t,2),log_sha256=sha(log)))
+    print('PASS',name,flush=True)
+def py(name,path,*args):run(name,[sys.executable,'-B',path,*args])
+try:
+    args=['--quick'] if quick else []
+    py('parent444',ROOT.parent/'r740-idle-hosted-replicas/verify.py',out/'parent444',*args)
+    base=out/'parent444/base443/candidate';host=out/'bit'
+    py('geometry',ROOT/'code/geometry.py','--source',ROOT.parent/'e8-r740-replica32/parent436','--out',host)
+    py('emit',ROOT/'code/emit.py','--word',ROOT.parent/'e8-r740-replica32/data/word.json.gz',
+       '--local-check',base,'--out',host,'--isometries',ROOT.parent/'e8-r740-replica32/data/residual-isometries.json')
+    py('independent-audit',ROOT/'code/audit.py',base,host)
+    assert len(read(host/'AUDIT.json')['mutations_rejected'])==22
+    py('exact-assembly',ROOT/'code/assemble.py',out/'parent444',host)
+    (out/'RESULT.json').write_bytes((host/'RESULT.json').read_bytes())
+    actual=read(out/'RESULT.json')
+    for k,v in read(ROOT/'EXPECTED.json').items():assert actual[k]==v,(k,actual[k],v)
+    integrity()
+    receipt=dict(status='PASS_R740_ELEVEN_STAGE_HOSTING',mode='quick' if quick else 'full',kappa=actual['kappa'],
+                 manifest_sha256=sha(ROOT/'MANIFEST.json'),source_sha256=sha(ROOT/'SOURCE.json'),
+                 emitted_program_sha256=actual['emitted_program_sha256'],checks=steps,python=sys.version.split()[0])
+    (out/'RECEIPT.json').write_text(json.dumps(receipt,indent=2)+'\n');print(json.dumps(receipt,indent=2))
+except BaseException as e:
+    (out/'FAILURE.json').write_text(json.dumps(dict(error=repr(e),completed=steps),indent=2)+'\n');raise
diff --git a/research/e8-eleven-hosting-selected/verify.py b/research/e8-eleven-hosting-selected/verify.py
new file mode 100644
index 0000000000..5a582d0fb0
--- /dev/null
+++ b/research/e8-eleven-hosting-selected/verify.py
@@ -0,0 +1,38 @@
+"""Full reconstruction; Python3.11+, SymPy. OpenAI Codex assistance, Apache-2.0."""
+from pathlib import Path
+import gzip,hashlib,json,os,subprocess,sys,time
+assert __debug__
+ROOT=Path(__file__).resolve().parent;PARENT=ROOT.parent/'e8-hosting-selected-kernel'
+OUT=Path(sys.argv[1]).resolve();assert not OUT.exists() and not OUT.is_relative_to(ROOT.parent)
+read=lambda p:json.loads(p.read_text());sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+def integrity():
+ actual={p.relative_to(ROOT).as_posix():sha(p) for p in ROOT.rglob('*') if p.is_file() and p!=ROOT/'MANIFEST.json' and '__pycache__' not in p.parts}
+ assert actual==read(ROOT/'MANIFEST.json')
+ assert sha(PARENT/'MANIFEST.json')==read(ROOT/'SOURCE.json')['parent_manifest_sha256']
+integrity();OUT.mkdir(parents=True);steps=[]
+env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONINTMAXSTRDIGITS='0');env.pop('PYTHONOPTIMIZE',None)
+def run(name,path,*args):
+ log=OUT/(name+'.log');t=time.monotonic();print('RUN',name,flush=True)
+ with log.open('w') as f:q=subprocess.run([sys.executable,'-B',str(path),*map(str,args)],env=env,stdout=f,stderr=subprocess.STDOUT)
+ assert q.returncode==0,(name,log.read_text()[-3000:])
+ steps.append(dict(name=name,seconds=round(time.monotonic()-t,2),log_sha256=sha(log)));print('PASS',name,flush=True)
+try:
+ run('parent-full',PARENT/'verify.py',OUT/'parent')
+ b=OUT/'parent/changed/bit426-source-centres';candidate=OUT/'candidate';candidate.mkdir()
+ for n in ('records','nine'):(candidate/n).symlink_to(b/('global' if n=='nine' else n),target_is_directory=True)
+ (candidate/'word.json.gz').write_bytes(gzip.compress((b/'bit-source-centres.json').read_bytes(),mtime=0))
+ template=json.loads(gzip.decompress((b/'global/GLOBAL-TEMPLATE.json.gz').read_bytes()))
+ (candidate/'isometries.json').write_text(json.dumps(template['residual_isometries']))
+ host=OUT/'bit'
+ run('geometry',ROOT/'code/geometry.py','--source',ROOT.parent/'e8-rank138-idle-hosting/upstream443/parent436','--out',host)
+ run('emit',ROOT/'code/emit.py','--word',candidate/'word.json.gz','--local-check',candidate,'--out',host,'--isometries',candidate/'isometries.json')
+ run('independent-audit',ROOT/'code/audit.py',candidate,host)
+ assert len(read(host/'AUDIT.json')['mutations_rejected'])==22
+ run('exact-assembly',ROOT/'code/assemble.py',OUT/'parent',host)
+ (OUT/'RESULT.json').write_bytes((host/'RESULT.json').read_bytes())
+ actual=read(OUT/'RESULT.json')
+ for k,v in read(ROOT/'EXPECTED.json').items():assert actual[k]==v,(k,actual[k],v)
+ integrity();receipt=dict(status='PASS_FULL_ELEVEN_HOSTING_SELECTED',python=sys.version.split()[0],kappa=actual['kappa'],manifest_sha256=sha(ROOT/'MANIFEST.json'),checks=steps)
+ (OUT/'RECEIPT.json').write_text(json.dumps(receipt,indent=2)+'\n');print(json.dumps(receipt,indent=2))
+except BaseException as e:
+ (OUT/'FAILURE.json').write_text(json.dumps(dict(error=repr(e),completed=steps),indent=2)+'\n');raise
diff --git a/research/e8-hosting-selected-kernel/AUDIT.json b/research/e8-hosting-selected-kernel/AUDIT.json
new file mode 100644
index 0000000000..2a88108913
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/AUDIT.json
@@ -0,0 +1,41 @@
+{
+  "status": "PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT",
+  "bit_template_sha256": "b099b89581f7dd9034e64239a67d9d67e2cd10023632e5df5c8bbb29831e5772",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f",
+  "bit_profile": {
+    "1": 1465920,
+    "2": 619328,
+    "3": 153728,
+    "4": 228672,
+    "5": 62208,
+    "6": 16000,
+    "7": 31552,
+    "8": 5184
+  },
+  "complex_profile": {
+    "1": 138384,
+    "2": 56448,
+    "3": 15936,
+    "4": 16128,
+    "5": 32064,
+    "7": 3840,
+    "8": 7488
+  },
+  "bit_live": 74528,
+  "complex_live": 8400,
+  "bit_hosted_residuals": 321536,
+  "complex_hosted_residuals": 34560,
+  "bit_maxchild": 8,
+  "complex_maxchild": 8,
+  "mutations_rejected": [
+    "bit: hosted residual outside its window",
+    "bit: overlapping hosted coordinates",
+    "bit: understated live stock",
+    "bit: hosted owner on the active pair",
+    "bit: missing remainder child",
+    "complex: hosted residual outside its window",
+    "complex: remainder child understated",
+    "complex: dropped bank",
+    "complex: duplicated hosted residual"
+  ]
+}
diff --git a/research/e8-hosting-selected-kernel/CERTIFICATE.json b/research/e8-hosting-selected-kernel/CERTIFICATE.json
new file mode 100644
index 0000000000..d277d21ac4
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/CERTIFICATE.json
@@ -0,0 +1,116 @@
+{
+  "status": "PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY",
+  "kappa": "312258824824501/250000000000000000",
+  "kappa_decimal": "0.001249035299298004",
+  "bit_lower": "625298669760136826673/500000000000000000000000",
+  "complex_lower": "1267453159029119/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr434_percent": 10.231638028931764,
+  "bit": {
+    "live": 74528,
+    "physical": 74537,
+    "maxchild": 8,
+    "rank_mass": 4749824,
+    "hosted_residuals": 321536,
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 288,
+    "charged_two_level_coefficient_bits": 320,
+    "row_coefficient": 18355
+  },
+  "complex": {
+    "live": 8400,
+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
+  },
+  "strict_outer_constraints": {
+    "bit_positive": "16007645945859502703459697719263921004407398109158311718718546725928705628143217765348018079869732567625774608014604714307774384027019774524485530915302137457211/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "215754489713220496540302280736078995592601890841688281281453274071294371856782234651981920130267432374225391985395285692225615972980225475514469084697862542789/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "29982546840970881/1000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "215754489713220480316901845163355795592601890841688281281453274071294371856782234651981920130267432374225391985395285692225615972980225475514469084697862542789/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_positive": "8003822972929751335722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_internal": "16007645945859502703459697719263921004407398109158311718718546725928705628143217765348018079869732567625774608014604714307774384027019774524485530915302137457211/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_leaf": "107877244856610256166096868441180601255998664684765145048124746193958904646937843254696588208351481535130775862430210471887416001094827045531618569368705795880030915302137457211/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_positive": "8003822972929752935722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_below_one": "6391996177027070247064277797086227542201255998664684765145048124746193958904646937843254696588208351481535130775862430210471887416001094827045531618569368705795880030915302137457211/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_reservations": "1/4000000000000000000",
+    "lambda_above_tau": "16007645945859502703459697719263921004407398109158311718718546725928705628143217765348018079869732567625774608014604714307774384027019774524485530915302137457211/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_sigma": "215754489713220512547948226595581699052299610105609285688851383229606090575328960580687548273485197722243471855127853318000223987584939783288853111717637067274530915302137457211/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_internal": "16007645945859502703459697719263921004407398109158311718718546725928705628143217765348018079869732567625774608014604714307774384027019774524485530915302137457211/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_prime_above_lambda": "16007645945859502703459697719263921004407398109158311718718546725928705628143217765348018079869732567625774608014604714307774384027019774524485530915302137457211/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_leaf": "107877244856610256166096868441180601255998664684765145048124746193958904646937843254696588208351481535130775862430210471887416001094827045531618569368705795880030915302137457211/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_reservations": "1/4000000000000000000",
+    "lambda_prime_below_one": "8003822972929751335722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "epsilon_positive": "6399999999999999993600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/6408003822972929751335722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789",
+    "epsilon_below_one": "8003822972929757735722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789/6408003822972929751335722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789",
+    "guard_width": "8003822972929757735722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789/6408003822972929751335722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789",
+    "K_geometry": "4808003822972929752935722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789/6408003822972929751335722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789000000000000000000",
+    "K_dominates_log": "8003822972929752927718379940842704863021798421542777056207873918490806240401186902939262316438586361719565812345921271063243359861335383426355797431726121249651587654066568338669030915302137457211/6408003822972929751335722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789000000000000000000",
+    "record_suffix": "8003822972929757735722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789/6408003822972929751335722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789",
+    "phase_local": "64030583783438055477773800337249911054229807768749421040871000695133093907872622000156386198980125990973650381308909797760031447853671594107634467446145180678491371246951606138192030915302137457211/51264030583783438010685777623310179662389952010682521878839615002030448328762824497253962427294333188147718953793100558316224900671991241383635747051445050353632959752677582900342312000000000000000000",
+    "phase_boundary": "12806116756687605969151701689106181142268199222731917969178999070774430897613024196986444363513575472798487346828463144780110910260678487199036826290104897772123569104885285864342430915302137457211/10252806116756687602137155524662035932477990402136504375767923000406089665752564899450792485458866637629543790758620111663244980134398248276727149410289010070726591950535516580068462400000000000000000",
+    "gamma_sublinear": "1/2000000000000000000",
+    "cell_above_band": "12799999999999999980791996177027070248664277797086227542201255998664684765145048124746193958904646937843254696588208351481535130775862430210471887416001094827045531618569368705795880030915302137457211/25632015291891719005342888811655089831194976005341260939419807501015224164381412248626981213647166594073859476896550279158112450335995620691817873525722525176816479876338791450171156000000000000000000",
+    "prime_interval_packing": "8003822972929757735722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789/6408003822972929751335722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789",
+    "alpha_positive": "16007645945859509063440582854615164261765799756858011911159749172296847335754249059684565728230234880184435036483491060591355943860240556380824178862357415453771556738764430881458030915302137457211/12816007645945859502671444405827544915597488002670630469709903750507612082190706124313490606823583297036929738448275139579056225167997810345908936762861262588408239938169395725085578000000000000000000",
+    "alpha_below_one": "12799999999999999993608003822972929751335722202913772457798744001335315234854951875253806041095353062156745303411791648518464869224137569789528112583998905172954468381430631294204119969084697862542789/12816007645945859502671444405827544915597488002670630469709903750507612082190706124313490606823583297036929738448275139579056225167997810345908936762861262588408239938169395725085578000000000000000000",
+    "alpha_below_one_fourth": "3187994265540605366604420518602271064637606200910799605516316188454606173211922282018688085977665589379047999575585293834172700348139212030096410011852958231648288427803584500389936469084697862542789/12816007645945859502671444405827544915597488002670630469709903750507612082190706124313490606823583297036929738448275139579056225167997810345908936762861262588408239938169395725085578000000000000000000",
+    "delta_positive": "1/8000000000000000000",
+    "delta_below_one_eighth": "999999999999999999/8000000000000000000",
+    "short_record_fallback": "81817422943582135104691635556785323569626762018831877177661277590973460301598234661046146051387644062223441412286753777975282124200867722924981511980260058043275928672060753182885461956467155336523145287047019946807761008345576409812174404623085175039082386078418106566118496399120623420234384735159567744623476316002734380886899179928855898521/82022448934053500817097244197296287459823923217092035006143384003248717326020519195606339883670933101036350326068960893305959841075185986213817195282312080565812735604284132640547699200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "small_field_exposure": "1/1000000000000000000",
+    "artificial_boundary": "358912244670267504155910232455400226553126782694201492404113152020249532334667451603793117541640724691651987540580179412085193813048342640437670314163557118347927083165712557085350855907254093587628367/51264030583783438010685777623310179662389952010682521878839615002030448328762824497253962427294333188147718953793100558316224900671991241383635747051445050353632959752677582900342312000000000000000000",
+    "literal_scalar_guard": "1",
+    "row_product_gap": "23971789/25",
+    "balanced_prefix_above_kappa": "2645898842131264516196585566598067266520987908983855019421823096585443301965735724222308494497690026654285161519620271475538403135141320979050566278820970570406114022584815471926711/1602000955743232437833930550728443114449686000333828808713737968813451510273838265539186325852947912129616217306034392447382028145999726293238617095357657823551029992271174465635697250000000000000000",
+    "coordinate_movement_above_kappa": "19994114845051503459697719263921004407398109158311718718546725928705628143217765348018079869732567625774608014604714307774384027019774524485530915302137457211/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_phase_layer_above_kappa": "835118309110425662690124012695699321657041526920020968566468102217593433353517966946497734915793691619735155370868703222525099991313275748649559346770650197484067224250912805032811/1281600764594585950267144440582754491559748800267063046970990375050761208219070612431349060682358329703692973844827513957905622516799781034590893676286126258840823993816939572508557800000000000000000",
+    "bulk_exposure_above_kappa": "19994114845051503459697719263921004407398109158311718718546725928705628143217765348018079869732567625774608014604714307774384027019774524485530915302137457211/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "Gaussian_arithmetic_above_kappa": "52628743833335815761612127116569290239677893080806784447223579714465155457426777864330145306867122610344800822507160838269588337404527745464845779015117901781975048877290605788940807/51264030583783438010685777623310179662389952010682521878839615002030448328762824497253962427294333188147718953793100558316224900671991241383635747051445050353632959752677582900342312000000000000000000",
+    "scalar_work_above_kappa": "78260759125227534766955015928224380070872869086148045386643387215480379621808190112957126520514289204418660299403711117427700787740523366156663652540840426958791528753629397239111963/51264030583783438010685777623310179662389952010682521878839615002030448328762824497253962427294333188147718953793100558316224900671991241383635747051445050353632959752677582900342312000000000000000000",
+    "dimension_above_kappa": "1597999044256767561611968291402821401746899566264238457807249940170403509147984831046256976112787812092692277191655634206903133373620545182299786039783663155499536286549796104770416772584815471926711/1602000955743232437833930550728443114449686000333828808713737968813451510273838265539186325852947912129616217306034392447382028145999726293238617095357657823551029992271174465635697250000000000000000"
+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "60635834279878833657621288270998129187561/40000000000000000000000000000000000000000000000",
+      "cutoff_log2": "15666203684619"
+    },
+    {
+      "gap": "15166202606001735527811873638490069557427922716450327640008309/8000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "10016794587070683047"
+    },
+    {
+      "gap": "3793362525938242303531654446273018863642198826327324781094893932955821181917128721/1600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "6404625895300929569587758"
+    },
+    {
+      "gap": "948793816554854176593164799976559622596462848760620538101644058340477446057919335560726765941459444349/320000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "4095045825508429519876901673793"
+    },
+    {
+      "gap": "237311804547357441198117541697802072526688310936973526787583684722628795042632495936204365514791859899793562164721589039481/64000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "2618326282775972067811110728595613513"
+    },
+    {
+      "gap": "59356302280736078995592601890841688281281453274071294371856782234651981920130267432374225391985395285692225615972980225475514469084697862542789/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1674128401780281260605462057785744226537336"
+    }
+  ],
+  "bit_template_sha256": "b099b89581f7dd9034e64239a67d9d67e2cd10023632e5df5c8bbb29831e5772",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f"
+}
diff --git a/research/e8-hosting-selected-kernel/EXACT-LOCAL.json b/research/e8-hosting-selected-kernel/EXACT-LOCAL.json
new file mode 100644
index 0000000000..a52d92c2f8
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/EXACT-LOCAL.json
@@ -0,0 +1,22 @@
+{
+  "status": "PASS_EXACT_LOCAL_KERNEL_AND_TWO_AGGREGATE_MOMENTS_GLOBAL_PENDING",
+  "entries": 123,
+  "entrance_rank": 147,
+  "donors": 118,
+  "word_sha256": "f5ae52ba95d0edd76f85fdb4da04cd78ad46b55c9ad3b86cc098146b62032336",
+  "local_profile": {
+    "1": 2545,
+    "2": 1022,
+    "3": 266,
+    "5": 108,
+    "4": 357,
+    "8": 9,
+    "7": 14
+  },
+  "bit_lower": "625298669760136826673/500000000000000000000000",
+  "bit_upper": "1250597339520273653347/1000000000000000000000000",
+  "live": 74528,
+  "replicas": 64,
+  "local_columns": 980,
+  "scope": "Global emitted program, ownership, banks, invoice and outer assembly not yet verified."
+}
diff --git a/research/e8-hosting-selected-kernel/EXPECTED.json b/research/e8-hosting-selected-kernel/EXPECTED.json
new file mode 100644
index 0000000000..688a76200a
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/EXPECTED.json
@@ -0,0 +1,33 @@
+{
+  "kappa": "312258824824501/250000000000000000",
+  "kappa_decimal": "0.001249035299298004",
+  "bit_lower": "625298669760136826673/500000000000000000000000",
+  "complex_lower": "1267453159029119/1000000000000000000",
+  "binding_component": "bit",
+  "bit": {
+    "live": 74528,
+    "physical": 74537,
+    "maxchild": 8,
+    "rank_mass": 4749824,
+    "hosted_residuals": 321536,
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 288,
+    "charged_two_level_coefficient_bits": 320,
+    "row_coefficient": 18355
+  },
+  "complex": {
+    "live": 8400,
+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
+  },
+  "bit_template_sha256": "b099b89581f7dd9034e64239a67d9d67e2cd10023632e5df5c8bbb29831e5772",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f"
+}
diff --git a/research/e8-hosting-selected-kernel/INHERITED-HOSTING-PROOF.md b/research/e8-hosting-selected-kernel/INHERITED-HOSTING-PROOF.md
new file mode 100644
index 0000000000..ff3eba6770
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/INHERITED-HOSTING-PROOF.md
@@ -0,0 +1,109 @@
+# Idle-axis hosting: helper residuals on pending idle coordinates
+
+This package changes only the global nine-stage templates of #434's two suppliers. Both local words are unchanged:
+
+- the complex word is #433's split-centre word, R = 560, m = 73;
+- the bit word is #434's early-reset kernel word, R = 747, m = 64.
+
+So are their local programs, scalar replays, data routes, bridges, terminal exchange and cover correction. What
+changes is where whole dirty-helper residuals live. Many of them move from bank streams onto coordinates of *idle*
+data families that would otherwise be advanced later by an idle child.
+
+## 1. The two inherited facts used
+
+**(a) Dirty invocations act on a helper stream as its residual.** The complete dirty local invocation is block
+diagonal on helpers at its endpoint and admits arbitrary correlated helper values (#425/#433, #386/#434). On the
+physical stream that owns a helper residual of width w, it acts as an exact coordinate factor on w coordinates:
+
+- complex: P_g C_block P_g⁻¹ (PR425-COMPLEX §5, INHERITED-COMPLEX-GEOMETRY);
+- bit: D_P with P the width-w coordinate projector (PR386-BIT-GEOMETRY; mixed widths 8 − entrance rank, #434).
+
+This holds whatever the stream held before. Banks rely on exactly this: eight sequential residuals and a pad tile a
+bank stream.
+
+**(b) An idle child is a product of coordinate factors.** Advancing a data pair from level a to level b applies, on
+every physical data stream (F, g) of that pair, the commuting product of coordinate factors on its pending set S:
+
+- complex: C over S, in the basis U_q ⊕ I used by the inherited idle factorisation;
+- bit: D_{P_V−P_U}, an orthogonal coordinate projector difference.
+
+Factors on disjoint coordinate sets commute and multiply:
+
+- complex: C_{S'}·C_{S∖S'} = C_S;
+- bit: D_{P'}·D_{P−P'} = D_P for P' ≤ P (the parent's identity D_I·D_P = D_{I−P}).
+
+## 2. Hosting lemma
+
+Fix a data family F (replica r, pair j, side, port) and an idle child Γ that advances pair j at recipe position τ.
+Let λ be the position of the last local invocation or bridge that names pair j before τ; idle children do not
+count as touches, since they act on other coordinates or on the other member. Let ι be any local invocation with
+λ < ι < τ. Then:
+
+1. ι is an invocation on another pair, and nothing touches F between ι and τ.
+2. A helper residual of ι, of width w, may be owned by stream (F, d·σ⁻¹) instead of a bank slot. Here d is the
+   invocation's cover class, and σ is a coordinate isometry carrying the local residual block onto a set S' ⊂ S of
+   w pending coordinates. When S' meets the local block of a level −1 advance, σ is composed with U_q ⊕ I.
+3. Γ is replaced by Γ' acting on S ∖ ⋃S' over all hosted residuals of F, which have pairwise disjoint S'.
+
+The complete program's operator is unchanged:
+
+- By (a), ι applies exactly the factor on S' to (F, d·σ⁻¹), for any prior contents.
+- Nothing else acts on F between ι and τ, so this factor may be moved to τ.
+- By (b), the moved factors times Γ' equal Γ.
+
+Distinct slots of one invocation have distinct σ, so distinct physical classes for every d. They are also disjoint
+from the invocation's own data owners, because pair j is not active, and from bank owners, because the families
+differ. Residuals of different invocations on F occupy disjoint coordinates. They are sequential, exactly as the
+parent's banks are co-owned sequentially by different cover classes.
+
+Two further points:
+
+- **Phases.** The stored Z₄ translations after Γ remain valid, because Γ'·∏(hosted factors) = Γ as exact operators.
+  The final X_δ(g) correction still applies to every live family; hosting changes no data endpoint.
+- **Reflection.** The inverse-transpose program reverses chronology and reflects each factor. The window condition
+  (no touch strictly between ι and τ) is symmetric, so hosting commutes with reflection.
+
+## 3. What is checked here
+
+- `bit_hosted.py` and `complex_hosted.py` read #434's freshly regenerated templates and compute windows from each
+  recipe. They apply a frozen integer-programme selection (`SELECTION.json`; `--discover` recomputes it with scipy)
+  and emit new owners, remainder children and banks.
+  - Bit: unhosted residuals keep an exact width-64 tiling with no padding.
+  - Complex: eight per bank plus one paid pad; a final partial bank pays the larger pad.
+- `audit.py` shares no code with the generators. It re-derives every window from the template schedule. For every
+  replica and invocation it checks that:
+  - each helper has exactly one owner;
+  - each hosted slot is inside its child's pending set, disjoint from other slots, outside the active pair, and in
+    window;
+  - every remainder child is exact, and the bank tiling is exact.
+
+  It also recomputes the paid profile and the rank deficit 2496, and rejects nine mutations.
+- `assemble.py` prices both suppliers with the two inherited rational moment engines and recomputes both finite
+  invoices with the hosted stock. Route charging is conservative: two extra route factors per helper selector, and
+  the parent's larger complex per-vertex bill is kept. It then runs #434's strict outer assembly: six bootstrap
+  levels and 47 inequalities. The next grid point and the zero-η, zero-β and unit-β controls are rejected.
+
+## 4. Result
+
+| | live stock | max child | hosted residuals | certified saving |
+| --- | ---: | ---: | ---: | --- |
+| bit | 14,259 → 9,457 | 42 → 8 | 39,568 of 53,784 | c = 1239085165241180038597/10²⁴ |
+| complex | 12,720 → 8,400 | 48 → 8 | 34,560 of 40,320 | b = 1267453159029119/10¹⁸ |
+
+κ = 618775866623647/(5·10¹⁷) ≈ 1.237551733247294·10⁻³, bit-bound, +9.218% over #434.
+
+## 5. Scope
+
+This is a written finite extension of the inherited correlated dirty-bank and compressed-window interfaces. The
+streams that own residuals now include data streams during idle windows. It is the principal new review point.
+
+All other interfaces remain inherited assumptions: the all-size compiler, restored-work, tape/common-grid, precision
+and analytic interfaces.
+
+No Lean proof and no unconditional integer-multiplication theorem is claimed. The global operator identity is argued
+from (a) and (b) and checked combinatorially. It is not replayed numerically on the 2⁷³- and 2⁶⁴-point address
+spaces; neither parent does that either.
+
+## R740 composition and additional scope
+
+The above argument is inherited from PR442 and remains an explicit additional hosting assumption. Here the bit local word has R740 and matches PR441 after two joint B-frame sweeps. The assignment is regenerated for its actual residual-width census, rather than transferred by helper index. Parent residual isometries remain checked, and the finite selector invoice retains the parent extra-helper-route bound of 144 in addition to the two hosting factors. All host windows, owners, disjoint intervals, remainders and bank coverage are independently rechecked. Original PR442 numerical values above describe its historical R747 construction; EXPECTED.json and CERTIFICATE.json describe this R740 composition.
diff --git a/research/e8-hosting-selected-kernel/LICENSE b/research/e8-hosting-selected-kernel/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/LICENSE
@@ -0,0 +1,201 @@
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+      any Contribution intentionally submitted for inclusion in the Work
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+      the terms of any separate license agreement you may have executed
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+   6. Trademarks. This License does not grant permission to use the trade
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diff --git a/research/e8-hosting-selected-kernel/MANIFEST.json b/research/e8-hosting-selected-kernel/MANIFEST.json
new file mode 100644
index 0000000000..6eeb64acf9
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/MANIFEST.json
@@ -0,0 +1,46 @@
+{
+  "parent_manifest_sha256": "ff4b2cadd18913f1948adcc3860e446aee39e4e3889df4d15e80117516374b4d",
+  "files": {
+    "AUDIT.json": "2d3b59641b26f884e68290cf6b4a566eac766df14a6d666dd3188b8f5ef2014f",
+    "CERTIFICATE.json": "c8765a22f3a0e43f55b9f6bbf0047477962fe9f045dcb0747a1133fa0b96ee29",
+    "EXACT-LOCAL.json": "1b7653a551e993dfaa6664a35314b9d58adc3760391082555d5459424993dc4b",
+    "EXPECTED.json": "fa9736c0cf8546016ee0edba61cd434034be3729f5b23dda5371e72972d1d51a",
+    "INHERITED-HOSTING-PROOF.md": "4f06d1dead63c62b076f0a6c1521c68c0b0544aa2c5df5e74a408fdfc34f91c4",
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE.md": "df28c5271e72421eba3c422658449f8388760bdee97cc02e13719dd781955918",
+    "PRECURSOR.json": "0c5adceaed6ac3b435674be21b781acace7156c66acea091b5aace67c516ef2f",
+    "PROOF.md": "a840e8463eebb8cbbc88b50aa67851428433e4c43dbe6051c97c3eee771e79c8",
+    "README.md": "75b6e071f7e8fa06b026bea44f024b3628e30166c2499fa2398796fe66e0901d",
+    "SELECTION.json": "4d766dd7796fbcdcff8e8497c2d51db6b7ee26a264cea66525e8cf60ae98bdeb",
+    "VALIDATION.json": "7f018e8e6c23f99707ea7a412b5422b21474b6ed58392934b5bafe67194ed203",
+    "WORD.json": "f5ae52ba95d0edd76f85fdb4da04cd78ad46b55c9ad3b86cc098146b62032336",
+    "code/SELECTION.json": "a52eff0c0ed4f30424ceebb319ec80b449a5661dfa88c53a1cc35c8854962b77",
+    "code/assemble.py": "38a5c2811199503db6f24e74669e5d18d4fbd1a2adb3a3759930fa0f93448fa5",
+    "code/audit.py": "f74bf5912399068bc5cbef420562255feba4d79d4813ef6df593ac4cd0f94686",
+    "code/bit_audit.py": "0128a0f46f54614dfdcb130fedfe8975da26cd8c801f247cb22e3a1f9f906479",
+    "code/bit_global.py": "7e3ef6deadff3c50acd48769eef35a932023e252c41f9f247bd08e1fad7f3107",
+    "code/bit_hosted.py": "a5c5bee943dce467ac5a15508db7764eefe67f41985d8f13412d0362bff7ac20",
+    "code/complex_hosted.py": "829c5c4f4bdfccedadd31505f1f0a394f7a208d1446b7bbf9cc92d3aa1530c0c",
+    "code/hosting_core.py": "d8b90cd5d152df3c7c351230863d9e61816ad5e1f21d69bea1a86a5daad559a3",
+    "code/residual_routes.py": "402924994a880d1ee45e42be2e7a51bd0281822046e474f5f5cc0adf885b52c7",
+    "evidence/assembly.log": "4813c9b302a6b07e1d276c9b939926cf8ebce5197d75703cdb061794827a21b2",
+    "evidence/bit-hosting.log": "20295c72cee3f6a3856f68889c5ae1a6874bd5892bef548122cc69842555f933",
+    "evidence/complex-hosting.log": "3b42f65586cb5c37e06df560fae4dcde1c42526238697a73d103f9895df24fcd",
+    "evidence/discovery.log": "a4482fec34eabed198c1281d33b085daa8ab1538f4573d107dba28783f568a97",
+    "evidence/export.log": "76145fe1bd54c65d5f4041e92b2589cb0dede760b5030bbe2042c3e502119594",
+    "evidence/global-audit.log": "42f3e7906f3f4a40b62923e48c792f93ccf1e58668a7993e5c5805f05666550b",
+    "evidence/global.log": "fdb53d5389baaf6e3074fd6bb98f320a6351d4ff6b3a7a97c1c7f92ebf85f382",
+    "evidence/hosting-audit.log": "1359977f74843042c039a81bf2c687cd0b931916b906fe7ca60efd9f745e9c52",
+    "evidence/rebuild.log": "c04d4e939822acd4f0f91c7690293f2b321c9e1fb2de342ce61b997d19e686d9",
+    "rebuild.py": "cb55809a7cb4bbc16be97ef0f056f0dc50e9c9e08cf80e176a0bbdabd37f3d63",
+    "vendor/pr439/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "vendor/pr439/NOTICE.md": "750f199a92e02e1ae45d092c1768f0e1833542787158348ab4af63adbde003e7",
+    "vendor/pr439/bank_routes.py": "0dd88bd715477cdf804a41577bc096ba7911427f748f3ac6d6added365f7da60",
+    "vendor/pr439/e8core.py": "1cb286196c1530d06f50f0997febc5993b388f33464e295611b920ba30a24eeb",
+    "vendor/pr439/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "vendor/pr439/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "vendor/pr439/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "vendor/pr439/tile_m.py": "d6ae4a556472d403773cd2117c992bfc10e1187112da1b3893f3fae628a131dd",
+    "verify.py": "ce37fbf2b1c48fc332825d5b731ffb3bc472b71481f8be02487836d4f6518e90"
+  }
+}
diff --git a/research/e8-hosting-selected-kernel/NOTICE.md b/research/e8-hosting-selected-kernel/NOTICE.md
new file mode 100644
index 0000000000..fa3b0ac153
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/NOTICE.md
@@ -0,0 +1,5 @@
+# Attribution
+
+Rohan Arun with substantial OpenAI Codex assistance: hosting-aware kernel search, nine added relations, frozen hosting assignment, 64-replica composition, independent finite audits and reproducible wrapper. Apache-2.0.
+
+Credit chafreaky PR443/PR444/PR417/PR439 for the rank138 precursor, replica construction, kernel and residual routes; eumemic PR436/PR440/PR441 for R740 and joint retiming; DaysSky PR442 for the additional idle-data hosting extension with Claude assistance; Rohan Arun PR434/PR435/PR438, icekylinx PR433, the retained PR426/PR389/PR376/PR370, PR425/PR386 and Jacob Sussman lineage. Original source-specific licenses and assistance disclosures remain in the sibling pinned parent and retained vendor subtree.
diff --git a/research/e8-hosting-selected-kernel/PRECURSOR.json b/research/e8-hosting-selected-kernel/PRECURSOR.json
new file mode 100644
index 0000000000..2c6d86903f
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/PRECURSOR.json
@@ -0,0 +1 @@
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diff --git a/research/e8-hosting-selected-kernel/PROOF.md b/research/e8-hosting-selected-kernel/PROOF.md
new file mode 100644
index 0000000000..1238db907f
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/PROOF.md
@@ -0,0 +1,9 @@
+# Composition and proof scope
+
+The precursor is reconstructed from the byte-pinned PR436 R740 word, the 57 PR443 A-frame witnesses and the final PR443 B-frame choices. The B scalar operands are checked unchanged and the canonical precursor hash is bound before applying the selected kernel. Each selected pivot response is the exact XOR of its donor responses. Pivots and donors are disjoint; each donor serves a single entrance; each entrance is contained in every participating first frame. All 980 local columns, arbitrary helper restoration and integer source spans are replayed after construction.
+
+Sixty-four independent bit replicas make the rank147 residual coordinates integral in complete width-64 banks. The global emitter checks the 7,620-column one-replica identity and emits all 576 calls and 426,240 helper assignments. The independent audit recomputes exact frame ranks, nested projectors, reflected programs, residual isometries, all data owners and bank partitions. The host audit then checks last-touch windows, non-overlapping slots, complete remaining banks and exact remainder children. Nine hosting mutations are rejected.
+
+The paid profile is reconstructed from emitted local instructions and child remainders, not accepted from the discovery score. Two rational moment engines agree. Both finite invoices are recomputed, including all 64-replica bit costs, extra residual route bound 144 and the two hosting factors. Prefix charge is 128 bits; the two-level coefficient is 288 bits charged at 320. Six bootstrap levels satisfy all 47 strict outer inequalities; the next kappa grid point fails.
+
+The idle-data hosting extension is inherited from PR442 as an additional mathematical assumption. See INHERITED-HOSTING-PROOF.md for that argument with its historical parameters. The all-size compiler, dirty-bank/compressed-window, restored-work, common-grid, tape, precision and analytic interfaces remain conditional. This is a finite conditional construction, not an unconditional multiplication theorem.
diff --git a/research/e8-hosting-selected-kernel/README.md b/research/e8-hosting-selected-kernel/README.md
new file mode 100644
index 0000000000..302a20363d
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/README.md
@@ -0,0 +1,11 @@
+# Hosting-selected response kernel
+
+Conditional kappa = 0.001249035299298004, 0.23769014% above PR444 and the preceding PR434 result, under the same additional idle-data hosting assumption.
+
+Discovery prices kernel relations together with their optimal idle-slot assignment. It retains nine additional rank-one relations that the unhosted cost model rejected. The final word has 123 pivots, 118 donor slots, total entrance rank 147, R740 and 64 bit replicas. Hosting leaves 74,528 live / 74,537 physical families and 321,536 hosted residuals; rank deficit is 19,968. The unchanged complex supplier remains eight replicas, 8,400 live families and deficit 2,496. Bit binds.
+
+Run `python -B research/e8-hosting-selected-kernel/verify.py /absolute/new/output`. Standard library only for verification; scipy was used only to nominate the frozen hosting assignment. The wrapper fully reruns the preceding rank138 construction and its complex phase replay, reconstructs the new precursor from pinned witnesses, checks every new response relation and local source span, emits/audits the 64-replica global template, then checks hosting, both exact moment engines, the fresh invoice and strict assembly.
+
+Changed-program reconstruction, global emission, independent global and hosting audits, two rational moments, fresh invoice, six bootstrap levels and 47 strict outer inequalities PASS. Full uninterrupted Python 3.11/3.14 wrappers and GitHub CI are pending at draft publication. The preceding rank138 result remains fully verified with published receipts.
+
+The additional hosting operator extension remains an assumption; the finite combinatorial audit does not prove it. This is not a stronger result under only the pre-hosting assumptions. All inherited compiler, dirty-bank/compressed-window, restored-work, tape/common-grid, precision and analytic obligations remain. No unconditional theorem or new Lean proof is claimed. The historical gain_over_pr434_percent field in CERTIFICATE.json compares to the old pre-hosting baseline, not the immediately preceding result.
diff --git a/research/e8-hosting-selected-kernel/SELECTION.json b/research/e8-hosting-selected-kernel/SELECTION.json
new file mode 100644
index 0000000000..1b700ec0de
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/SELECTION.json
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diff --git a/research/e8-hosting-selected-kernel/VALIDATION.json b/research/e8-hosting-selected-kernel/VALIDATION.json
new file mode 100644
index 0000000000..22bd0422b4
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/VALIDATION.json
@@ -0,0 +1,6 @@
+{
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diff --git a/research/e8-hosting-selected-kernel/WORD.json b/research/e8-hosting-selected-kernel/WORD.json
new file mode 100644
index 0000000000..dc716fc5f9
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/WORD.json
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+        [
+          9,
+          9,
+          9
+        ],
+        120
+      ],
+      [
+        6,
+        [
+          9,
+          9,
+          9
+        ],
+        120
+      ],
+      [
+        8,
+        [
+          9,
+          9,
+          9,
+          9,
+          9
+        ],
+        120
+      ],
+      [
+        10,
+        [
+          9,
+          9,
+          9,
+          9,
+          9
+        ],
+        120
+      ],
+      [
+        12,
+        [
+          9,
+          9,
+          9,
+          9,
+          9
+        ],
+        120
+      ],
+      [
+        13,
+        [
+          9,
+          9,
+          9,
+          9,
+          9
+        ],
+        120
+      ],
+      [
+        14,
+        [
+          9,
+          9,
+          9
+        ],
+        120
+      ],
+      [
+        15,
+        [
+          9,
+          9,
+          9
+        ],
+        120
+      ],
+      [
+        16,
+        [
+          9
+        ],
+        120
+      ],
+      [
+        17,
+        [
+          9
+        ],
+        120
+      ]
+    ],
+    "proxy_saving": 17393.16581129622,
+    "stages": [
+      [
+        0,
+        9,
+        0,
+        120
+      ],
+      [
+        2,
+        9,
+        0,
+        80
+      ],
+      [
+        2,
+        9,
+        1,
+        40
+      ],
+      [
+        4,
+        9,
+        3,
+        360
+      ],
+      [
+        6,
+        9,
+        0,
+        360
+      ],
+      [
+        8,
+        9,
+        1,
+        520
+      ],
+      [
+        8,
+        9,
+        5,
+        80
+      ],
+      [
+        10,
+        9,
+        2,
+        560
+      ],
+      [
+        10,
+        9,
+        3,
+        40
+      ],
+      [
+        12,
+        9,
+        4,
+        560
+      ],
+      [
+        12,
+        9,
+        7,
+        40
+      ],
+      [
+        13,
+        9,
+        5,
+        360
+      ],
+      [
+        13,
+        9,
+        6,
+        200
+      ],
+      [
+        13,
+        9,
+        7,
+        40
+      ],
+      [
+        14,
+        9,
+        6,
+        360
+      ],
+      [
+        15,
+        9,
+        7,
+        360
+      ],
+      [
+        16,
+        9,
+        8,
+        120
+      ],
+      [
+        17,
+        9,
+        7,
+        120
+      ]
+    ]
+  }
+}
diff --git a/research/e8-hosting-selected-kernel/code/assemble.py b/research/e8-hosting-selected-kernel/code/assemble.py
new file mode 100644
index 0000000000..a6fd3e0926
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/code/assemble.py
@@ -0,0 +1,82 @@
+"""Two exact moments for both hosted suppliers, fresh finite invoices with the hosted stock, and the strict outer
+assembly of #434 (six bootstrap levels, 47 inequalities, next-grid and parameter controls).
+usage: assemble.py PARENT_CHANGED_DIR BIT_DIR COMPLEX_DIR AUDIT.json OUT.json"""
+import gzip, hashlib, importlib.util, json, math, sys
+from fractions import Fraction as Q
+from pathlib import Path
+par, bd, cd, ap, outp = map(Path, sys.argv[1:6])
+def load(name):
+    sp = importlib.util.spec_from_file_location('hosted_' + name, par / 'work/pr361/code/engines' / (name + '.py'))
+    mod = importlib.util.module_from_spec(sp); sp.loader.exec_module(mod); return mod
+M, Other, Outer = load('moment'), load('base_two_moment'), load('outer')
+audit = json.loads(ap.read_text()); bg = json.loads((bd / 'GLOBAL.json').read_text()); ch = json.loads((cd / 'HOSTED.json').read_text())
+assert audit['bit_template_sha256'] == bg['template_sha256'] and audit['complex_template_sha256'] == ch['template_sha256']
+# ---------------- bit: two moments and the parent's invoice formulas with the hosted stock
+P = {int(r): n for r, n in audit['bit_profile'].items()}; m, W = 64, audit['bit_live']; E = sum(P.values())
+geo = json.loads((par / 'bit426-source-centres/global/GEOMETRY.json').read_text())
+pg = json.loads((par / 'bit426-source-centres/global/GLOBAL.json').read_text())
+T, L, R, V, K = pg['replicas'], 9, pg['R'], 120, 4
+mass = sum(r * z for r, z in P.items()); assert m * W - mass == 312*T
+physical = W + 9; d = m * m; N = 2 * m
+unit = L * T * pg['local_additions'] + pg['bridge_additions']
+J = 8 * T * L * (2 * V + R) + 8 * (2 * K * V * T) + 2 * L * T * R + 2 * pg['copy_erase_episodes']   # every helper route charged (bank or hosted)
+high = 16 * (d + 1) ** 2; good = 8 * m * m + 8; compiler = 128 * N ** 3
+selectors = 2 * L * T * ((W - 1) + R * m * (geo['max_route_factors'] + pg.get('extra_helper_route_factor_bound', 0) + 2 + (m - 1) + m))   # +2: hosted route may add a slot permutation and U_q
+prefix = int(pg['global_prefix_bound']); charged_prefix = 64 * ((prefix.bit_length() + 63) // 64)
+coefficient = unit + J * high + J * physical + E * (good + compiler) + 16 * m ** 3 + pg['copy_erase_episodes'] + selectors + prefix + 1
+two = (coefficient + 1) ** 2 * (E + 1) ** 2; charged_two = 64 * ((two.bit_length() + 63) // 64)
+assert two < 1 << charged_two and 2 * max(P) ** 2 < m * m
+row = 2 * (m * m + 1) + 9909 + 252; assert row == 18355 < 20161
+root = M.certify(P, m, W, True); c = Q(root['lower']); chi = Q(root['upper'])
+fb = 32 * m * m * E
+lo, hi = Other.moment(m, W, list(P.items()), c); bl, bh = Other.moment(m, W, [(1, fb)], c); assert hi + bh / 10 ** 16 < 1
+lo2, hi2 = Other.moment(m, W, list(P.items()), chi); bl2, bh2 = Other.moment(m, W, [(1, fb)], chi); assert lo2 + bl2 / 10 ** 16 > 1
+# ---------------- complex: two moments and the parent's invoice with the hosted stock
+PC = {int(r): n for r, n in audit['complex_profile'].items()}; mc, WC = 73, audit['complex_live']; EC = sum(PC.values())
+massc = sum(r * z for r, z in PC.items()); assert mc * WC - massc == 2496
+rc = M.certify(PC, mc, WC, True); b = Q(int(Q(rc['lower']) * 10 ** 18), 10 ** 18)
+fbc = 32 * mc * mc * EC
+l3, h3 = Other.moment(mc, WC, list(PC.items()), b); b3, bh3 = Other.moment(mc, WC, [(1, fbc)], b); assert h3 + bh3 / 10 ** 16 < 1
+integ = json.loads((par / 'split-centres/INTEGRATION.json').read_text()); inv = integ['finite_invoice']
+physc = ch['physical']; Rc = 560; v = 120
+compilerc = 64 * (mc + 1) ** 3
+pervertex = inv['pervertex'] - integ['physical'] * (64 + 1) + physc * (64 + 1) - integ['live'] + WC   # stock-dependent terms re-based
+r_ = mc // 2; group = 2 ** (r_ * r_) * math.prod(2 ** (2 * i) - 1 for i in range(1, r_ + 1)); stock = group * physc
+smass = group * massc; logical = group * max(pervertex, inv['pervertex']) + 64; router = compilerc * (logical + 1) * (stock + 1) ** 2
+GG, EE, C0 = 1 << 30000, 1 << 100000, 1 << 210000; BB = smass + EE
+literal = 2 * GG * stock ** 2 + 8 * smass + 4 * stock + 4 + 32 * mc
+assert logical < 1 << 6050 and router < GG and literal < EE and BB < 1 << 100001 and 32 * mc * BB * BB < C0 and 2 * BB + 18 < C0
+depth = 2; assert mc ** depth > 2 * max(PC) ** depth
+rowc = depth * stock.bit_length() + 9909 + 252; assert rowc < 20161
+# ---------------- outer assembly exactly as #434's combined.py
+eta = beta = Q(1, 10 ** 18); grid = Q(1, 10 ** 18); s = min(c, (1 - beta) * b) - Q(1, 10 ** 24)
+assert 0 < s < c and s < (1 - beta) * b
+chain = [Q(384599, 10 ** 10)]; cutoffs = []
+def ceil(x): return -((-x.numerator) // x.denominator)
+for j in range(6):
+    old = chain[-1]; a = (1 - s) * s + s * old
+    gap = min(s - a, 1 - a - s, 1 - a - s * (1 - old), 1 - s); assert old < a < s < 1 - a and gap > 0
+    cutoff = max(ceil(36 / gap ** 2), ceil(2 * (4 + charged_two) / gap)); assert cutoff * gap ** 2 >= 36 and cutoff * gap >= 2 * (4 + charged_two)
+    cutoffs.append(dict(gap=str(gap), cutoff_log2=str(cutoff))); chain.append(a)
+q = chain[-1] * (1 - 2 * eta); margin = (1 - eta) * q / (1 + q); ticks = margin / grid; k = grid * ((ticks.numerator - 1) // ticks.denominator)
+bridge = {'semantic': {'C0': {'base': 2, 'exponent': 210000}, 'strict_literal_gap': 1}, 'rows': {'degree_gap': Q(10 ** 6) - Q(51 * 20161, 25)}}
+a = Outer.assembly(chain[-1], b, bridge, k, eta=eta, beta=beta)
+assert len(a['strict_constraints']) == 47 and all(x > 0 for x in a['strict_constraints'].values())
+controls = []
+for name, kk, ee, bb in [('next_grid', k + grid, eta, beta), ('zero_eta', k, Q(0), beta), ('zero_beta', k, eta, Q(0)), ('unit_beta', k, eta, Q(1))]:
+    try: Outer.assembly(chain[-1], b, bridge, kk, eta=ee, beta=bb)
+    except AssertionError: controls.append(name)
+    else: raise AssertionError(name)
+parent_k = Q(566550276142217, 500000000000000000)
+res = dict(status='PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY', kappa=str(k), kappa_decimal=format(float(k), '.18f'),
+           bit_lower=str(c), complex_lower=str(b), binding_component='bit' if c < (1 - beta) * b else 'complex',
+           gain_over_pr434_percent=float(100 * (k / parent_k - 1)),
+           bit=dict(live=W, physical=physical, maxchild=max(P), rank_mass=mass, hosted_residuals=audit['bit_hosted_residuals'],
+                    prefix_bits=prefix.bit_length(), charged_prefix_bits=charged_prefix, coefficient_bits=coefficient.bit_length(),
+                    two_level_coefficient_bits=two.bit_length(), charged_two_level_coefficient_bits=charged_two, row_coefficient=row),
+           complex=dict(live=WC, physical=physc, maxchild=max(PC), rank_mass=massc, hosted_residuals=audit['complex_hosted_residuals'],
+                        physical_stock_bits=stock.bit_length(), router_bits=router.bit_length(), literal_bits=literal.bit_length(), row_coefficient=rowc),
+           strict_outer_constraints={n: str(x) for n, x in a['strict_constraints'].items()}, outer_controls=controls, bootstrap=cutoffs,
+           bit_template_sha256=bg['template_sha256'], complex_template_sha256=ch['template_sha256'])
+outp.write_text(json.dumps(res, indent=2) + '\n')
+print(res['status'], res['kappa_decimal'], 'binding', res['binding_component'], 'gain over #434 %.4f%%' % res['gain_over_pr434_percent'])
diff --git a/research/e8-hosting-selected-kernel/code/audit.py b/research/e8-hosting-selected-kernel/code/audit.py
new file mode 100644
index 0000000000..1485c4d7d9
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/code/audit.py
@@ -0,0 +1,161 @@
+"""Independent audit of the two idle-axis-hosted templates (no code shared with the generators).
+Re-derives hosting windows from each template's own schedule and checks, for every replica and invocation:
+  * every helper residual has exactly one owner: a bank slot or a hosted slot;
+  * a hosted slot lies on the data family of the idle child it names, inside that child's pending coordinates,
+    disjoint from every other hosted slot of the family, and its invocation lies strictly between the last
+    local invocation or bridge naming that pair and the child (the window);
+  * the child keeps exactly the remaining coordinates; banks are tiled exactly (bit) or padded (complex);
+  * the emitted paid profile, live stock and rank deficit 2496 are recomputed from scratch.
+Mutation controls must be rejected.  usage: audit.py PARENT_CHANGED_DIR BIT_DIR COMPLEX_DIR OUT.json"""
+import copy, gzip, hashlib, json, sys
+from collections import Counter, defaultdict
+from pathlib import Path
+V, K, T, L = 120, 4, 8, 9
+DATA = 2 * K * V * T
+
+def wins(events):
+    """events: ('local', stage, pair) | ('bridge', a, b) | ('idle', idx, pair); window = local stages after the last
+    local/bridge touch of the pair and before the child"""
+    last = {}; seen = []; w = {}
+    for pos, e in enumerate(events):
+        if e[0] == 'local': seen.append((pos, e[1], e[2])); last[e[2]] = pos
+        elif e[0] == 'bridge': last[e[1]] = pos; last[e[2]] = pos
+        else:
+            lo = last.get(e[2], -1); w[e[1]] = {s for q, s, p in seen if lo < q < pos and p != e[2]}
+    return w
+
+def audit_bit(t, parent_t, widths):
+    T=64; DATA=960*T
+    assert t['replicas']==parent_t['replicas']==T
+    assert t['local_programs'] == parent_t['local_programs'] and len(t['calls']) == 9*T
+    ev = []; rank = {}; pair = {}
+    for e in t['schedule']:
+        if e['kind'] == 'local_cover_sweep': ev.append(('local', e['stage'], e['pair']))
+        elif e['kind'] == 'bridge': ev.append(('bridge', e['dst'], e['src']))
+        elif e['kind'] == 'idle':
+            ev.append(('idle', e['idx'], e['pair'])); rank[e['idx']] = e['rank']; pair[e['idx']] = e['pair']
+    W = wins(ev); hs = t['hosting']
+    used = defaultdict(set); hosted = {}
+    for i, cp, off, w, s, h in hs['slots']:
+        assert s in W[i], ('window', i, s)
+        assert w == widths[h] and 0 <= off and off + w <= rank[i]
+        cells = set(range(off, off + w)); assert not cells & used[i, cp], ('overlap', i, cp); used[i, cp] |= cells
+        assert (s, h) not in hosted; hosted[s, h] = (i, cp, off, w)
+    rem = {}
+    for i in rank:
+        if rank[i] == 0: continue
+        for cp in range(2 * V): rem[i, cp] = rank[i] - len(used[i, cp])
+        rr = Counter(rem[i, cp] for cp in range(2 * V))
+        if str(i) in hs['remainders']: assert {int(k): v for k, v in hs['remainders'][str(i)].items()} == dict(rr)
+        else: assert rr == Counter({rank[i]: 2 * V})
+    occ = defaultdict(set); LIVE = t['live']; bank_lo = {}
+    for c in t['calls']:
+        s, rep, p = c['stage'], c['replica'], c['pair']; own = c['owners']; assert len(own) == 2 * V + len(widths)
+        assert own[:2 * V] == next(q for q in parent_t['calls'] if (q['stage'], q['replica']) == (s, rep))['owners'][:2 * V]
+        for h, (f, r) in enumerate(own[2 * V:]):
+            if (s, h) in hosted:
+                i, cp, off, w = hosted[s, h]; side, port = divmod(cp, V)
+                assert r == ['hosted', i, off, w] and f == rep * 960 + (2 * pair[i] + side) * V + port
+                assert pair[i] != p
+                occ['h', f, i, s, rep, h] = True
+            else:
+                assert r[0] == 'bank' and r[2] == widths[h] and DATA <= f < LIVE
+                cells = set(range(r[1], r[1] + r[2])); assert cells <= set(range(64)) and not cells & occ[f]; occ[f] |= cells
+                bank_lo[f] = s
+    banks = [f for f in occ if isinstance(f, int)]
+    assert sorted(banks) == list(range(DATA, LIVE)) and all(occ[f] == set(range(64)) for f in banks)
+    paid = Counter()
+    for c in t['calls']:
+        for z in t['local_programs'][c['orientation']]:
+            if z[0] == 0 and z[4]: paid[z[4]] += 1
+            if z[0] == 2: paid[z[5]] += 1
+    for (i, cp), r_ in rem.items():
+        if r_: paid[r_] += T
+    mass = sum(r * n for r, n in paid.items()); assert 64 * LIVE - mass == 312*T
+    assert 64 * 64 > 2 * max(paid) ** 2
+    return paid, sum(1 for _ in hosted) * T
+
+def audit_complex(t, parent_t, local_checks):
+    R = 560; m = 73
+    assert t['local_programs'] == parent_t['local_programs'] and len(t['calls']) == 72
+    prank = {}
+    for it in parent_t['idle_children']: prank.setdefault(it['child'], it['rank'])
+    stage_pair = {e['stage']: e['pair'] for e in t['recipe'] if e['kind'] == 'local'}
+    ev = []; side = {}; pairs = {}
+    for e in t['execution_schedule']:
+        if e['kind'] == 'local_cover_sweep': ev.append(('local', e['stage'], stage_pair[e['stage']]))
+        elif e['kind'] == 'bridge': ev.append(('bridge', e['dst'], e['src']))
+        elif e['kind'] == 'idle_cover_sweep':
+            for sd, ch in enumerate(e['child_indices']):
+                if ch in prank: ev.append(('idle', ch, e['pair'])); side[ch] = sd; pairs[ch] = e['pair']
+    W = wins(ev); hs = t['hosting']
+    used = defaultdict(set); hosted = {}
+    for i, port, off, w, s, h in hs['slots']:
+        assert w == 9 and s in W[i] and 0 <= off and off + 9 <= prank[i]
+        cells = set(range(off, off + 9)); assert not cells & used[i, port]; used[i, port] |= cells
+        assert (s, h) not in hosted; hosted[s, h] = (i, port, off)
+    rem = {}
+    for it in parent_t['idle_children']: rem[it['child'], it['port']] = it['rank'] - len(used[it['child'], it['port']])
+    got = {(it['child'], it['port']): it['rank'] for it in t['idle_children']}
+    assert got == {k: r for k, r in rem.items() if r} and all(it['replicas'] == T for it in t['idle_children'])
+    LIVE = t['live']; occ = defaultdict(set)
+    for c in t['calls']:
+        s, rep, p = c['stage'], c['replica'], c['pair']; own = c['owners']; assert len(own) == 2 * V + R
+        assert own[:2 * V] == next(q for q in parent_t['calls'] if (q['stage'], q['replica']) == (s, rep))['owners'][:2 * V]
+        for h, (f, r) in enumerate(own[2 * V:]):
+            if (s, h) in hosted:
+                i, port, off = hosted[s, h]
+                assert r == [3, i, off] and f == rep * 960 + (2 * pairs[i] + side[i]) * V + port and pairs[i] != p
+            else:
+                assert r[0] == 2 and 0 <= r[1] < 8 and DATA <= f < LIVE and r[1] not in occ[f]; occ[f].add(r[1])
+    banks = sorted(occ); assert banks == list(range(DATA, LIVE))
+    paid = Counter()
+    for c in t['calls']:
+        for r_, z in local_checks[c['orientation']]['paid_profile'].items(): paid[int(r_)] += z
+    for (ch, port), r_ in rem.items():
+        if r_: paid[r_] += T
+    for f in banks: paid[m - 9 * len(occ[f])] += 1
+    mass = sum(r * n for r, n in paid.items()); assert m * LIVE - mass == 2496
+    assert m * m > 2 * max(paid) ** 2
+    return paid, len(hosted) * T
+
+def main():
+    par, bd, cd, outp = map(Path, sys.argv[1:5])
+    pbt = json.loads(gzip.decompress((par / 'bit426-source-centres/global/GLOBAL-TEMPLATE.json.gz').read_bytes()))
+    bt = json.loads(gzip.decompress((bd / 'GLOBAL-TEMPLATE.json.gz').read_bytes()))
+    bg = json.loads((bd / 'GLOBAL.json').read_text())
+    assert hashlib.sha256(gzip.decompress((bd / 'GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest() == bg['template_sha256']
+    st = json.loads((par / 'bit426-source-centres/records/249-states.json').read_text())
+    fs = json.loads((par / 'bit426-source-centres/records/frames.json').read_text())['frames']
+    widths = [8 - fs[str(st['initial'][str(i)])]['dim'] for i in range(240, st['n'])]
+    pct = json.loads(gzip.decompress((par / 'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes()))
+    ct = json.loads(gzip.decompress((cd / 'GLOBAL-TEMPLATE.json.gz').read_bytes()))
+    ch = json.loads((cd / 'HOSTED.json').read_text())
+    assert hashlib.sha256(gzip.decompress((cd / 'GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest() == ch['template_sha256']
+    lc = json.loads((par / 'split-centres/LOCAL-CHECKS.json').read_text())
+    bp, bh = audit_bit(bt, pbt, widths); assert bp == Counter({int(k): v for k, v in bg['profile'].items()})
+    cp, chh = audit_complex(ct, pct, lc); assert cp == Counter({int(k): v for k, v in ch['global_profile'].items()})
+    controls = []
+    def reject(name, fn, which):
+        q = copy.deepcopy(bt if which == 'bit' else ct); fn(q)
+        try:
+            (audit_bit(q, pbt, widths) if which == 'bit' else audit_complex(q, pct, lc))
+        except (AssertionError, KeyError, IndexError, StopIteration): controls.append(name)
+        else: raise AssertionError('mutation accepted: ' + name)
+    def outside(q):           # move one hosted residual to a stage outside its window
+        sl = q['hosting']['slots'][0]; i = sl[0]; s_bad = next(s for s in range(9) if s not in q['hosting']['windows'][str(i)][2]); sl[4] = s_bad
+    reject('bit: hosted residual outside its window', outside, 'bit')
+    reject('bit: overlapping hosted coordinates', lambda q: q['hosting']['slots'][1].__setitem__(2, q['hosting']['slots'][0][2]) if q['hosting']['slots'][1][:2] == q['hosting']['slots'][0][:2] else q['hosting']['slots'][1].__setitem__(1, q['hosting']['slots'][0][1]) or q['hosting']['slots'][1].__setitem__(2, q['hosting']['slots'][0][2]), 'bit')
+    reject('bit: understated live stock', lambda q: q.__setitem__('live', q['live'] - 1), 'bit')
+    reject('bit: hosted owner on the active pair', lambda q: q['calls'][0]['owners'].__setitem__(240 + next(h for h in range(len(widths)) if q['calls'][0]['owners'][240 + h][1][0] == 'hosted'), [0, ['hosted', 0, 0, 8]]), 'bit')
+    reject('bit: missing remainder child', lambda q: q['hosting']['slots'].pop(), 'bit')
+    reject('complex: hosted residual outside its window', lambda q: q['hosting']['slots'][0].__setitem__(4, next(s for s in range(9) if s not in q['hosting']['windows'][str(q['hosting']['slots'][0][0])][2])), 'complex')
+    reject('complex: remainder child understated', lambda q: q['idle_children'][0].__setitem__('rank', q['idle_children'][0]['rank'] - 1), 'complex')
+    reject('complex: dropped bank', lambda q: q.__setitem__('live', q['live'] - 1), 'complex')
+    reject('complex: duplicated hosted residual', lambda q: q['hosting']['slots'].append(list(q['hosting']['slots'][0])), 'complex')
+    res = dict(status='PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT', bit_template_sha256=bg['template_sha256'], complex_template_sha256=ch['template_sha256'],
+               bit_profile={str(k): v for k, v in sorted(bp.items())}, complex_profile={str(k): v for k, v in sorted(cp.items())},
+               bit_live=bt['live'], complex_live=ct['live'], bit_hosted_residuals=bh, complex_hosted_residuals=chh,
+               bit_maxchild=max(bp), complex_maxchild=max(cp), mutations_rejected=controls)
+    outp.write_text(json.dumps(res, indent=2) + '\n'); print(json.dumps({k: v for k, v in res.items() if 'profile' not in k}))
+if __name__ == '__main__': main()
diff --git a/research/e8-hosting-selected-kernel/code/bit_audit.py b/research/e8-hosting-selected-kernel/code/bit_audit.py
new file mode 100644
index 0000000000..41d2b35d55
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/code/bit_audit.py
@@ -0,0 +1,134 @@
+# Adapted with exact rational span checks by icekylinx; Codex assistance.
+"""Independent audit of the emitted bit template, including mutation controls.
+Prepared by Zhihao Chen with OpenAI Codex assistance; Apache-2.0.
+"""
+import argparse, copy, gzip, hashlib, json, struct, time
+from collections import Counter, defaultdict
+from pathlib import Path
+from fractions import Fraction as Q
+from residual_routes import validate_isometries
+
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out
+    blob=gzip.decompress((out/'GLOBAL-TEMPLATE.json.gz').read_bytes()); t=json.loads(blob)
+    g=json.loads((out/'GLOBAL.json').read_text()); geo=json.loads((out/'GEOMETRY.json').read_text())
+    assert hashlib.sha256(blob).hexdigest()==g['template_sha256']
+    assert t['geometry_sha256']==sha(out/'GEOMETRY.json') and t['source_record_sha256']==sha(a.local_check/'records/249-records.bin')
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    records=list(struct.iter_unpack('<6i',(a.local_check/'records/249-records.bin').read_bytes()))
+    word=json.loads((a.local_check/'bit-source-centres.json').read_text())
+    assert g['word_sha256']==sha(a.local_check/'bit-source-centres.json')
+    def rank(rows):
+        piv={}
+        for rr in rows:
+            row=list(map(Q,rr))
+            for k,b in sorted(piv.items()):
+                q=row[k]
+                if q:row=[x-q*y for x,y in zip(row,b)]
+            k=next((j for j,x in enumerate(row) if x),None)
+            if k is not None:
+                q=row[k];piv[k]=[x/q for x in row]
+        return len(piv)
+    dimensions={};proj={}
+    for key,f in fs.items():
+        k=int(key);B=f['B'];roots=[word['lines'][j] for j in word['frames'][k]]
+        assert rank(B)==f['dim']==rank(B+roots)==rank(roots)
+        dimensions[k]=f['dim'];proj[k]=B
+    sets=[set(f) for f in word['frames']];pairs={}
+    for op,x,y,c,r,z in records:
+        if op==0:
+            assert sets[y]<=sets[c] and dimensions[c]-dimensions[y]==r
+            pairs[y,c]=r
+    # Positive definite rational form: exact inclusion implies commuting
+    # orthogonal projectors and rank(P_V-P_U)=dim(V)-dim(U), also in reflection.
+    assert len(proj)==len(word['frames'])
+    expected={}
+    for rev in (False,True):
+        es=[]
+        for op,x,y,c,f,z in (reversed(records) if rev else records):
+            if op==0: es.append([0,x,c if rev else y,y if rev else c,f,int(rev)])
+            elif op==1: es.append([1,x,y,-c if rev else c,f,int(rev)])
+            elif op==(3 if rev else 2): es.append([2,x,y,c,f,abs(dimensions[c]-dimensions[f]),int(rev)])
+            else: es.append([3,x,y,c,f,z,int(rev)])
+        expected['reverse' if rev else 'forward']=es
+    assert t['local_programs']==expected
+
+    st=json.loads((a.local_check/'records/249-states.json').read_text())
+    RR=st['n']-240; width=[8-dimensions[st['initial'][str(i)]] for i in range(240,240+RR)]; ENT=sum(8-x for x in width); T=64; DATA=960*T; assert T*(8*RR-ENT)%64==0
+    NB=T*(8*RR-ENT)//64; LIVE=DATA+9*NB; assert g['live']==LIVE
+    def validate(q,check_profile=True):
+        assert validate_isometries(q['residual_isometries'],word['frames'],word['lines'],dimensions)==set(word['start'][240:])
+        assert (q['m'],q['live'],q['replicas'],q['stages'])==(64,LIVE,T,9)
+        assert q['bank_padding'] is None and q['local_programs']==expected
+        hist=Counter(); occupation=defaultdict(set); calls=set()
+        for c in q['calls']:
+            st,rep,p=c['stage'],c['replica'],c['pair']; rev=c['orientation']=='reverse'
+            assert 0<=st<9 and 0<=rep<T and p==max(0,(st-1)//2)
+            assert rev==(st in (1,3,5,7)) and (st,rep) not in calls; calls.add((st,rep))
+            own=c['owners']; assert len(own)==240+RR
+            assert len({(f,tuple(r)) for f,r in own})==240+RR
+            for i,(family,route) in enumerate(own):
+                assert 0<=family<LIVE
+                if i<240:
+                    side=i//120; side=1-side if rev else side
+                    assert family==rep*960+(2*p+side)*120+i%120 and route==['data',st,i%120]
+                else:
+                    j=i-240; assert len(route)==4 and route[0]=='bank' and route[2]==width[j] and route[3]==word['start'][i] and DATA+st*NB<=family<DATA+(st+1)*NB
+                    cells=set(range(route[1],route[1]+route[2])); assert cells<=set(range(64)) and not (cells & occupation[family])
+                    occupation[family]|=cells
+            for e in q['local_programs'][c['orientation']]:
+                if e[0]==0 and e[4]: hist[e[4]]+=1
+                if e[0]==2: hist[e[5]]+=1
+        assert calls=={(s,r) for s in range(9) for r in range(T)}
+        assert set(occupation)==set(range(DATA,LIVE)) and all(s==set(range(64)) for s in occupation.values())
+        levels=[-1]*4; scalar=[1<<i for i in range(8)]; seen=[]; br=0; exchanged=False
+        for e in q['schedule']:
+            if e['kind']=='local_cover_sweep':
+                s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1 and not exchanged
+                src,dst=(2*p+1,2*p) if rev else (2*p,2*p+1)
+                scalar[dst]^=scalar[src]; levels[p]=s; seen.append(s)
+            elif e['kind']=='idle':
+                p,src,dst,r=e['pair'],e['source_level'],e['target_level'],e['rank']
+                assert levels[p]==src and src<=dst<=8
+                assert r==7*(dst-src); levels[p]=dst
+                if r: hist[r]+=240*T
+            elif e['kind']=='bridge':
+                d,s=e['dst'],e['src']; assert levels[d]==levels[s] and e['coefficient'] in (-1,1)
+                scalar[2*d]^=scalar[2*s]; scalar[2*s+1]^=scalar[2*d+1]; br+=1
+            else:
+                assert e['kind']=='exchange' and levels==[8]*4 and not exchanged
+                for p in range(4): scalar[2*p],scalar[2*p+1]=scalar[2*p+1],scalar[2*p]
+                exchanged=True
+        assert exchanged and scalar==[1<<i for i in range(8)] and seen==list(range(9)) and br==9
+        assert 64*LIVE-sum(r*n for r,n in hist.items())==312*T
+        if check_profile: assert hist==Counter({int(k):v for k,v in g['profile'].items()})
+        return hist
+    hist=validate(t)
+    controls=[]
+    def rejects(name,mutator):
+        q=copy.deepcopy(t); mutator(q)
+        try: validate(q)
+        except (AssertionError,KeyError,IndexError): controls.append(name)
+        else: raise AssertionError('mutation accepted: '+name)
+    rejects('omit an idle child',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='idle')))
+    rejects('omit a bridge',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='bridge')))
+    rejects('omit terminal exchange',lambda q:q['schedule'].pop())
+    rejects('remove a local invocation',lambda q:q['calls'].pop())
+    rejects('re-use a helper bank slot',lambda q:q['calls'][0]['owners'].__setitem__(241,q['calls'][0]['owners'][240]))
+    rejects('understate live stock',lambda q:q.__setitem__('live',LIVE-1))
+    rejects('omit a local paid move',lambda q:q['local_programs']['forward'].pop(next(i for i,e in enumerate(q['local_programs']['forward']) if e[0]==0)))
+    rejects('wrong reflected copy charge',lambda q:q['local_programs']['reverse'][next(i for i,e in enumerate(q['local_programs']['reverse']) if e[0]==2)].__setitem__(5,0))
+    rejects('alter residual orthogonal basis',lambda q:q['residual_isometries'][0]['orthogonal_rows_numerator'][0].__setitem__(0,99))
+    rejects('wrong residual frame',lambda q:q['calls'][0]['owners'][240][1].__setitem__(3,-1))
+    rejects('omit a residual route factor',lambda q:next(r for r in q['residual_isometries'] if r['gaussian_reduction'])['gaussian_reduction'].pop())
+    result=dict(status='PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT',template_sha256=g['template_sha256'],
+                source_frames=len(proj),exact_nested_frame_pairs=len(pairs),exact_reflected_pairs=len(pairs),
+                orthogonal_lift_argument='Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.',
+                exact_bank_families=LIVE-DATA,mixed_width_slots=True,entrance_rank_total=ENT,residual_isometries=len(t['residual_isometries']),mutations_rejected=controls,
+                profile=dict(sorted(hist.items())),seconds=time.monotonic()-start)
+    (out/'AUDIT.json').write_text(json.dumps(result,indent=2)+'\n'); print(json.dumps(result),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-hosting-selected-kernel/code/bit_global.py b/research/e8-hosting-selected-kernel/code/bit_global.py
new file mode 100644
index 0000000000..66f2a4bbb5
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/code/bit_global.py
@@ -0,0 +1,275 @@
+# Adapted for the PR426/source-centre composition by icekylinx with Codex assistance.
+"""Source-bound compressed nine-stage bit template and exact scalar audits.
+
+Prepared by Zhihao Chen with OpenAI Codex assistance, Apache-2.0.
+The local E8 bit word is Dylan Crow's pinned PR #370 contribution.
+"""
+import argparse, gzip, hashlib, json, struct, time
+from collections import Counter
+from pathlib import Path
+from residual_routes import generate
+
+import sys as _sys
+H,V,L,K,T,M=8,120,9,4,64,64
+R=json.loads((Path(_sys.argv[_sys.argv.index('--source')+1])/'bit-source-centres.json').read_bytes())['R']
+LOCAL=2*V+R; DATA=2*K*V*T
+
+def tile_banks(width):
+    """exact width-64 bank tiling of the per-stage helper slots (8 replicas x R helpers, slot width = 8 - entrance rank);
+    returns {(replica, helper): (bank, offset)} and the bank count; every bank is filled exactly (no padding)."""
+    slots=sorted(((width[h],rep,h) for rep in range(T) for h in range(R)),key=lambda x:(-x[0],x[1],x[2]))
+    bins=[]; place={}
+    by={}
+    for w_,rep,h in slots: by.setdefault(w_,[]).append((rep,h))
+    def take(w_):
+        return by[w_].pop(0) if by.get(w_) else None
+    # Exact mixed widths: eight width-7 slots plus one width-8; divisor-width remainders filled with width-8 slots.
+    for w_ in sorted(by,reverse=True):
+        if w_==8: continue
+        while by.get(w_):
+            b=len(bins); off=0; cont=[]
+            if w_==7:
+                for _ in range(8): rep,h=take(7); cont.append((rep,h,off,7)); off+=7
+                rep,h=take(8); cont.append((rep,h,off,8)); off+=8
+            else:
+                assert 64%w_==0
+                for _ in range(min(64//w_,len(by[w_]))): rep,h=take(w_); cont.append((rep,h,off,w_)); off+=w_
+                assert (64-off)%8==0
+                while off<64: rep,h=take(8); cont.append((rep,h,off,8)); off+=8
+            assert off==64; bins.append(cont)
+    while by.get(8):
+        cont=[]; off=0
+        for _ in range(8): rep,h=take(8); cont.append((rep,h,off,8)); off+=8
+        bins.append(cont)
+    for b,cont in enumerate(bins):
+        for rep,h,off,w_ in cont: place[rep,h]=(b,off,w_)
+    assert len(place)==T*R
+    return place,len(bins)
+
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+def write(p,x): p.write_text(json.dumps(x,indent=2)+'\n')
+
+def recipe():
+    out=[dict(kind='local',stage=0,pair=0,reverse=False)]; stage=1
+    for j in range(K):
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=True)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=1))
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=False)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=-1))
+    for j in reversed(range(K-1)): out.append(dict(kind='bridge',dst=j+1,src=j,coefficient=1))
+    out.append(dict(kind='exchange'))
+    return out
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--source',type=Path,required=True)
+    ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out; out.mkdir(parents=True,exist_ok=True)
+    wp=a.source/'bit-source-centres.json'; w=json.loads(wp.read_bytes())
+    inherited=Path('inherited/bit-geometry.json.gz')
+    geo=json.loads(gzip.decompress(inherited.read_bytes()))
+    base=Path('work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz')
+    original=json.loads(gzip.decompress(base.read_bytes()))
+    assert geo['word_sha256']==sha(base)
+    assert w['lines']==original['lines'] and w['form']==original['form']
+    # PR436 regenerates the same root-closed frame family in a different order.
+    # Bind every actual frame by its exact root set; all record IDs remain actual IDs.
+    original_ids={tuple(sorted(fr)):i for i,fr in enumerate(original['frames'])}
+    actual_keys=[tuple(sorted(fr)) for fr in w['frames']]
+    assert len(original_ids)==len(original['frames'])==len(actual_keys)==len(set(actual_keys))
+    assert set(actual_keys)==set(original_ids)
+    frame_map=[original_ids[k] for k in actual_keys]
+    assert sorted(frame_map)==list(range(len(original['frames'])))
+    geo['actual_frame_to_pinned_frame']=frame_map
+    geo['frame_binding']='Exact bijection of root sets; frame IDs in emitted records are those of the reconstructed PR436 word.'
+    kr=json.loads((a.source/'bit-kernel-receipt.json').read_text()); assert kr['output_sha256'] and len(w['frames'])==len(original['frames'])+kr['new_frames']
+    geo['inherited_geometry_sha256']=sha(inherited);geo['word_sha256']=sha(wp)
+    geo['reuse_scope']='Unchanged ports and compressed windows; nonzero helper entrances use mixed-width residual slots, with every owner and coordinate checked independently.'
+    write(out/'GEOMETRY.json',geo)
+    rp=a.local_check/'records/249-records.bin';raw=rp.read_bytes();rec=list(struct.iter_unpack('<6i',raw))
+    state=json.loads((a.local_check/'records/249-states.json').read_text())
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    dims={int(f):z['dim'] for f,z in fs.items()}
+    assert (state['v'],state['n'])==(V,LOCAL)
+    expected_adds=sum(e[0]==1 for e in rec)
+    initial=[state['initial'][str(i)] for i in range(LOCAL)]
+    final=[state['final'][str(i)] for i in range(LOCAL)]
+    assert all(dims[final[i]]==H for i in range(2*V,LOCAL))
+    width={i-2*V:H-dims[initial[i]] for i in range(2*V,LOCAL)}; ENT=sum(H-x for x in width.values()); assert T*(8*R-ENT)%64==0
+    place,NB=tile_banks(width); assert NB==T*(8*R-ENT)//64
+    isometries=generate(w,dims)
+    LIVE=DATA+L*NB
+    streams={}; checks={}; localH=None
+    for reverse in (False,True):
+        cur=(final if reverse else initial)[:]+[-1]; val=[1<<i for i in range(LOCAL)]+[0]
+        norm=[1]*LOCAL+[0]; maxnorm=1; center=None; hist=Counter(); events=[]; copies=0; adds=0
+        dim=lambda f:H-dims[f] if reverse else dims[f]
+        for op,x,y,c,f,z in (reversed(rec) if reverse else rec):
+            if op==0:
+                oldf,newf=(c,y) if reverse else (y,c)
+                assert cur[x]==oldf and dim(newf)-dim(oldf)==f>=0
+                cur[x]=newf
+                if f: hist[f]+=1
+                events.append([0,x,oldf,newf,f,int(reverse)])
+            elif op==1:
+                assert cur[x]==cur[y]==f and x!=y and x<LOCAL
+                if center is not None: assert x!=center
+                if y==LOCAL: assert center is not None
+                if c&1: val[x]^=val[y]
+                norm[x]+=abs(c)*norm[y]; maxnorm=max(maxnorm,norm[x]); adds+=1
+                events.append([1,x,y,-c if reverse else c,f,int(reverse)])
+            elif op==(3 if reverse else 2):
+                assert center is None and y==LOCAL and cur[x]==c and val[LOCAL]==0
+                copy_rank=abs(dim(c)-dim(f)); assert copy_rank==8
+                assert z==(0 if reverse else copy_rank)
+                center=x; cur[LOCAL]=f; val[LOCAL]=val[x]; norm[LOCAL]=norm[x]
+                hist[copy_rank]+=1; copies+=1; events.append([2,x,LOCAL,c,f,copy_rank,int(reverse)])
+            else:
+                assert op==(2 if reverse else 3)
+                assert center==x and y==LOCAL and cur[x]==c and cur[LOCAL]==f
+                assert val[LOCAL]==val[x]
+                val[LOCAL]=0; norm[LOCAL]=0; cur[LOCAL]=-1; center=None
+                events.append([3,x,LOCAL,c,f,z,int(reverse)])
+        assert center is None and copies==9 and adds==expected_adds
+        assert cur[:LOCAL]==(initial if reverse else final)
+        for i in range(LOCAL):
+            want=(1<<i) ^ ((1<<(i-V)) if V<=i<2*V else 0)
+            assert val[i]==want
+        assert val[LOCAL]==0
+        if localH is None: localH=hist
+        else: assert localH==hist
+        key='reverse' if reverse else 'forward'; streams[key]=events
+        checks[key]=dict(copies=copies,adds=adds,records=len(events),all_columns=LOCAL,
+                         cancellation_free_row_l1=maxnorm,profile=dict(sorted(hist.items())),
+                         sha256=hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest())
+    assert sum(r*n for r,n in localH.items())==H*R-ENT+72+2*V*(H-1)
+
+    events=recipe(); levels=[-1]*K; schedule=[]; bridge_controls=[]
+    # Full scalar replay on separate dirty helpers for all nine stages.
+    # Physical banking then uses the separately checked injective cover owners.
+    n=2*K*V+L*R; vals=[1<<i for i in range(n)]+[0]; temp=n
+    stages=[]
+    for e in events:
+        if e['kind']=='local':
+            s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1
+            def mapper(i):
+                if i==LOCAL: return temp
+                if i<2*V:
+                    side=i//V; side=1-side if rev else side
+                    return (2*p+side)*V+i%V
+                return 2*K*V+s*R+i-2*V
+            before=vals[:]; opened=False
+            for z in streams['reverse' if rev else 'forward']:
+                if z[0]==0: continue
+                x,y=mapper(z[1]),mapper(z[2])
+                if z[0]==1:
+                    if z[3]&1: vals[x]^=vals[y]
+                elif z[0]==2:
+                    assert not opened; vals[temp]=vals[x]; opened=True
+                else:
+                    assert opened and vals[temp]==vals[x]; vals[temp]=0; opened=False
+            assert not opened
+            d=(2*p+(0 if rev else 1))*V; src=(2*p+(1 if rev else 0))*V
+            for t in range(V): before[d+t]^=before[src+t]
+            assert vals==before
+            levels[p]=s; schedule.append(dict(kind='local_cover_sweep',**{k:v for k,v in e.items() if k!='kind'}))
+            if s in (1,3,5):
+                j=(s+1)//2; assert levels[j]==-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7*(s+1),source_level=-1,target_level=s))
+            elif s in (2,4,6):
+                j=s//2; assert levels[j]==s-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7,source_level=s-1,target_level=s))
+            elif s==8:
+                for j in range(4):
+                    oldlevel=levels[j]; assert oldlevel==2*j+2
+                    schedule.append(dict(kind='idle',pair=j,rank=7*(8-oldlevel),source_level=oldlevel,target_level=8))
+                    levels[j]=8
+            stages.append(dict(stage=s,all_columns=n,helper_columns=L*R,reverse=rev))
+        elif e['kind']=='bridge':
+            d,s=e['dst'],e['src']; assert levels[d]==levels[s]
+            for t in range(V): vals[2*d*V+t]^=vals[2*s*V+t]; vals[(2*s+1)*V+t]^=vals[(2*d+1)*V+t]
+            schedule.append(e)
+        else:
+            assert levels==[8]*4
+            for j in range(K):
+                for t in range(V):
+                    x=2*j*V+t; y=(2*j+1)*V+t; vals[x],vals[y]=vals[y],vals[x]
+            schedule.append(e)
+    assert vals==[1<<i for i in range(n)]+[0]
+    # Integer scalar eight-bank matrix, with each individual bridge shear omitted.
+    def small(skip=-1):
+        z=[[int(i==j) for j in range(8)] for i in range(8)]; count=0
+        def add(d,s,c): z[d]=[x+c*y for x,y in zip(z[d],z[s])]
+        for e in events:
+            if e['kind']=='local':
+                p=e['pair']; add(2*p,2*p+1,-1) if e['reverse'] else add(2*p+1,2*p,1)
+            elif e['kind']=='bridge':
+                d,s,c=e['dst'],e['src'],e['coefficient']
+                for x,y,sgn in [(2*d,2*s,c),(2*s+1,2*d+1,-c)]:
+                    if count!=skip: add(x,y,sgn)
+                    count+=1
+            else:
+                for j in range(4): z[2*j],z[2*j+1]=z[2*j+1],[-x for x in z[2*j]]
+        return z,count
+    ident=[[int(i==j) for j in range(8)] for i in range(8)]
+    z,nb=small(); assert z==ident and nb==18
+    for skip in range(nb): assert small(skip)[0]!=ident; bridge_controls.append(skip)
+
+    paid=Counter(); calls=[]; assignment=set(); expanded=hashlib.sha256(); full_event_count=0
+    for e in events:
+        if e['kind']!='local': continue
+        s,p,rev=e['stage'],e['pair'],e['reverse']; ori='reverse' if rev else 'forward'
+        for rep in range(T):
+            owners=[]
+            for i in range(2*V):
+                side=i//V; side=1-side if rev else side
+                owners.append([rep*(2*K*V)+(2*p+side)*V+i%V, ['data',s,i%V]])
+            for r in range(R):
+                bank,off,w_=place[rep,r]
+                owners.append([DATA+s*NB+bank,['bank',off,w_,initial[2*V+r]]])
+                assignment.add((s,rep,r,bank,off))
+            assert len({(f,tuple(route)) for f,route in owners})==LOCAL
+            assert all(0<=f<LIVE for f,route in owners)
+            # Stream one full renamed instruction program into a source-bound
+            # digest, including exact owner route descriptors and reflection.
+            for z in streams[ori]:
+                op=z[0]
+                if op==0: paid[z[4]]+=bool(z[4]); mapped=[op,owners[z[1]],*z[2:]]
+                else:
+                    ox=owners[z[1]]; oy=owners[z[2]] if z[2]<LOCAL else [LIVE,['private',0]]
+                    mapped=[op,ox,oy,*z[3:]]
+                    if op==2: paid[z[5]]+=1
+                expanded.update((json.dumps(mapped,separators=(',',':'))+'\n').encode()); full_event_count+=1
+            calls.append(dict(stage=s,replica=rep,pair=p,orientation=ori,owners=owners,local_hash=checks[ori]['sha256']))
+    paid.pop(0,None)
+    assert len(assignment)==L*T*R and len(calls)==L*T
+    for e in schedule:
+        if e['kind']=='idle' and e['rank']: paid[e['rank']]+=2*V*T
+    mass=sum(r*c for r,c in paid.items()); assert M*LIVE-mass==312*T
+    cf=checks['forward']['cancellation_free_row_l1']; cb=checks['reverse']['cancellation_free_row_l1']
+    prefix=(1<<nb)*cf**5*cb**4; charged_prefix=64*((prefix.bit_length()+63)//64);assert prefix<1<<charged_prefix
+    print('Fresh prefix bits',prefix.bit_length(),'charged',charged_prefix,flush=True)
+    template=dict(version='compressed-nine-e8-bit-v1',m=M,h=H,stages=L,replicas=T,live=LIVE,private_centre_reserve=9,
+                  cover='O(I_64/2,F_q) for admitted odd address primes q',loop_order='Each recipe phase: replicas then all cover classes; finish every local invocation before the next.',
+                  schedule=schedule,local_programs=streams,calls=calls,bank_padding=None,
+                  helper_route='Exact listed residual coordinate isometry, extended by identity on exterior coordinates and permuted to the assigned bank interval.',banks_per_stage=NB,entrance_rank_total=ENT,residual_isometries=isometries,
+                  data_route='owner (replica*960 + (2*pair+side)*120+port, d*rho_stage,port)',
+                  bit_operator='D_U exchanges the two address halves on projector U; D_I D_P = D_(I-P) exactly.',
+                  geometry_sha256=sha(out/'GEOMETRY.json'),source_record_sha256=sha(rp))
+    blob=json.dumps(template,separators=(',',':'),sort_keys=True).encode(); (out/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+    result=dict(status='PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE',h=H,m=M,v=V,R=R,replicas=T,live=LIVE,physical=LIVE+9,
+                word_sha256=sha(wp),source_records_sha256=sha(rp),local_checks=checks,scalar_stages=stages,
+                independent_unbanked_scalar_columns=n,all_scalar_columns_restored=True,
+                geometry_sha256=sha(out/'GEOMETRY.json'),template_sha256=hashlib.sha256(blob).hexdigest(),
+                emitted_program_sha256=expanded.hexdigest(),emitted_events=full_event_count,local_invocations=len(calls),
+                bank_assignments=len(assignment),banks_per_stage=NB,entrance_rank_total=ENT,mixed_width_slots=True,padding_calls=0,residual_isometries=len(isometries),extra_helper_route_factor_bound=144,
+                profile=dict(sorted(paid.items())),paid_calls=sum(paid.values()),rank_mass=mass,deficit=312*T,
+                maxchild=max(paid),halving_depth=2,halving_integer_inequality=[64**2,2*42**2],
+                local_additions=expected_adds,bridge_additions=18*V*T,copy_erase_episodes=9*L*T,
+                global_prefix_bound=str(prefix),global_prefix_bits=prefix.bit_length(),charged_prefix_bits=charged_prefix,
+                omitted_bridge_shears_rejected=bridge_controls,
+                scope='Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.',
+                seconds=time.monotonic()-start)
+    write(out/'GLOBAL.json',result)
+    print(json.dumps({k:v for k,v in result.items() if k not in ('local_checks','scalar_stages','global_prefix_bound')}),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-hosting-selected-kernel/code/bit_hosted.py b/research/e8-hosting-selected-kernel/code/bit_hosted.py
new file mode 100644
index 0000000000..be9fc18f5b
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/code/bit_hosted.py
@@ -0,0 +1,116 @@
+"""Idle-axis hosting for #434's compressed nine-stage bit template (m=64).
+Reads the emitted parent template, keeps every local program and scalar replay unchanged, and moves whole helper
+residuals from banks onto pending idle-advance coordinates of untouched data families.  Emits a new template,
+GLOBAL.json with the new live stock and paid profile.  usage: bit_hosted.py PARENT_GLOBAL_DIR LOCAL_CHECK_DIR OUT"""
+import gzip, hashlib, importlib.util, json, sys, time
+from collections import Counter
+from pathlib import Path
+HERE = Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE))
+import hosting_core as HC
+H, V, L, K, T, M = 8, 120, 9, 4, 64, 64
+DATA = 2 * K * V * T
+DISCOVER = False
+sha = lambda p: hashlib.sha256(Path(p).read_bytes()).hexdigest()
+def main(parent, local, out):
+    t0 = time.monotonic(); out.mkdir(parents=True, exist_ok=False)
+    blob = gzip.decompress((parent / 'GLOBAL-TEMPLATE.json.gz').read_bytes()); t = json.loads(blob)
+    g = json.loads((parent / 'GLOBAL.json').read_text())
+    assert hashlib.sha256(blob).hexdigest() == g['template_sha256']
+    st = json.loads((local / 'records/249-states.json').read_text()); R = st['n'] - 2 * V; assert R == g['R']
+    fs = json.loads((local / 'records/frames.json').read_text())['frames']; dims = {int(f): z['dim'] for f, z in fs.items()}
+    width = [H - dims[st['initial'][str(i)]] for i in range(2 * V, 2 * V + R)]
+    # schedule with indexed idle children
+    sched = []; idx = 0
+    for e in t['schedule']:
+        if e['kind'] == 'local_cover_sweep': sched.append(dict(kind='local', stage=e['stage'], pair=e['pair']))
+        elif e['kind'] == 'bridge': sched.append(dict(kind='bridge', dst=e['dst'], src=e['src']))
+        elif e['kind'] == 'idle':
+            sched.append(dict(kind='idle', pair=e['pair'], rank=e['rank'], idx=idx)); e['idx'] = idx; idx += 1
+    win = {k: x for k, x in HC.windows(sched).items() if x[1] > 0 and x[2]}
+    avail = Counter()
+    for s in range(L):
+        for w in width: avail[s, w] += 1
+    sel = HERE / 'SELECTION.json'; key = 'bit'
+    if DISCOVER:
+        ys, zs, val = HC.solve(win, 2 * V, dict(avail), M, group=None); HC.save_selection(sel, key, ys, zs, val)
+    ys, zs, val = HC.load_selection(sel, key)
+    helpers = {s: [(h, width[h]) for h in range(R)] for s in range(L)}
+    slots, rem = HC.expand(win, ys, zs, helpers, 2 * V)
+    hosted = {(s, h): (i, c, off, w) for i, c, off, w, s, h in slots}
+    # remaining helpers -> exact width-64 banks (per stage, same set of helpers in every replica)
+    left = {s: [h for h in range(R) if (s, h) not in hosted] for s in range(L)}
+    nb = {}; place = {}
+    for s in range(L):
+        wl = {h: width[h] for h in left[s]}
+        slotsS = sorted(((wl[h], rep, h) for rep in range(T) for h in left[s]), key=lambda x: (-x[0], x[1], x[2]))
+        by = {}
+        for w_, rep, h in slotsS: by.setdefault(w_, []).append((rep, h))
+        bins = []
+        def take(w_): return by[w_].pop(0)
+        for w_ in sorted(by, reverse=True):
+            if w_ == 8: continue
+            while by.get(w_):
+                cont = []; off = 0
+                if w_ == 7:
+                    for _ in range(8): rep, h = take(7); cont.append((rep, h, off, 7)); off += 7
+                    rep, h = take(8); cont.append((rep, h, off, 8)); off += 8
+                else:
+                    for _ in range(64 // w_): rep, h = take(w_); cont.append((rep, h, off, w_)); off += w_
+                assert off == 64; bins.append(cont)
+        while by.get(8):
+            cont = []; off = 0
+            for _ in range(8): rep, h = take(8); cont.append((rep, h, off, 8)); off += 8
+            bins.append(cont)
+        nb[s] = len(bins)
+        for b, cont in enumerate(bins):
+            for rep, h, off, w_ in cont: place[s, rep, h] = (b, off, w_)
+    base = [DATA]
+    for s in range(L): base.append(base[-1] + nb[s])
+    LIVE = base[-1]
+    # owners
+    for c in t['calls']:
+        s, rep, p = c['stage'], c['replica'], c['pair']; own = c['owners'][:2 * V]
+        for h in range(R):
+            if (s, h) in hosted:
+                i, cp, off, w = hosted[s, h]; pair = win[i][0]; side, port = divmod(cp, V)
+                own.append([rep * 960 + (2 * pair + side) * V + port, ['hosted', i, off, w]])
+            else:
+                b, off, w = place[s, rep, h]; own.append([base[s] + b, ['bank', off, w]])
+        assert len({(f, tuple(r)) for f, r in own}) == 2 * V + R and all(0 <= f < LIVE for f, r in own)
+        c['owners'] = own
+    # profile: local programs unchanged; idle children replaced by remainders
+    paid = Counter()
+    for c in t['calls']:
+        for z in t['local_programs'][c['orientation']]:
+            if z[0] == 0 and z[4]: paid[z[4]] += 1
+            if z[0] == 2: paid[z[5]] += 1
+    remainder = {}
+    for e in t['schedule']:
+        if e['kind'] == 'idle' and e['rank']:
+            i = e['idx']
+            if i in win:
+                rr = Counter(rem[i, cp] for cp in range(2 * V)); remainder[i] = {str(k): v for k, v in sorted(rr.items())}
+                for r_, n in rr.items():
+                    if r_: paid[r_] += n * T
+            else:
+                paid[e['rank']] += 2 * V * T
+    mass = sum(r * n for r, n in paid.items()); assert M * LIVE - mass == 312*T, M * LIVE - mass
+    t.update(version='compressed-nine-e8-bit-v1+idle-axis-hosting', live=LIVE,
+             hosting=dict(windows={str(i): [w[0], w[1], sorted(w[2])] for i, w in win.items()},
+                          slots=[list(x) for x in slots], remainders=remainder, banks_per_stage=nb,
+                          rule='helper (stage s, helper h) of replica r owns coordinates [off, off+w) of the pending idle-child '
+                               'projector of data family r*960+(2*pair+side)*120+port (copy = side*120+port); s lies strictly between '
+                               'the last local/bridge touch of that pair and the child; the child keeps the remaining coordinates.'),
+             helper_route='bank owner (exact width-64 tiling of the unhosted residuals of each stage) or hosted owner (data family, pending idle coordinates)')
+    tb = json.dumps(t, separators=(',', ':'), sort_keys=True).encode(); (out / 'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(tb, mtime=0))
+    res = dict(g); res.update(status='PASS_IDLE_AXIS_HOSTED_BIT_TEMPLATE', live=LIVE, physical=LIVE + 9, template_sha256=hashlib.sha256(tb).hexdigest(),
+               parent_template_sha256=g['template_sha256'], profile=dict(sorted(paid.items())), paid_calls=sum(paid.values()), rank_mass=mass,
+               maxchild=max(paid), banks_per_stage_hosted=nb, hosted_residuals_per_replica=len(slots), hosted_residuals=len(slots) * T,
+               hosted_coordinates_per_replica=sum(x[3] for x in slots), saved_idle_cost_proxy=val, seconds=time.monotonic() - t0)
+    res['bank_assignments'] = sum(1 for c in t['calls'] for f, r in c['owners'][2 * V:] if r[0] == 'bank')
+    (out / 'GLOBAL.json').write_text(json.dumps(res, indent=2) + '\n')
+    print(json.dumps({k: res[k] for k in ('live', 'maxchild', 'hosted_residuals', 'banks_per_stage_hosted', 'rank_mass')}), flush=True)
+if __name__ == '__main__':
+    DISCOVER = '--discover' in sys.argv; args = [a for a in sys.argv[1:] if a != '--discover']
+    main(Path(args[0]), Path(args[1]), Path(args[2]))
diff --git a/research/e8-hosting-selected-kernel/code/complex_hosted.py b/research/e8-hosting-selected-kernel/code/complex_hosted.py
new file mode 100644
index 0000000000..56e15c15ae
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/code/complex_hosted.py
@@ -0,0 +1,87 @@
+"""Idle-axis hosting for #433's compressed nine-stage complex template (m=73, R=560, whole rank-nine residuals).
+Local programs, data routes and the cover correction are unchanged; bank slots of hosted residuals move onto pending
+idle-child coordinates of untouched data families; unhosted residuals are re-tiled eight per bank with one paid pad
+(a final partial bank pays the larger pad).  usage: complex_hosted.py SPLIT_CENTRES_DIR OUT"""
+import gzip, hashlib, json, math, sys, time
+from collections import Counter
+from pathlib import Path
+HERE = Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE))
+import hosting_core as HC
+V, K, T, L, M, R = 120, 4, 8, 9, 73, 560
+DATA = 2 * K * V * T
+DISCOVER = False
+def main(src, out):
+    t0 = time.monotonic(); out.mkdir(parents=True, exist_ok=False)
+    blob = gzip.decompress((src / 'GLOBAL-TEMPLATE.json.gz').read_bytes()); t = json.loads(blob)
+    integ = json.loads((src / 'INTEGRATION.json').read_text()); checks = json.loads((src / 'LOCAL-CHECKS.json').read_text())
+    assert hashlib.sha256(blob).hexdigest() == integ['global_template_sha256'] and t['live'] == integ['live']
+    rank = {}
+    for it in t['idle_children']:
+        assert it['replicas'] == T; rank.setdefault(it['child'], it['rank']); assert rank[it['child']] == it['rank']
+    pair_of_stage = {e['stage']: e['pair'] for e in t['recipe'] if e['kind'] == 'local'}
+    sched = []; side_of = {}; pair_of = {}
+    for e in t['execution_schedule']:
+        if e['kind'] == 'local_cover_sweep': sched.append(dict(kind='local', stage=e['stage'], pair=pair_of_stage[e['stage']]))
+        elif e['kind'] == 'bridge': sched.append(dict(kind='bridge', dst=e['dst'], src=e['src']))
+        elif e['kind'] == 'idle_cover_sweep':
+            for sd, ch in enumerate(e['child_indices']):
+                if ch in rank:
+                    sched.append(dict(kind='idle', pair=e['pair'], rank=rank[ch], idx=ch)); side_of[ch] = sd; pair_of[ch] = e['pair']
+    win = {k: x for k, x in HC.windows(sched).items() if x[1] >= 9 and x[2]}
+    avail = {(s, 9): R for s in range(L)}
+    sel = HERE / 'SELECTION.json'; key = 'complex'
+    if DISCOVER:
+        ys, zs, val = HC.solve(win, V, avail, M, pad_value=HC.cost(1, M) / 8); HC.save_selection(sel, key, ys, zs, val)
+    ys, zs, val = HC.load_selection(sel, key)
+    slots, rem = HC.expand(win, ys, zs, {s: [(h, 9) for h in range(R)] for s in range(L)}, V)
+    hosted = {(s, h): (i, port, off) for i, port, off, w, s, h in slots}
+    # re-tile unhosted residuals: per stage, z = rank among (replica, helper) unhosted pairs; eight per bank
+    base = [DATA]; tile = {}; partial = Counter()
+    for s in range(L):
+        left = [(rep, h) for rep in range(T) for h in range(R) if (s, h) not in hosted]
+        for z, (rep, h) in enumerate(left): tile[s, rep, h] = divmod(z, 8)
+        nb = -(-len(left) // 8); base.append(base[-1] + nb)
+        if len(left) % 8: partial[M - 9 * (len(left) % 8)] += 1
+        full = len(left) // 8
+        partial[M - 72] += full
+    W = base[-1]
+    for c in t['calls']:
+        s, rep, p = c['stage'], c['replica'], c['pair']; own = c['owners'][:2 * V]
+        for h in range(R):
+            if (s, h) in hosted:
+                i, port, off = hosted[s, h]; own.append([rep * 960 + (2 * pair_of[i] + side_of[i]) * V + port, [3, i, off]])
+            else:
+                b, sl = tile[s, rep, h]; own.append([base[s] + b, [2, sl]])
+        assert len({(f, tuple(r)) for f, r in own}) == 2 * V + R and all(f < W for f, r in own)
+        c['owners'] = own
+    paid = Counter()
+    for c in t['calls']:
+        for r_, z in checks[c['orientation']]['paid_profile'].items(): paid[int(r_)] += z
+    newidle = []
+    for it in t['idle_children']:
+        ch, port = it['child'], it['port']; rr = rem.get((ch, port), it['rank']) if ch in win else it['rank']
+        if rr: newidle.append(dict(child=ch, port=port, rank=rr, hosted=it['rank'] - rr, replicas=T)); paid[rr] += T
+    for r_, n in partial.items(): paid[r_] += L * n if False else n * 1
+    # padding: one pad child per bank per stage (already per-stage counted above), the template replays all stages
+    mass = sum(r * n for r, n in paid.items()); D = M * W - mass
+    assert D == 2496, D
+    t.update(version='hamming-mutable-basis-nine-v1+idle-axis-hosting', live=W, idle_children=newidle,
+             physical=W + R + (integ['physical'] - integ['live'] - R),
+             hosting=dict(windows={str(i): [w[0], w[1], sorted(w[2])] for i, w in win.items()}, sides=side_of, pairs=pair_of,
+                          slots=[list(x) for x in slots], banks=[base[s + 1] - base[s] for s in range(L)]))
+    t['bank_padding']['families'] = list(range(DATA, W)); t['cover_final_correction']['families'] = [0, W]
+    t['cover_final_correction']['charged_calls_per_cover'] = W
+    for e in t['execution_schedule']:
+        if e['kind'] == 'bank_padding_cover_sweep': e['families'] = [DATA, W]
+        elif e['kind'] == 'translate_every_live_family': e.update(t['cover_final_correction'])
+    tb = json.dumps(t, sort_keys=True, separators=(',', ':')).encode(); (out / 'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(tb, mtime=0))
+    res = dict(status='PASS_IDLE_AXIS_HOSTED_COMPLEX_TEMPLATE', parent_template_sha256=integ['global_template_sha256'],
+               template_sha256=hashlib.sha256(tb).hexdigest(), live=W, physical=t['physical'], global_profile=dict(sorted(paid.items())),
+               rank_mass=mass, deficit=D, maxchild=max(paid), hosted_residuals=len(slots) * T, banks_per_stage=t['hosting']['banks'],
+               saved_cost_proxy=val, seconds=time.monotonic() - t0)
+    (out / 'HOSTED.json').write_text(json.dumps(res, indent=2) + '\n')
+    print(json.dumps({k: res[k] for k in ('live', 'maxchild', 'hosted_residuals', 'banks_per_stage', 'deficit')}))
+if __name__ == '__main__':
+    DISCOVER = '--discover' in sys.argv; args = [a for a in sys.argv[1:] if a != '--discover']
+    main(Path(args[0]), Path(args[1]))
diff --git a/research/e8-hosting-selected-kernel/code/hosting_core.py b/research/e8-hosting-selected-kernel/code/hosting_core.py
new file mode 100644
index 0000000000..68b536daa9
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/code/hosting_core.py
@@ -0,0 +1,138 @@
+"""Idle-axis hosting: place whole dirty-helper residuals on the pending coordinates of an idle data family.
+
+A data family that is advanced by an idle child from level a to level b receives the commuting coordinate factors of
+that child.  If the family is untouched (no local invocation on its pair and no bridge naming its pair) during an
+interval of local invocations ending at the child, a helper residual of width w from an invocation inside that
+interval may own w of those pending coordinates instead of a bank slot.  The child keeps only the remaining
+coordinates.  This module computes the windows from the recipe and chooses, per replica, how many residuals of each
+width each child hosts (exact integer programme), then expands that choice into explicit slot assignments.
+Standard library plus scipy for the integer programme; the emitted assignment is re-checked without scipy."""
+import math
+from collections import Counter, defaultdict
+
+def windows(schedule):
+    """schedule: ordered events dict(kind='local',stage,pair) | dict(kind='bridge',dst,src) | dict(kind='idle',pair,rank,idx).
+    Returns {idx: (pair, rank, frozenset(stages))} - stages whose invocation lies strictly between the last touch of
+    the pair and the idle child."""
+    last = {}; out = {}; locals_ = []
+    for pos, e in enumerate(schedule):
+        k = e['kind']
+        if k == 'local':
+            locals_.append((pos, e['stage'], e['pair'])); last[e['pair']] = pos
+        elif k == 'bridge':
+            last[e['dst']] = pos; last[e['src']] = pos
+        elif k == 'idle':
+            p = e['pair']; lo = last.get(p, -1)
+            st = frozenset(s for q, s, pp in locals_ if lo < q < pos and pp != p)
+            out[e['idx']] = (p, e['rank'], st)      # an idle child acts on other coordinates (or the other member): not a touch
+    return out
+
+def patterns(rank, widths, maxk=12):
+    """multisets of widths with sum <= rank (as sorted tuples)"""
+    ws = sorted(set(widths), reverse=True); res = []
+    def rec(i, cur, s):
+        if i == len(ws): res.append(tuple(cur)); return
+        w = ws[i]; k = 0
+        while s + k * w <= rank and len(cur) + k <= maxk:
+            rec(i + 1, cur + [w] * k, s + k * w); k += 1
+    rec(0, [], 0)
+    return res
+
+def cost(r, m):
+    return r * math.log(m / r) if r else 0.0
+
+def solve(win, copies, avail, m, pad_value=0.0, group=None):
+    """win: {idx: (pair, rank, stages)}; copies: piece copies per replica of each idx (2V);
+    avail: {(stage, width): count per replica}; maximise saved idle cost (+ pad_value per hosted residual).
+    group: optional {width: g} - remaining count of that width per stage must be a multiple of g (exact bank tiling).
+    Returns {(idx, pattern): copies} and {(idx, width, stage): count}."""
+    import numpy as np
+    from scipy.optimize import milp, LinearConstraint, Bounds
+    widths = sorted({w for (_, w) in avail})
+    var = []; index = {}
+    for idx, (p, r, st) in win.items():
+        for pat in patterns(r, widths):
+            index[('y', idx, pat)] = len(var); var.append(('y', idx, pat))
+        for w in widths:
+            for s in st:
+                if avail.get((s, w), 0):
+                    index[('z', idx, w, s)] = len(var); var.append(('z', idx, w, s))
+    stages = sorted({s for (s, _) in avail})
+    if group:
+        for w, g in group.items():
+            for s in stages:
+                index[('g', w, s)] = len(var); var.append(('g', w, s))
+    n = len(var); c = np.zeros(n); integ = np.ones(n); lb = np.zeros(n); ub = np.full(n, np.inf)
+    for key, j in index.items():
+        if key[0] == 'y':
+            _, idx, pat = key; r = win[idx][1]; c[j] = -(cost(r, m) - cost(r - sum(pat), m) + pad_value * len(pat))
+    rows, lo, hi = [], [], []
+    for idx in win:
+        row = np.zeros(n)
+        for key, j in index.items():
+            if key[0] == 'y' and key[1] == idx: row[j] = 1
+        rows.append(row); lo.append(copies); hi.append(copies)
+        for w in widths:
+            row = np.zeros(n)
+            for key, j in index.items():
+                if key[0] == 'y' and key[1] == idx: row[j] = key[2].count(w)
+                if key[0] == 'z' and key[1] == idx and key[2] == w: row[j] = -1
+            rows.append(row); lo.append(0); hi.append(0)
+    for (s, w), a in avail.items():
+        row = np.zeros(n)
+        for key, j in index.items():
+            if key[0] == 'z' and key[2] == w and key[3] == s: row[j] = 1
+        if group and w in group:
+            row[index[('g', w, s)]] = group[w]; rows.append(row); lo.append(a); hi.append(a)   # used + g*k = avail
+        else:
+            rows.append(row); lo.append(0); hi.append(a)
+    res = milp(c, constraints=LinearConstraint(np.array(rows), lo, hi), integrality=integ, bounds=Bounds(lb, ub),
+               options=dict(time_limit=600, disp=False))
+    assert res.x is not None, res.message
+    x = [int(round(t)) for t in res.x]
+    ys = {(k[1], k[2]): x[j] for k, j in index.items() if k[0] == 'y' and x[j]}
+    zs = {(k[1], k[2], k[3]): x[j] for k, j in index.items() if k[0] == 'z' and x[j]}
+    return ys, zs, -res.fun
+
+def expand(win, ys, zs, helpers, V2):
+    """helpers: {stage: [(helper, width), ...]} for ONE replica; returns list of
+    (idx, copy, offset, width, stage, helper) and the remainder rank of every (idx, copy).
+    Copies of a piece are the 2V (side, port) data families; residuals packed from offset 0 in decreasing width."""
+    pool = defaultdict(list)                    # (stage, width) -> helpers
+    for s, hs in helpers.items():
+        for h, w in hs: pool[s, w].append(h)
+    for k in pool: pool[k].sort()
+    need = defaultdict(list)                    # (idx, width) -> stages multiset in deterministic order
+    for (idx, w, s), cnt in sorted(zs.items()): need[idx, w] += [s] * cnt
+    out = []; rem = {}
+    for idx in sorted(win):
+        pats = sorted([(pat, cnt) for (i, pat), cnt in ys.items() if i == idx], key=lambda t: (-sum(t[0]), t[0]))
+        copy = 0; ptr = Counter()
+        r = win[idx][1]
+        for pat, cnt in pats:
+            for _ in range(cnt):
+                off = 0
+                for w in sorted(pat, reverse=True):
+                    s = need[idx, w][ptr[idx, w]]; ptr[idx, w] += 1
+                    h = pool[s, w].pop(0)
+                    out.append((idx, copy, off, w, s, h)); off += w
+                rem[idx, copy] = r - off; copy += 1
+        while copy < V2: rem[idx, copy] = r; copy += 1
+    return out, rem
+
+def save_selection(path, key, ys, zs, val):
+    """freeze the integer-programme choice (patterns per child, residual stages per child) for stdlib-only replay"""
+    import json
+    from pathlib import Path
+    p = Path(path); d = json.loads(p.read_text()) if p.exists() else {}
+    d[key] = dict(patterns=sorted([[i, list(pat), n] for (i, pat), n in ys.items()]),
+                  stages=sorted([[i, w, s, n] for (i, w, s), n in zs.items()]), proxy_saving=val)
+    p.write_text(json.dumps(d, indent=1, sort_keys=True) + '\n')
+
+def load_selection(path, key):
+    import json
+    from pathlib import Path
+    d = json.loads(Path(path).read_text())[key]
+    ys = {(i, tuple(pat)): n for i, pat, n in d['patterns']}
+    zs = {(i, w, s): n for i, w, s, n in d['stages']}
+    return ys, zs, d['proxy_saving']
diff --git a/research/e8-hosting-selected-kernel/code/residual_routes.py b/research/e8-hosting-selected-kernel/code/residual_routes.py
new file mode 100644
index 0000000000..04feccfe52
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/code/residual_routes.py
@@ -0,0 +1,26 @@
+"""Generate exact coordinate isometries for this kernel's residuals.
+OpenAI Codex. Route witness/check conventions follow chafreaky's PR439.
+"""
+import sys
+from pathlib import Path
+sys.path.insert(0,str(Path(__file__).resolve().parent.parent/'vendor/pr439'))
+from bank_routes import validate_isometries
+
+def generate(word,dimensions):
+    roots=word['lines'];index={tuple(r):i for i,r in enumerate(roots)};out=[]
+    for f in sorted(set(word['start'][240:])):
+        e=dimensions[f];rs=[roots[j] for j in word['frames'][f]]
+        axes=sorted({i for r in rs for i,x in enumerate(r) if x})
+        assert len(axes)==e, 'This finite selection must have coordinate entrances'
+        order=axes+[i for i in range(8) if i not in axes]
+        matrix=[[2*int(i==j) for j in range(8)] for i in order]
+        basis=[index[tuple(r)] for r in matrix]
+        assert set(basis[:e])<=set(word['frames'][f])
+        reduced=order[:];ops=[]
+        for i in range(8):
+            j=reduced.index(i)
+            if i!=j:reduced[i],reduced[j]=reduced[j],reduced[i];ops.append(['swap',i,j,None])
+        assert reduced==list(range(8)) and len(ops)<=7
+        out.append(dict(frame=f,entrance_rank=e,denominator=2,entrance_basis=basis[:e],residual_basis=basis[e:],orthogonal_rows_numerator=matrix,gaussian_reduction=ops))
+    assert validate_isometries(out,word['frames'],roots,dimensions)==set(word['start'][240:])
+    return out
diff --git a/research/e8-hosting-selected-kernel/evidence/assembly.log b/research/e8-hosting-selected-kernel/evidence/assembly.log
new file mode 100644
index 0000000000..c080c241fb
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/evidence/assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY 0.001249035299298004 binding bit gain over #434 10.2316%
diff --git a/research/e8-hosting-selected-kernel/evidence/bit-hosting.log b/research/e8-hosting-selected-kernel/evidence/bit-hosting.log
new file mode 100644
index 0000000000..742edb4ccb
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/evidence/bit-hosting.log
@@ -0,0 +1 @@
+{"live": 74528, "maxchild": 8, "hosted_residuals": 321536, "banks_per_stage_hosted": {"0": 0, "1": 3784, "2": 272, "3": 4936, "4": 0, "5": 0, "6": 4096, "7": 0, "8": 0}, "rank_mass": 4749824}
diff --git a/research/e8-hosting-selected-kernel/evidence/complex-hosting.log b/research/e8-hosting-selected-kernel/evidence/complex-hosting.log
new file mode 100644
index 0000000000..b8925ed69d
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/evidence/complex-hosting.log
@@ -0,0 +1 @@
+{"live": 8400, "maxchild": 8, "hosted_residuals": 34560, "banks_per_stage": [0, 0, 0, 160, 0, 120, 0, 0, 440], "deficit": 2496}
diff --git a/research/e8-hosting-selected-kernel/evidence/discovery.log b/research/e8-hosting-selected-kernel/evidence/discovery.log
new file mode 100644
index 0000000000..9fb2d39fdb
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/evidence/discovery.log
@@ -0,0 +1,10 @@
+add {'pivot': 950, 'entrance': 1, 'donors': [749, 819, 830, 948], 'moment': 0.9999987839981915, 'candidates': 22}
+add {'pivot': 954, 'entrance': 1, 'donors': [803, 817, 952], 'moment': 0.9999974065317905, 'candidates': 21}
+add {'pivot': 963, 'entrance': 1, 'donors': [783, 853, 962], 'moment': 0.9999962719365906, 'candidates': 18}
+add {'pivot': 969, 'entrance': 1, 'donors': [778, 844, 898, 968], 'moment': 0.9999951361271407, 'candidates': 16}
+add {'pivot': 971, 'entrance': 1, 'donors': [807, 835, 970], 'moment': 0.9999939141423637, 'candidates': 13}
+add {'pivot': 775, 'entrance': 1, 'donors': [758, 759, 774], 'moment': 0.9999929285371466, 'candidates': 10}
+add {'pivot': 859, 'entrance': 1, 'donors': [740, 741, 858], 'moment': 0.9999921873182623, 'candidates': 7}
+add {'pivot': 885, 'entrance': 1, 'donors': [740, 741, 884], 'moment': 0.9999908677882754, 'candidates': 4}
+add {'pivot': 920, 'entrance': 1, 'donors': [904, 906, 918], 'moment': 0.9999900390922772, 'candidates': 2}
+FINAL 123 147 0.9999900390922772 added 9
diff --git a/research/e8-hosting-selected-kernel/evidence/export.log b/research/e8-hosting-selected-kernel/evidence/export.log
new file mode 100644
index 0000000000..2530c07239
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/evidence/export.log
@@ -0,0 +1 @@
+exported 19776 records, 944 frames, n 980 ZERO 0
diff --git a/research/e8-hosting-selected-kernel/evidence/global-audit.log b/research/e8-hosting-selected-kernel/evidence/global-audit.log
new file mode 100644
index 0000000000..b264fea3e9
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/evidence/global-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT", "template_sha256": "965c825fd8a08e0121156536603d8ffa982a044626fdadd0acc41f05b8ac14eb", "source_frames": 944, "exact_nested_frame_pairs": 3360, "exact_reflected_pairs": 3360, "orthogonal_lift_argument": "Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.", "exact_bank_families": 51957, "mixed_width_slots": true, "entrance_rank_total": 147, "residual_isometries": 16, "mutations_rejected": ["omit an idle child", "omit a bridge", "omit terminal exchange", "remove a local invocation", "re-use a helper bank slot", "understate live stock", "omit a local paid move", "wrong reflected copy charge", "alter residual orthogonal basis", "wrong residual frame", "omit a residual route factor"], "profile": {"1": 1465920, "2": 588672, "3": 153216, "4": 205632, "5": 62208, "7": 54144, "8": 5184, "14": 30720, "28": 30720, "42": 30720}, "seconds": 13.70359254104551}
diff --git a/research/e8-hosting-selected-kernel/evidence/global.log b/research/e8-hosting-selected-kernel/evidence/global.log
new file mode 100644
index 0000000000..7251e9cc24
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/evidence/global.log
@@ -0,0 +1,2 @@
+Fresh prefix bits 123 charged 128
+{"status": "PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE", "h": 8, "m": 64, "v": 120, "R": 740, "replicas": 64, "live": 113397, "physical": 113406, "word_sha256": "f5ae52ba95d0edd76f85fdb4da04cd78ad46b55c9ad3b86cc098146b62032336", "source_records_sha256": "f9e0f3cdbc6a4eb5bfaf3fd843731a79c26740a6c4715079f2228e94b8706403", "independent_unbanked_scalar_columns": 7620, "all_scalar_columns_restored": true, "geometry_sha256": "40eb149ca9d6034c0e9584e476171b88b124f92c0da1345ff459bdea5d182fb9", "template_sha256": "965c825fd8a08e0121156536603d8ffa982a044626fdadd0acc41f05b8ac14eb", "emitted_program_sha256": "257e0291da1be27c83ce6eaebf508bdffe472cd48a2d73816a2a72fe87a5bb29", "emitted_events": 11390976, "local_invocations": 576, "bank_assignments": 426240, "banks_per_stage": 5773, "entrance_rank_total": 147, "mixed_width_slots": true, "padding_calls": 0, "residual_isometries": 16, "extra_helper_route_factor_bound": 144, "profile": {"1": 1465920, "2": 588672, "3": 153216, "4": 205632, "5": 62208, "7": 54144, "8": 5184, "14": 30720, "28": 30720, "42": 30720}, "paid_calls": 2627136, "rank_mass": 7237440, "deficit": 19968, "maxchild": 42, "halving_depth": 2, "halving_integer_inequality": [4096, 3528], "local_additions": 15446, "bridge_additions": 138240, "copy_erase_episodes": 5184, "global_prefix_bits": 123, "charged_prefix_bits": 128, "omitted_bridge_shears_rejected": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], "scope": "Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.", "seconds": 20.562781999935396}
diff --git a/research/e8-hosting-selected-kernel/evidence/hosting-audit.log b/research/e8-hosting-selected-kernel/evidence/hosting-audit.log
new file mode 100644
index 0000000000..2007d906a0
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/evidence/hosting-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT", "bit_template_sha256": "b099b89581f7dd9034e64239a67d9d67e2cd10023632e5df5c8bbb29831e5772", "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f", "bit_live": 74528, "complex_live": 8400, "bit_hosted_residuals": 321536, "complex_hosted_residuals": 34560, "bit_maxchild": 8, "complex_maxchild": 8, "mutations_rejected": ["bit: hosted residual outside its window", "bit: overlapping hosted coordinates", "bit: understated live stock", "bit: hosted owner on the active pair", "bit: missing remainder child", "complex: hosted residual outside its window", "complex: remainder child understated", "complex: dropped bank", "complex: duplicated hosted residual"]}
diff --git a/research/e8-hosting-selected-kernel/evidence/rebuild.log b/research/e8-hosting-selected-kernel/evidence/rebuild.log
new file mode 100644
index 0000000000..0c4d6fcc6d
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/evidence/rebuild.log
@@ -0,0 +1 @@
+{"donor_slots": 118, "entries": 123, "local_columns": 980, "local_profile": {"1": 2545, "2": 1022, "3": 266, "4": 357, "5": 108, "7": 14, "8": 9}, "new_frames": 0, "output_sha256": "f5ae52ba95d0edd76f85fdb4da04cd78ad46b55c9ad3b86cc098146b62032336", "status": "PASS_RECONSTRUCTED_HOSTING_SELECTED_KERNEL", "total_entrance_rank": 147}
diff --git a/research/e8-hosting-selected-kernel/rebuild.py b/research/e8-hosting-selected-kernel/rebuild.py
new file mode 100644
index 0000000000..50ced32fc0
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/rebuild.py
@@ -0,0 +1,30 @@
+"""Reconstruct the hosted-cost-selected kernel from the pinned R740 precursor.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+import gzip,hashlib,json,sys
+ROOT=Path(__file__).resolve().parent
+PRIOR=ROOT.parent/'e8-rank138-idle-hosting'
+UP=PRIOR/'upstream443'
+read=lambda p:json.loads(p.read_text())
+canonical=lambda x:json.dumps(x,sort_keys=True,separators=(',',':')).encode()
+w=json.loads(gzip.decompress((UP/'parent436/data/bit/bitE8-r740.json.gz').read_bytes()))
+for ph in ('D','A','B','C'):w[ph]=[[f,d,[s]] for f,d,ss in w[ph] for s in ss]
+ids={tuple(sorted(f)):i for i,f in enumerate(w['frames'])}
+for ph,i,old,new in read(UP/'data/retiming.json')['changes']:
+    assert sorted(w['frames'][w[ph][i][0]])==sorted(old)
+    w[ph][i][0]=ids[tuple(sorted(new))]
+priorword=json.loads(gzip.decompress((UP/'data/word.json.gz').read_bytes()))
+assert len(w['B'])==len(priorword['B']) and all(a[1:]==b[1:] for a,b in zip(w['B'],priorword['B']))
+w['B']=priorword['B']
+sel=read(ROOT/'SELECTION.json')
+assert hashlib.sha256(canonical(w)).hexdigest()==sel['frozen_precursor_sha256'] and w==read(ROOT/'PRECURSOR.json')
+sys.path.insert(0,str(UP/'code'))
+from replica_kernel import kernel
+from e8core import replay
+out,entries,rank,donors=kernel(w,sel['entries'],sel['replicas'])
+a=replay(out,span_mode='z');assert not a['viol']
+assert dict(a['H'])=={int(k):n for k,n in sel['local_profile'].items()}
+assert out==read(ROOT/'WORD.json') and out['frames']==w['frames']
+raw=canonical(out);receipt=dict(status='PASS_RECONSTRUCTED_HOSTING_SELECTED_KERNEL',entries=entries,total_entrance_rank=rank,donor_slots=donors,new_frames=0,output_sha256=hashlib.sha256(raw).hexdigest(),local_columns=a['n'],local_profile=dict(a['H']))
+d=Path(sys.argv[1]);d.mkdir();(d/'bit-source-centres.json').write_bytes(raw);(d/'bit-kernel-receipt.json').write_text(json.dumps(receipt,indent=2)+'\n');print(json.dumps(receipt,sort_keys=True))
diff --git a/research/e8-hosting-selected-kernel/vendor/pr439/LICENSE b/research/e8-hosting-selected-kernel/vendor/pr439/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/vendor/pr439/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
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+      and distribution as defined by Sections 1 through 9 of this document.
+
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diff --git a/research/e8-hosting-selected-kernel/vendor/pr439/NOTICE.md b/research/e8-hosting-selected-kernel/vendor/pr439/NOTICE.md
new file mode 100644
index 0000000000..3dfad2ad57
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/vendor/pr439/NOTICE.md
@@ -0,0 +1,26 @@
+# Attribution and scope
+
+New kernel selection, explicit residual route witnesses, integration and audits:
+chafreaky, with substantial OpenAI Codex assistance. Apache-2.0.
+
+- eumemic, PR #436 (`da8ca2025472553ac9b36f4400138ed48a6a0e3b`): R740 bit word,
+  reconstruction, elimination/reuse, independent checkers and #433 composition.
+  The entire parent package is byte-identical, including its notices, licenses,
+  source pins and Anthropic Claude disclosure.
+- chafreaky, PR #417: shared-donor kernel, exact local replay and tiling code;
+  the earlier implementation had substantial Anthropic Claude assistance.
+- rohanarun, PR #435 (`2c9c833ac8709402c37fc88a6a23393fb0d397fb`): prior mixed-width
+  residual-bank composition on #433. The new implementation derives from the
+  pinned #436 global/audit code and adds explicit residual isometries and controls.
+- icekylinx, PR #433: split-centre complex supplier, bit finite invoice and tail,
+  with OpenAI Codex assistance; the complex result is cited, not rebuilt here.
+- jacklightChen, PRs #386 and #425: compressed nine-stage geometry and the
+  mutable-basis complex interface, with OpenAI Codex assistance.
+- utcorvusvolat-dotcom / Dylan Crow, PR #370: E8 bit format, producer and
+  independent checker lineage, with Anthropic Claude assistance.
+- applecrusher (#376), ai-nanachi (#389/#426), DaysSky (#363/#375/#381),
+  DreamingOfClouds (#315), Jacob Sussman, and all earlier credited contributors:
+  see the unchanged `parent436/NOTICE.md` and source-specific notices.
+
+Do not infer an unconditional theorem or a new Lean proof from the finite
+certificates. No inherited author or AI-assistance disclosure has been removed.
diff --git a/research/e8-hosting-selected-kernel/vendor/pr439/bank_routes.py b/research/e8-hosting-selected-kernel/vendor/pr439/bank_routes.py
new file mode 100644
index 0000000000..919fe32f7e
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/vendor/pr439/bank_routes.py
@@ -0,0 +1,64 @@
+"""Exact residual bank routes for the kernel word; chafreaky with OpenAI Codex.
+
+The stored integer rows divided by two are an orthonormal basis. Entrance
+rows span E; the remaining rows span E-perp. A coordinate permutation sends
+the latter to the assigned contiguous block in a width-64 bank. This gives
+an explicit rational isometry, with only powers of two in denominators.
+"""
+from collections import Counter, deque
+from tile_m import tile
+
+
+def placement(widths):
+    by_width = {}
+    for rep in range(8):
+        for helper, width in enumerate(widths):
+            assert 0 < width <= 8
+            by_width.setdefault(width, deque()).append((rep, helper))
+    patterns = tile({w: len(q) for w, q in by_width.items()}, 64)
+    result = {}
+    bank = 0
+    for widths_in_bank, count in patterns:
+        for _ in range(count):
+            offset = 0
+            for width in widths_in_bank:
+                key = by_width[width].popleft()
+                result[key] = (bank, offset, width)
+                offset += width
+            assert offset == 64
+            bank += 1
+    assert all(not q for q in by_width.values())
+    assert len(result) == 8 * len(widths)
+    return result, bank
+
+
+def validate_isometries(rows, frames, roots, dimensions):
+    seen = set()
+    dot = lambda a, b: sum(x*y for x, y in zip(a, b))
+    for record in rows:
+        f = record['frame']
+        assert f not in seen
+        seen.add(f)
+        e = record['entrance_rank']
+        assert e == dimensions[f] and record['denominator'] == 2
+        basis = record['entrance_basis'] + record['residual_basis']
+        matrix = record['orthogonal_rows_numerator']
+        assert len(basis) == len(matrix) == 8
+        assert matrix == [roots[i] for i in basis]
+        assert all(len(r) == 8 and all(type(x) is int for x in r) for r in matrix)
+        assert all(dot(a,b) == 4*(i==j) for i,a in enumerate(matrix) for j,b in enumerate(matrix))
+        # The first e rows span precisely the frame, not only its dimension.
+        for i in frames[f]:
+            assert sum(dot(roots[i], q)**2 for q in matrix[:e]) == 4*dot(roots[i], roots[i])
+        assert len(record['entrance_basis']) == e
+        # This selected family needs coordinate permutations only. Checking the
+        # elementary reduction also bounds the literal route cost and primes.
+        reduced = [[x // 2 for x in row] for row in matrix]
+        assert all(x % 2 == 0 for row in matrix for x in row)
+        operations = record['gaussian_reduction']
+        assert len(operations) <= 7
+        for kind, i, j, scalar in operations:
+            assert kind == 'swap' and scalar is None and 0 <= i < 8 and 0 <= j < 8
+            reduced[i], reduced[j] = reduced[j], reduced[i]
+        assert reduced == [[int(i == j) for j in range(8)] for i in range(8)]
+    return seen
diff --git a/research/e8-hosting-selected-kernel/vendor/pr439/e8core.py b/research/e8-hosting-selected-kernel/vendor/pr439/e8core.py
new file mode 100644
index 0000000000..78983b3687
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/vendor/pr439/e8core.py
@@ -0,0 +1,203 @@
+"""Our own engine for bitE8/1 words (E8 root-line labels, h = 8): frame algebra over Q via root-line masks,
+legality/F2 replay, five-stage histogram, exact bit coarse saving and PR #315 outer assembly (our engine copies).
+Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0."""
+import gzip, json, os, importlib.util
+from fractions import Fraction as Q
+from collections import Counter
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+def _load(n):
+    s = importlib.util.spec_from_file_location('e8_' + n, os.path.join(HERE, "engines", n + ".py"))
+    m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+moment = _load('moment'); other = _load('base_two_moment'); outer = _load('outer')
+
+B2 = Q(876248285600677, 10**18)   # Sussman E8 five-stage (PR #352)
+B3 = Q(932783231884153, 10**18)   # DaysSky seven-stage B_3 (PR #363; no Lean proof)
+
+
+def load_word(p):
+    with (gzip.open(p, 'rt') if p.endswith('.gz') else open(p)) as f:
+        return json.load(f)
+
+
+def save_word(c, p):
+    with gzip.open(p, 'wt') as f:
+        json.dump(c, f, separators=(',', ':'))
+
+
+def rank(vecs):
+    rows = [[Q(x) for x in r] for r in vecs]; rk = 0
+    n = len(rows[0]) if rows else 0
+    for col in range(n):
+        p = next((i for i in range(rk, len(rows)) if rows[i][col] != 0), None)
+        if p is None: continue
+        rows[rk], rows[p] = rows[p], rows[rk]
+        for i in range(len(rows)):
+            if i != rk and rows[i][col] != 0:
+                f = rows[i][col] / rows[rk][col]; rows[i] = [a - f * b for a, b in zip(rows[i], rows[rk])]
+        rk += 1
+    return rk
+
+
+class Lat:
+    """Root-spanned subspaces of Q^8 represented by the mask of root lines they contain."""
+    def __init__(self, lines):
+        self.lines = [tuple(x) for x in lines]; self.v = len(lines)
+        self._dim = {0: 0}; self._close = {}
+        # Gram (form <x,y>/2) for orthogonality
+        self.ip = [[sum(a * b for a, b in zip(x, y)) // 2 for y in self.lines] for x in self.lines]
+
+    def close(self, mask):
+        """mask of all root lines in span(roots of mask)"""
+        if mask in self._close: return self._close[mask]
+        idx = [i for i in range(self.v) if mask >> i & 1]
+        basis = []
+        for i in idx:
+            if rank([self.lines[j] for j in basis] + [self.lines[i]]) > len(basis): basis.append(i)
+        d = len(basis); out = 0
+        if d == 8: out = (1 << self.v) - 1
+        elif d:
+            B = [self.lines[j] for j in basis]
+            for i in range(self.v):
+                if rank(B + [self.lines[i]]) == d: out |= 1 << i
+        self._close[mask] = out; self._close[out] = out; self._dim[out] = d
+        return out
+
+    def dim(self, mask):
+        if mask not in self._dim: self.close(mask)
+        return self._dim[mask]
+
+    def basis(self, mask):
+        b = []
+        for i in range(self.v):
+            if mask >> i & 1 and rank([self.lines[j] for j in b] + [self.lines[i]]) > len(b): b.append(i)
+        return b
+
+    def perp(self, t):
+        return self.close(sum(1 << j for j in range(self.v) if self.ip[t][j] == 0))
+
+
+def to_masks(c, L):
+    return [L.close(sum(1 << i for i in fr)) for fr in c['frames']]
+
+
+PHASES = ('D', 'A', 'B', 'C')
+
+
+def replay(c, L=None, masks=None, check_f2=True, span=True, span_mode='z'):
+    """Exact legality + F2 replay + histogram of a bitE8/1 word. Returns dict(H_local, steps, ...).
+    Legality: each register's frames nested (mask inclusion = exact Q-subspace inclusion for root-spanned frames) and
+    strictly increasing at each move; every gate at one common frame; D compensation at frame 0; y at frame 0 at the
+    scatter; COPY of retained totals; final frames (x, helpers FULL; y_t at its cap t-perp).
+    Source-span: every non-target operand's x-support lies in the gate frame."""
+    L = L or Lat(c['lines']); masks = masks or to_masks(c, L)
+    v, R, h = c['v'], c['R'], c['h']; n = 2 * v + R; FULL = (1 << v) - 1
+    cur = [masks[f] for f in c['start']]
+    for r in range(v): assert cur[r] == L.close(1 << r), 'x start'
+    for r in range(v, 2 * v): assert cur[r] == 0, 'y start at 0'
+    sig = [L.dim(cur[r]) for r in range(n)]
+    H = Counter(); steps = 0; viol = []
+    val = [1 << i for i in range(n)]
+    zsupp = [{i: 1} if i < v else {} for i in range(n)]  # integer support of each register over the x columns (all ADDs are +1)
+    def climb(r, m):
+        nonlocal steps
+        if cur[r] == m: return
+        assert cur[r] & ~m == 0 and cur[r] != m, ('not nested', r)
+        H[L.dim(m) - L.dim(cur[r])] += 1; steps += 1; cur[r] = m
+    def run(gates, ph):
+        for k, (f, d, srcs) in enumerate(gates):
+            m = masks[f]
+            assert d >= v and d not in srcs and len(set(srcs)) == len(srcs), (ph, k)
+            for x in [d] + srcs: climb(x, m)
+            for s in srcs:
+                val[d] ^= val[s]
+                if span:
+                    if s < v or s >= 2 * v:
+                        ms = sum(1 << i for i in zsupp[s])
+                        if ms & ~m: viol.append((ph, k, s))
+                    zd = zsupp[d]
+                    for i, a in zsupp[s].items():
+                        w = zd.get(i, 0) + a
+                        if w: zd[i] = w
+                        else: zd.pop(i, None)
+                    if span_mode == 'f2':
+                        zsupp[d] = {i: 1 for i in range(v) if val[d] >> i & 1}
+            if span and d >= 2 * v:
+                md = sum(1 << i for i in zsupp[d])
+                if md & ~m: viol.append((ph, k, d))
+    run(c['D'], 'D')
+    for r in range(v, n): assert cur[r] == masks[c['start'][r]], 'D compensation at frame 0 (helpers untouched otherwise)'
+    run(c['A'], 'A')
+    for t in range(v): assert cur[v + t] == 0, 'y at frame 0 at the scatter'
+    copies = [val[q] for q in c['ret']]
+    for q in c['ret']:
+        assert q >= 2 * v; H[L.dim(cur[q])] += 1
+    for t, row in enumerate(c['scatter']):
+        for k in row: val[v + t] ^= copies[k]
+    run(c['B'], 'B'); run(c['C'], 'C')
+    for r in range(n): climb(r, masks[c['final'][r]])
+    for r in range(v): assert cur[r] == FULL
+    for r in range(2 * v, n): assert cur[r] == FULL
+    for t in range(v): assert cur[v + t] == L.perp(t), 'y final at cap'
+    if check_f2:
+        for s in range(v): assert val[s] == 1 << s
+        for t in range(v): assert val[v + t] == (1 << (v + t)) | (1 << t), ('target', t)
+        for r in range(2 * v, n): assert val[r] == 1 << r, ('helper', r)
+    return dict(sig=sig, viol=viol, H=H, steps=steps, n=n, v=v, R=R, h=h, L=L, masks=masks, ncopy=len(c['ret']))
+
+
+def profile(H_local, v, h=8):
+    prof = Counter({j: 5 * c for j, c in H_local.items()})
+    for j in (2 * h - 2, h - 1, 2 * h + 2, 4): prof[j] += 2 * v
+    return prof
+
+
+def coarse(H, m, W):
+    grid = Q(1, 10**18)
+    root = moment.certify(dict(H), m, W, True); c = Q(int(Q(root['lower']) * 10**18), 10**18)
+    assert moment.moment(H, m, W, c, True)[1] < 1 < moment.moment(H, m, W, c + grid, True)[0]
+    fb = 32 * m * m * sum(H.values())
+    _, up = other.moment(m, W, list(H.items()), c); _, bad = other.moment(m, W, [(1, fb)], c)
+    lo, _ = other.moment(m, W, list(H.items()), c + grid); blo, _ = other.moment(m, W, [(1, fb)], c + grid)
+    assert up + Q(1, 10**16) * bad < 1 < lo + Q(1, 10**16) * blo
+    return c
+
+
+def kappa(c, b):
+    grid = Q(1, 10**18); eta = Q(1, 10**12); beta = Q(1, 10**9); cap = (1 - beta) * b
+    sv = min(c, Q(((cap - grid) * 10**18).__floor__(), 10**18)); binding = 'bit' if sv == c else 'complex'
+    chain = [Q(384599, 10**10)]
+    for _ in range(3):
+        a = (1 - sv) * sv + sv * chain[-1]; assert chain[-1] < a < sv < 1 - a; chain.append(a)
+    bit = chain[-1]
+    bridge = dict(proof='PROOF.md', representation='Exact powers with source-bound finite overcharges',
+                  semantic=dict(G=dict(base=2, exponent=30000), E=dict(base=2, exponent=100000), B_upper=dict(base=2, exponent=100001),
+                                C0=dict(base=2, exponent=210000), C1=1, strict_literal_gap=1, induction_gap_lower=1),
+                  rows=dict(coefficient=20161, degree=10**6, suffix_slope=4 * 10**6, degree_gap=Q(10**6) - Q(51 * 20161, 25)))
+    q = bit * (1 - 2 * eta); mn = (1 - eta) * q / (1 + q); t = mn * 10**18; k = Q((t.numerator - 1) // t.denominator, 10**18)
+    asm = outer.assembly(bit, b, bridge, k, eta=eta, beta=beta)
+    assert len(asm['strict_constraints']) == 47 and min(asm['strict_constraints'].values()) > 0
+    try:
+        outer.assembly(bit, b, bridge, k + grid, eta=eta, beta=beta); raise SystemExit('ADJACENT ADMITTED')
+    except AssertionError: pass
+    return k, binding
+
+
+def price_word(c, **kw):
+    r = replay(c, **kw)
+    v, h, R = r['v'], r['h'], r['R']; m = 5 * h
+    resid = sum(h - r['sig'][x] for x in range(2 * v, 2 * v + R))
+    T = 1 if resid % h == 0 else h
+    W = (4 * v * h + resid) * T // h; assert (4 * v * h + resid) * T % h == 0
+    prof = Counter({j: T * k for j, k in profile(r['H'], v, h).items()}); mass = sum(a * b for a, b in prof.items())
+    L_copy = h * r['ncopy']
+    assert m * W - mass == T * (4 * v - 5 * L_copy), ('deficit', m * W - mass)
+    assert 2 * max(prof) < m
+    cc = coarse(prof, m, W)
+    return dict(c=cc, H=r['H'], prof=prof, W=W, T=T, resid=resid, m=m, deficit=m * W - mass, replay=r)
+
+
+def phi_fn(m, W, a):
+    """linearized moment term per child of rank r (float), for search scoring"""
+    import math
+    return lambda r: r / (m * W) * math.exp(a * math.log(m / r))
diff --git a/research/e8-hosting-selected-kernel/vendor/pr439/engines/base_two_moment.py b/research/e8-hosting-selected-kernel/vendor/pr439/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/vendor/pr439/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/e8-hosting-selected-kernel/vendor/pr439/engines/moment.py b/research/e8-hosting-selected-kernel/vendor/pr439/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/vendor/pr439/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/e8-hosting-selected-kernel/vendor/pr439/engines/outer.py b/research/e8-hosting-selected-kernel/vendor/pr439/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/vendor/pr439/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/e8-hosting-selected-kernel/vendor/pr439/tile_m.py b/research/e8-hosting-selected-kernel/vendor/pr439/tile_m.py
new file mode 100644
index 0000000000..cd5fd9b539
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/vendor/pr439/tile_m.py
@@ -0,0 +1,93 @@
+"""Residual census (8 - sigma per helper) and an exact zero-padding bank tiling of width m = (2K+1)h with T replicas:
+tile() and economy_tile() verbatim from our PR #329 bank_template.py (via code/tile.py of our dtst3 package).
+usage: tile_m.py WORD.json.gz M [replicas]  (replicas default: the least T with T x residual sum = 0 mod M that tiles)"""
+import sys,os,collections
+from collections import Counter
+sys.path.insert(0,os.path.dirname(os.path.abspath(__file__)))
+from e8core import *
+def economy_tile(blocks, m):
+    """Exact zero-padding tiling used when the filler search of tile() runs out of filler blocks (the kernel pivots
+    and early restorations of the stage stack add many residual widths that do not divide m; the PR #299 analogue at
+    p = 12 was the (r^4, 24, 4^(24-r)) re-tiling). The fillers are the two most numerous widths dividing m (here the
+    full helper width h and the rank-4 entrance residual). Each other width w, in decreasing order, gets the bank
+    w^a F^c f^b (w*a + F*c + f*b = m) that spends the fewest narrow fillers f per w block (then the largest a), plus
+    at most one bank w^r F^c' f^b' for the remainder r = n mod a. The leftover fillers fill pure banks F^(m/F),
+    f^(m/f) and y residue banks F^j f^k. Every bank sums to m and every block is used exactly once (no padding)."""
+    from fractions import Fraction
+    blocks = {w: n for w, n in blocks.items() if n}
+    div = sorted((w for w in blocks if m % w == 0), key=lambda w: (-blocks[w], w))
+    assert len(div) >= 2, ('economy tiling needs two filler widths', blocks)
+    F, f = sorted(div[:2], reverse=True)
+
+    def fill(rest):
+        """(c, b) with F*c + f*b = rest, c maximal (fewest narrow fillers); None if impossible."""
+        return next(((c, (rest - F*c)//f) for c in range(rest//F, -1, -1) if (rest - F*c) % f == 0), None)
+
+    left = {F: blocks[F], f: blocks[f]}; out = []
+    for w in sorted((x for x in blocks if x not in (F, f)), reverse=True):
+        n = blocks[w]
+        opts = [(Fraction(cb[1], a), -a, a, cb) for a in range(m//w, 0, -1) for cb in [fill(m - w*a)] if cb]
+        assert opts, ('no bank for width', w)
+        _, _, a, (c, b) = min(opts); q, r = divmod(n, a)
+        if q: out.append(((w,)*a + (F,)*c + (f,)*b, q)); left[F] -= q*c; left[f] -= q*b
+        if r:
+            cb = fill(m - w*r); assert cb, ('no remainder bank', w, r)
+            out.append(((w,)*r + (F,)*cb[0] + (f,)*cb[1], 1)); left[F] -= cb[0]; left[f] -= cb[1]
+    assert left[F] >= 0 and left[f] >= 0, ('fillers exhausted', left)
+    pF, pf = m//F, m//f
+    for y in range((pF*pf) + 1):
+        for j in range(1 if y else 0, pF if y else 1):
+            if (m - F*j) % f: continue
+            k = (m - F*j)//f; aF, af = left[F] - y*j, left[f] - y*k
+            if aF >= 0 and af >= 0 and aF % pF == 0 and af % pf == 0:
+                out += ([((F,)*j + (f,)*k, y)] if y else []) + ([((F,)*pF, aF//pF)] if aF else []) + ([((f,)*pf, af//pf)] if af else [])
+                return out
+    raise AssertionError(('no exact zero-padding tiling', blocks, m))
+
+
+def tile(blocks, m):
+    """Exact tiling of {width: number of blocks} into banks of total width m, as ((widths, banks), ...).
+
+    A width dividing m fills pure banks. A width w not dividing m is mixed with a filler width f dividing m:
+    banks w^a f^b with a maximal (w*a + f*b = m), then at most one bank w^r f^t for the remainder r. Fillers
+    are tried in a fixed order (most blocks first) with backtracking until every pure width also divides out.
+    Fails (AssertionError) unless every block is used and every bank is full; there is no padding."""
+    blocks = {w: n for w, n in blocks.items() if n}
+    assert all(0 < w <= m for w in blocks)
+    mixed = sorted(x for x in blocks if m % x)
+
+    def search(i, left, out):
+        if i == len(mixed):
+            if any(left[w] % (m // w) for w in left): return None
+            return out + [(tuple([w]*(m // w)), left[w]//(m // w)) for w in sorted(left) if left[w]]
+        w = mixed[i]; n = blocks[w]
+        for f in sorted(left, key=lambda x: (-left[x], x)):
+            a = next((a for a in range(m // w, 0, -1) if (m - w*a) % f == 0), None)
+            if a is None: continue
+            b = (m - w*a)//f; q, r = divmod(n, a)
+            if r and (m - w*r) % f: continue
+            t = (m - w*r)//f if r else 0
+            if q*b + t > left[f]: continue
+            rest = dict(left); rest[f] -= q*b + t
+            found = search(i + 1, rest, out + ([(tuple([w]*a + [f]*b), q)] if q else []) + ([(tuple([w]*r + [f]*t), 1)] if r else []))
+            if found is not None: return found
+        return None
+    out = search(0, {w: n for w, n in blocks.items() if not m % w}, [])
+    if out is None: out = economy_tile(blocks, m)
+    assert all(sum(widths) == m and count > 0 for widths, count in out)
+    used = Counter()
+    for widths, count in out:
+        for x in widths: used[x] += count
+    assert used == Counter(blocks), 'every block used exactly once'
+    return tuple(out)
+if __name__ == '__main__':
+    c = load_word(sys.argv[1]); m = int(sys.argv[2])
+    L = Lat(c['lines']); M = to_masks(c, L); v = c['v']; n = 2 * v + c['R']
+    res = Counter(8 - L.dim(M[c['start'][r]]) for r in range(2 * v, n)); tot = sum(k * x for k, x in res.items())
+    reps = [int(sys.argv[3])] if len(sys.argv) > 3 else [t for t in range(1, 200) if t * tot % m == 0]
+    for T in reps:
+        try: pat = tile({r: T * k for r, k in res.items() if r > 0}, m); break
+        except AssertionError: pat = None
+    assert pat, 'no tiling'
+    print('   residual census', dict(sorted(res.items())), 'sum', tot)
+    print('   PASS exact width-%d tiling with %d replicas: %d banks' % (m, T, sum(k for _, k in pat)), pat)
diff --git a/research/e8-hosting-selected-kernel/verify.py b/research/e8-hosting-selected-kernel/verify.py
new file mode 100644
index 0000000000..93371dbc86
--- /dev/null
+++ b/research/e8-hosting-selected-kernel/verify.py
@@ -0,0 +1,50 @@
+"""Full rank-138 / idle-hosting composition; Python 3.11+, standard library.
+Rebuild the full R740/complex parent, reconstruct the hosting-selected kernel, emit and audit
+64 bit replicas, then host both suppliers. Complex replication remains eight.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+import gzip, hashlib, json, os, subprocess, sys, time
+assert __debug__
+ROOT=Path(__file__).resolve().parent
+PARENT=ROOT.parent/'e8-rank138-idle-hosting'
+ORIGINAL=ROOT.parent/'e8-joint-frame-retiming'
+OUT=Path(sys.argv[1]).resolve()
+assert not OUT.exists() and not OUT.is_relative_to(ROOT.parent)
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+read=lambda p:json.loads(p.read_text())
+def integrity():
+    m=read(ROOT/'MANIFEST.json')
+    actual={p.relative_to(ROOT).as_posix():sha(p) for p in ROOT.rglob('*') if p.is_file() and p!=ROOT/'MANIFEST.json' and '__pycache__' not in p.parts}
+    assert actual==m['files']
+    assert sha(PARENT/'MANIFEST.json')==m['parent_manifest_sha256']
+integrity();OUT.mkdir(parents=True)
+env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONINTMAXSTRDIGITS='0');env.pop('PYTHONOPTIMIZE',None)
+steps=[]
+def run(name,file,*args,cwd=None):
+    log=OUT/(name+'.log');start=time.monotonic();print('RUN',name,flush=True)
+    with log.open('w') as f:q=subprocess.run([sys.executable,'-B',str(file),*map(str,args)],cwd=cwd,env=env,stdout=f,stderr=subprocess.STDOUT)
+    assert q.returncode==0,(name,log.read_text()[-3000:])
+    steps.append(dict(name=name,seconds=round(time.monotonic()-start,2),log_sha256=sha(log)))
+    print('PASS',name,flush=True)
+try:
+    run('parent-full',PARENT/'verify.py',OUT/'parent')
+    changed=OUT/'changed';changed.mkdir()
+    for d in ('work','inherited','split-centres'):
+        (changed/d).symlink_to(OUT/'parent/changed'/d,target_is_directory=True)
+    b=changed/'bit426-source-centres'
+    run('kernel-rebuild',ROOT/'rebuild.py',b)
+    run('export-records',ORIGINAL/'vendor/export_records.py',b/'bit-source-centres.json',b/'records')
+    run('bit-global-64',ROOT/'code/bit_global.py','--source',b,'--local-check',b,'--out',b/'global',cwd=changed)
+    run('bit-global-audit',ROOT/'code/bit_audit.py','--local-check',b,'--out',b/'global',cwd=changed)
+    run('bit-hosting',ROOT/'code/bit_hosted.py',b/'global',b,OUT/'bit',cwd=changed)
+    run('complex-hosting',ROOT/'code/complex_hosted.py',changed/'split-centres',OUT/'complex',cwd=changed)
+    run('independent-hosting-audit',ROOT/'code/audit.py',changed,OUT/'bit',OUT/'complex',OUT/'AUDIT.json')
+    run('exact-assembly',ROOT/'code/assemble.py',changed,OUT/'bit',OUT/'complex',OUT/'AUDIT.json',OUT/'RESULT.json')
+    actual=read(OUT/'RESULT.json')
+    for k,v in read(ROOT/'EXPECTED.json').items():assert actual[k]==v,(k,actual[k],v)
+    integrity()
+    receipt=dict(status='PASS_FULL_HOSTING_SELECTED_KERNEL',python=sys.version.split()[0],kappa=actual['kappa'],kappa_decimal=actual['kappa_decimal'],manifest_sha256=sha(ROOT/'MANIFEST.json'),checks=steps)
+    (OUT/'RECEIPT.json').write_text(json.dumps(receipt,indent=2)+'\n');print(json.dumps(receipt,indent=2))
+except BaseException as e:
+    (OUT/'FAILURE.json').write_text(json.dumps(dict(error=repr(e),completed=steps),indent=2)+'\n');raise
diff --git a/research/e8-joint-frame-retiming/.gitattributes b/research/e8-joint-frame-retiming/.gitattributes
new file mode 100644
index 0000000000..a251e913f2
--- /dev/null
+++ b/research/e8-joint-frame-retiming/.gitattributes
@@ -0,0 +1,6 @@
+# Hashes bind exact imported and generated bytes.
+* -text
+vendor/** -whitespace
+inputs/** -whitespace
+notices/** -whitespace
+proofs/** -whitespace
diff --git a/research/e8-joint-frame-retiming/CERTIFICATE.json b/research/e8-joint-frame-retiming/CERTIFICATE.json
new file mode 100644
index 0000000000..eab9a16c81
--- /dev/null
+++ b/research/e8-joint-frame-retiming/CERTIFICATE.json
@@ -0,0 +1,107 @@
+{
+  "status": "PASS_CONDITIONAL_SPLIT_CENTRE_ASSEMBLY",
+  "kappa": "1138798055343319/1000000000000000000",
+  "kappa_decimal": "0.001138798055343319",
+  "bit_lower": "17814006170324008149/15625000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr425_percent": 8.663365470849168,
+  "bit_invoice": {
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "extra_helper_route_factor_bound": 144,
+    "selector_charge": 2375347104,
+    "full_counted_coefficient": "8271410009661736653226855278395470361",
+    "two_level_coefficient": "7323242093316479963924177312150069573045566553609912891292783054664675728289084971684",
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 282,
+    "charged_two_level_coefficient_bits": 512,
+    "row_coefficient": 18355,
+    "live": 14187,
+    "physical": 14196
+  },
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+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f",
+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim."
+}
diff --git a/research/e8-joint-frame-retiming/EXPECTED.json b/research/e8-joint-frame-retiming/EXPECTED.json
new file mode 100644
index 0000000000..f9021cbb84
--- /dev/null
+++ b/research/e8-joint-frame-retiming/EXPECTED.json
@@ -0,0 +1,9 @@
+{
+  "kappa": "1138798055343319/1000000000000000000",
+  "kappa_decimal": "0.001138798055343319",
+  "bit_lower": "17814006170324008149/15625000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "bit_template_sha256": "b87ed8c20819237f2daacdd1383a2776419551a62a7014eb9720af146a9dd9ec",
+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f"
+}
diff --git a/research/e8-joint-frame-retiming/INDEPENDENT-AUDIT.json b/research/e8-joint-frame-retiming/INDEPENDENT-AUDIT.json
new file mode 100644
index 0000000000..48f8f635b6
--- /dev/null
+++ b/research/e8-joint-frame-retiming/INDEPENDENT-AUDIT.json
@@ -0,0 +1,102 @@
+{
+  "local_audit": {
+    "retiming_changes": 183,
+    "status": "PASS_INDEPENDENT_R740_KERNEL_AND_RETIMING",
+    "source_sha256": "d6ec8811541d6ab59a3bbbaaa15bccc8918b3b43b23d9f593198cfe90826fd20",
+    "candidate_sha256": "00d8aa8608e40b53fd8752399de06cb730cc55caaadc528f88379cb31b8460a6",
+    "entries": 112,
+    "donor_slots": 100,
+    "total_entrance_rank": 136,
+    "root_closed_frames": 944,
+    "source_span_checks": 20652,
+    "forward": {
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+      "dirty_columns": 740,
+      "copies": 9,
+      "paid_profile": {
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+        "2": 1004,
+        "3": 284,
+        "4": 347,
+        "5": 118,
+        "7": 14,
+        "8": 9
+      }
+    },
+    "reflected": {
+      "all_columns": 980,
+      "dirty_columns": 740,
+      "copies": 9,
+      "paid_profile": {
+        "1": 2528,
+        "2": 1004,
+        "3": 284,
+        "4": 347,
+        "5": 118,
+        "7": 14,
+        "8": 9
+      }
+    },
+    "negative_controls": [
+      "omitted_first_basis",
+      "omitted_final_basis",
+      "missing_donor"
+    ],
+    "events": 19727,
+    "scope": "Independent reconstruction, every F2 scalar column and dirty restoration, exact source span/first-frame relations and both complementary dimension ledgers; global banking and pricing audited separately."
+  },
+  "status": "PASS_INDEPENDENT_GLOBAL_INVOICE_AND_EXACT_ASSEMBLY",
+  "candidate_sha256": "00d8aa8608e40b53fd8752399de06cb730cc55caaadc528f88379cb31b8460a6",
+  "global_template_sha256": "b87ed8c20819237f2daacdd1383a2776419551a62a7014eb9720af146a9dd9ec",
+  "expanded_program_sha256": "ecb666b6a74fbf1e3482f37e84101588b15dd1deaeefe3c509644c251ac75332",
+  "events": 1420344,
+  "global_scalar_columns": 7620,
+  "global_dirty_columns": 6660,
+  "all_global_scalar_columns_restored": true,
+  "bank_assignments": 53280,
+  "bank_families": 6507,
+  "residual_isometries": 15,
+  "route_corruption_controls": [
+    "altered_basis",
+    "missing_factor",
+    "wrong_frame"
+  ],
+  "extra_route_factors": 144,
+  "banks_per_stage": 723,
+  "live": 14187,
+  "physical": 14196,
+  "paid_profile": {
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+    "14": 3840,
+    "28": 3840,
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+  },
+  "deficit": 2496,
+  "source_bound_invoice": {
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 282,
+    "charged_two_level_coefficient_bits": 512,
+    "row_coefficient": 18355,
+    "live": 14187,
+    "physical": 14196,
+    "extra_helper_route_factor_bound": 144,
+    "selector_charge": 2375347104,
+    "full_counted_coefficient": "8271410009661736653226855278395470361",
+    "two_level_coefficient": "7323242093316479963924177312150069573045566553609912891292783054664675728289084971684"
+  },
+  "independent_moment": "third rational enclosure; lower passes, adjacent upper fails",
+  "bit_lower": "17814006170324008149/15625000000000000000000",
+  "kappa": "1138798055343319/1000000000000000000",
+  "kappa_decimal": "0.001138798055343319",
+  "strict_outer_constraints": 47,
+  "bridge_omission_controls": 18,
+  "bootstrap_levels": 6
+}
diff --git a/research/e8-joint-frame-retiming/LICENSE b/research/e8-joint-frame-retiming/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-joint-frame-retiming/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
+      other entities that control, are controlled by, or are under common
+      control with that entity. For the purposes of this definition,
+      "control" means (i) the power, direct or indirect, to cause the
+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
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diff --git a/research/e8-joint-frame-retiming/MANIFEST.json b/research/e8-joint-frame-retiming/MANIFEST.json
new file mode 100644
index 0000000000..2536f16019
--- /dev/null
+++ b/research/e8-joint-frame-retiming/MANIFEST.json
@@ -0,0 +1,109 @@
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+    "vendor/pr436/code/bit/producer/ham2.py": "fdf0af785ce697bd7f80b4e75f7163735f3b599d9dc42f652f0ffdbdf18ea8bf",
+    "vendor/pr436/code/bit/producer/params-r865.json": "1256c54debe0a551da8e24896ab73ef0bd4a5233ff8e6fedf21a9e6301d6e6f3",
+    "vendor/pr436/code/bit/producer/price.py": "46c858e60ba0a117bf8227b864abf55e85ebee2d56a0dce64472b706499ac405",
+    "vendor/kernel417/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "vendor/kernel417/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "vendor/kernel417/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "local-evidence/upstream440/CERTIFICATE.json": "5d16af5ef43afbbe71046f7e2cf93bf4587b6dd56936bc2222e83b0887cd8aca",
+    "local-evidence/upstream440/INDEPENDENT-AUDIT.json": "8903f0b1100e7e9728e31b4a7fbe6996c696ad753dc92b730a05c15ab83d661e",
+    "local-evidence/upstream440/VALIDATION.json": "a95c25eb50dee90b21204442c31db3e22d3db8d9bc20c87bc92146507444bc7c"
+  }
+}
diff --git a/research/e8-joint-frame-retiming/NOTICE.md b/research/e8-joint-frame-retiming/NOTICE.md
new file mode 100644
index 0000000000..d2dee718d0
--- /dev/null
+++ b/research/e8-joint-frame-retiming/NOTICE.md
@@ -0,0 +1,21 @@
+New joint B-phase retiming search and composition: Rohan Arun with substantial OpenAI Codex assistance. Upstream #440 by eumemic with OpenAI Codex is retained and credited in full below. Apache-2.0.
+
+# Attribution and AI disclosure
+
+This R740 shared-donor kernel and primitive-retiming composition was prepared by eumemic with OpenAI Codex assistance. The new finite selections, deterministic reconstruction, residual-isometry generator, portable phase binding, integration and audit changes are licensed under Apache-2.0. The selected construction is not represented as an optimal solution or a new unconditional multiplication theorem.
+
+Direct sources and contributions:
+
+- **eumemic, PR #436**, with Anthropic Claude assistance: frozen R740 word, producer parameters, elimination-reuse reconstruction, retiming and provenance. The complete selected base is regenerated unchanged before the new kernel.
+- **Chafik Boukhalfa (chafreaky), PR #417**, with Anthropic Claude assistance: shared-donor response-kernel mechanism and E8 replay/stage code. Original source notices remain in vendored files.
+- **rohanarun, PR #438**, with Anthropic Claude assistance: composition of kernel entrances with compressed nine-stage mixed residual banks, bank admission and integration based on PR #433. Its original README, proof and notice are preserved under `proofs/` and `notices/`.
+- **rohanarun / OpenAI Codex, PR #434**: concurrent ordered primitive-gate expansion and retiming idea. The 57 A-only frame changes here were selected independently on this package's R740 kernel word, rather than copied from #434's word.
+- **chafreaky, PR #439**, with OpenAI Codex assistance: explicit residual-isometry witness format, validation, corruption controls and conservative 144-factor helper-route charge. `vendor/pr439/` preserves exact source files, license and notice. This package generates the witnesses anew from its own entrance frames.
+- **icekylinx, PR #433**, with OpenAI Codex assistance: unchanged split-centre complex supplier, finite invoices, six-level assembly and verifier lineage. The complex scalar word, both orientations, exact phases, banks, profiles and invoices are replayed in this package.
+- **Zhihao Chen / jacklightChen, PR #425 and #386**, with OpenAI Codex assistance: mutable-basis Hamming complex producer and scalar-interface extension, exact phase lowering, compressed nine-stage bit geometry and global audit.
+- **Dylan Crow / utcorvusvolat-dotcom, PR #370**, with Anthropic Claude assistance: E8 root family, bit producer, record format and exporter.
+- **ai-nanachi, PR #426**; **applecrusher, PR #376**; **Jacob Sussman**, and the PR #266/#315/#329 compiler, pricing and analytic lineage: original construction, reuse and interface contributions retained in the source notices.
+
+`SOURCES.json` records exact imported commits and hashes, adapted source hashes, and the frozen canonical complex reference. Python gzip metadata can vary; the phase adapter compares the decoded canonical bytes to a reference whose compressed hash is exactly the original PR #433 receipt hash. This is a portability change, not a change to the complex program or phase evidence.
+
+The original historical documents under `proofs/`, `notices/`, and `vendor/` state the scope of their own packages. The current result and remaining inherited assumptions are in the top-level README and PROOF.
diff --git a/research/e8-joint-frame-retiming/PROOF.md b/research/e8-joint-frame-retiming/PROOF.md
new file mode 100644
index 0000000000..f2f2d32fe4
--- /dev/null
+++ b/research/e8-joint-frame-retiming/PROOF.md
@@ -0,0 +1,11 @@
+# Joint frame movements
+
+The source is #440 at bd03373b6d4d4e380d0b6ea7d55cd2ac8f163544. Its exact R740 word, kernel mechanism and upstream mathematical assumptions are inherited, with full source notices and provenance preserved.
+
+A single frame change may be blocked by the next or previous gate on a register. Move connected gates at the same frame jointly: intersect the following frames and include all preceding frames to form the feasible interval. The search inspected 88,676 connected pairs, triples and components; 42 groups scored positively and 28 compatible groups in each of two sweeps were selected. They affect 126 B-phase gates. Score calculations only nominate candidates. The frozen combined selection records each of the 57 inherited A-phase and 126 new B-phase changes directly against the primitive kernel word.
+
+Construction verifies each old frame and unique gate index and preserves every primitive source/target operand. Independent reconstruction separately derives the kernel and the entire frame sequence. Exact scalar replay and integer source-span checks cover all 980 columns. Rational projectors certify all changed transitions and their reflected counterparts. Both emitted global words, every helper owner, residual coordinate isometry and complete bank are audited. Costs, coefficients, two rational moments, six finite bootstrap levels and all 47 outer inequalities are recomputed from the final emitted word; an independent audit supplies a third rational enclosure and repeats the invoice and assembly.
+
+No isolated improvements are added. The inherited all-size compiler, correlated dirty-bank, compressed-window, restored-work, tape/common-grid, precision and analytic interfaces remain conditional assumptions. The source-bound finite certificate is not an unconditional multiplication theorem or a Lean proof.
+
+The final canonical word matches PR441 exactly. The earlier one-sweep version passed full Python 3.11 and 3.14 replay at 38b6ea6a023e4cfc47db0177706dcf0b490fd389; the new two-sweep version is replayed as the parent of the idle-hosting composition.
diff --git a/research/e8-joint-frame-retiming/README.md b/research/e8-joint-frame-retiming/README.md
new file mode 100644
index 0000000000..feb15d7324
--- /dev/null
+++ b/research/e8-joint-frame-retiming/README.md
@@ -0,0 +1,9 @@
+# Joint B-phase frame retiming on the R740 shared-donor word
+
+Conditional kappa = 0.001138798055343319. This composes #440's kernel and 57 A-phase moves with two sweeps of 28 jointly moved groups affecting 126 B-phase gates. All primitive ADD operands and their order remain unchanged. The kernel has 112 pivots, entrance rank 136 and 100 donor slots. There are 723 complete banks per stage, 14,187 live and 14,196 physical families.
+
+Run `python -B research/e8-joint-frame-retiming/verify.py /absolute/new/output --replay-phases`. Python standard library only. The complete verifier rebuilds the pinned R740 producer and kernel, reconstructs all 183 frame changes, replays every upstream complex phase, emits and independently audits both global orientations and residual routes, and recomputes the finite invoice and exact outer assembly.
+
+The changed scalar/source-span, global banks, residual route mutation tests, two moment engines and finite assembly passed before publication. Full uninterrupted Python 3.11/3.14 runs are pending. Inherited #440 validation files are historical under local-evidence/upstream440. No unconditional multiplication theorem or new Lean proof is claimed; all inherited all-size interfaces remain assumptions.
+
+The final canonical word matches PR441 exactly. The earlier one-sweep version passed full Python 3.11 and 3.14 replay at 38b6ea6a023e4cfc47db0177706dcf0b490fd389; the new two-sweep version is replayed as the parent of the idle-hosting composition.
diff --git a/research/e8-joint-frame-retiming/SOURCE440-PINS.json b/research/e8-joint-frame-retiming/SOURCE440-PINS.json
new file mode 100644
index 0000000000..b5ead3ef79
--- /dev/null
+++ b/research/e8-joint-frame-retiming/SOURCE440-PINS.json
@@ -0,0 +1,475 @@
+{
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diff --git a/research/e8-joint-frame-retiming/SOURCES.json b/research/e8-joint-frame-retiming/SOURCES.json
new file mode 100644
index 0000000000..33c7465fde
--- /dev/null
+++ b/research/e8-joint-frame-retiming/SOURCES.json
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+    "CrocSwap/integer-mult-bounds@e3b56de7869f6af88d48ac0ab1d7959c4c9e6176:research/split-centres-kernel-r747/code/bit_audit.py": "b2b4b792f14ac9946bdcd1bf4c0d47c46fe05ff6ff9c5f0317037c9a1ee1e5fe",
+    "CrocSwap/integer-mult-bounds@e3b56de7869f6af88d48ac0ab1d7959c4c9e6176:research/split-centres-kernel-r747/code/combined.py": "825c32a81529da35a347666468585c69d66c0ee161717f2994769782fb57e29e"
+  },
+  "pr436": "da8ca2025472553ac9b36f4400138ed48a6a0e3b",
+  "new_work": "Rohan Arun with OpenAI Codex: two joint B-phase sweeps, 28 groups in each, yield 126 net changed B frames plus the inherited 57 A moves. This independently reaches the same word later published in PR441 at 6160c13526f5f957902910b462164c93c1d8f39a. Scalar operands/order are unchanged.",
+  "pr438": "e3b56de7869f6af88d48ac0ab1d7959c4c9e6176",
+  "canonical_reference": {
+    "path": "inputs/complex-canonical-reference.json.gz",
+    "sha256": "79ff8e19335d5d5d1563ef0bc218106945d6a2b88ece53ee24bb3d88b2594ba3",
+    "canonical_payload_sha256": "be2d8d412b948bce50a0fc852ab4c01f57bff4c3c8272da80c09be5bcdf253bf",
+    "provenance": "Frozen PR433 canonical complex word regenerated in the independently verified Python 3.14 full-phase replay; its original gzip SHA256 is pinned by inputs/complex-phase-receipt.json. This package compares decoded bytes to handle Python gzip metadata variation."
+  },
+  "pr439": "fa3a588ec1e383083abb8de9c51904fb9d689ad4",
+  "pr434_retiming_idea": "6a1c6a308429ea11f64b679df6abdf2bf40436b0",
+  "pr434_receipt_only_current_head": "1146ce018558e3cc4d913717f26675f4d11b861b",
+  "selected_witnesses": {
+    "kernel_base_sha256": "d6ec8811541d6ab59a3bbbaaa15bccc8918b3b43b23d9f593198cfe90826fd20",
+    "kernel_output_sha256": "b5789bffbf7bafe77a222366ea9a125b1d4a6f9d84b96afc4bb3c509d6b89b1a",
+    "primitive_input_sha256": "cb2afa377baeb8578e867ecda0f81caa68b2dac9cca805f41247754cfe91deb5",
+    "retimed_output_sha256": "00d8aa8608e40b53fd8752399de06cb730cc55caaadc528f88379cb31b8460a6",
+    "kernel_entries": 112,
+    "retiming_moves": 183,
+    "discovery_claim": "Selected finite witnesses are regenerated and exactly checked; optimization search is not claimed to be reproduced or globally optimal.",
+    "new_group_moves": 56,
+    "new_B_gates": 126
+  },
+  "pr440": {
+    "head": "bd03373b6d4d4e380d0b6ea7d55cd2ac8f163544",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/440",
+    "role": "Complete source package, preserved inherited construction and audit engine. Exact imported Git blobs listed in SOURCE440-PINS.json; local adaptations explicitly described here."
+  },
+  "upstream440_selected_witnesses": {
+    "kernel_base_sha256": "d6ec8811541d6ab59a3bbbaaa15bccc8918b3b43b23d9f593198cfe90826fd20",
+    "kernel_output_sha256": "b5789bffbf7bafe77a222366ea9a125b1d4a6f9d84b96afc4bb3c509d6b89b1a",
+    "primitive_input_sha256": "cb2afa377baeb8578e867ecda0f81caa68b2dac9cca805f41247754cfe91deb5",
+    "retimed_output_sha256": "bae58f0692326f180ba49642360fd55557f59a93a96a8fa62bf7babd55d2384e",
+    "kernel_entries": 112,
+    "retiming_moves": 57,
+    "discovery_claim": "Selected finite witnesses are regenerated and exactly checked; optimization search is not claimed to be reproduced or globally optimal."
+  },
+  "pr441_matching_word": {
+    "head": "6160c13526f5f957902910b462164c93c1d8f39a",
+    "word_sha256": "00d8aa8608e40b53fd8752399de06cb730cc55caaadc528f88379cb31b8460a6",
+    "role": "Independently published same final word; credited without importing its source package."
+  }
+}
diff --git a/research/e8-joint-frame-retiming/VALIDATION.json b/research/e8-joint-frame-retiming/VALIDATION.json
new file mode 100644
index 0000000000..70bc5df84c
--- /dev/null
+++ b/research/e8-joint-frame-retiming/VALIDATION.json
@@ -0,0 +1,6 @@
+{
+  "status": "CHANGED_PROGRAM_PASSED_FULL_WRAPPERS_PENDING",
+  "kappa": "0.001138798055343319",
+  "word_sha256": "00d8aa8608e40b53fd8752399de06cb730cc55caaadc528f88379cb31b8460a6",
+  "scope": "Two-sweep word matches PR441; changed program passed. Earlier one-sweep full311/full314 receipts remain historical. New full replay occurs through the hosting wrapper."
+}
diff --git a/research/e8-joint-frame-retiming/code/bit_audit.py b/research/e8-joint-frame-retiming/code/bit_audit.py
new file mode 100644
index 0000000000..33058e814a
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/bit_audit.py
@@ -0,0 +1,134 @@
+# Adapted with exact rational span checks by icekylinx; Codex assistance.
+"""Independent audit of the emitted bit template, including mutation controls.
+Prepared by Zhihao Chen with OpenAI Codex assistance; Apache-2.0.
+"""
+import argparse, copy, gzip, hashlib, json, struct, time
+from collections import Counter, defaultdict
+from pathlib import Path
+from fractions import Fraction as Q
+from residual_routes import validate_isometries
+
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out
+    blob=gzip.decompress((out/'GLOBAL-TEMPLATE.json.gz').read_bytes()); t=json.loads(blob)
+    g=json.loads((out/'GLOBAL.json').read_text()); geo=json.loads((out/'GEOMETRY.json').read_text())
+    assert hashlib.sha256(blob).hexdigest()==g['template_sha256']
+    assert t['geometry_sha256']==sha(out/'GEOMETRY.json') and t['source_record_sha256']==sha(a.local_check/'records/249-records.bin')
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    records=list(struct.iter_unpack('<6i',(a.local_check/'records/249-records.bin').read_bytes()))
+    word=json.loads((a.local_check/'bit-source-centres.json').read_text())
+    assert g['word_sha256']==sha(a.local_check/'bit-source-centres.json')
+    def rank(rows):
+        piv={}
+        for rr in rows:
+            row=list(map(Q,rr))
+            for k,b in sorted(piv.items()):
+                q=row[k]
+                if q:row=[x-q*y for x,y in zip(row,b)]
+            k=next((j for j,x in enumerate(row) if x),None)
+            if k is not None:
+                q=row[k];piv[k]=[x/q for x in row]
+        return len(piv)
+    dimensions={};proj={}
+    for key,f in fs.items():
+        k=int(key);B=f['B'];roots=[word['lines'][j] for j in word['frames'][k]]
+        assert rank(B)==f['dim']==rank(B+roots)==rank(roots)
+        dimensions[k]=f['dim'];proj[k]=B
+    sets=[set(f) for f in word['frames']];pairs={}
+    for op,x,y,c,r,z in records:
+        if op==0:
+            assert sets[y]<=sets[c] and dimensions[c]-dimensions[y]==r
+            pairs[y,c]=r
+    # Positive definite rational form: exact inclusion implies commuting
+    # orthogonal projectors and rank(P_V-P_U)=dim(V)-dim(U), also in reflection.
+    assert len(proj)==len(word['frames'])
+    expected={}
+    for rev in (False,True):
+        es=[]
+        for op,x,y,c,f,z in (reversed(records) if rev else records):
+            if op==0: es.append([0,x,c if rev else y,y if rev else c,f,int(rev)])
+            elif op==1: es.append([1,x,y,-c if rev else c,f,int(rev)])
+            elif op==(3 if rev else 2): es.append([2,x,y,c,f,abs(dimensions[c]-dimensions[f]),int(rev)])
+            else: es.append([3,x,y,c,f,z,int(rev)])
+        expected['reverse' if rev else 'forward']=es
+    assert t['local_programs']==expected
+
+    st=json.loads((a.local_check/'records/249-states.json').read_text())
+    RR=st['n']-240; width=[8-dimensions[st['initial'][str(i)]] for i in range(240,240+RR)]; ENT=sum(8-x for x in width); assert ENT%8==0
+    NB=(8*RR-ENT)//8; LIVE=7680+9*NB; assert g['live']==LIVE
+    def validate(q,check_profile=True):
+        assert validate_isometries(q['residual_isometries'],word['frames'],word['lines'],dimensions)==set(word['start'][240:])
+        assert (q['m'],q['live'],q['replicas'],q['stages'])==(64,LIVE,8,9)
+        assert q['bank_padding'] is None and q['local_programs']==expected
+        hist=Counter(); occupation=defaultdict(set); calls=set()
+        for c in q['calls']:
+            st,rep,p=c['stage'],c['replica'],c['pair']; rev=c['orientation']=='reverse'
+            assert 0<=st<9 and 0<=rep<8 and p==max(0,(st-1)//2)
+            assert rev==(st in (1,3,5,7)) and (st,rep) not in calls; calls.add((st,rep))
+            own=c['owners']; assert len(own)==240+RR
+            assert len({(f,tuple(r)) for f,r in own})==240+RR
+            for i,(family,route) in enumerate(own):
+                assert 0<=family<LIVE
+                if i<240:
+                    side=i//120; side=1-side if rev else side
+                    assert family==rep*960+(2*p+side)*120+i%120 and route==['data',st,i%120]
+                else:
+                    j=i-240; assert len(route)==4 and route[0]=='bank' and route[2]==width[j] and route[3]==word['start'][i] and 7680+st*NB<=family<7680+(st+1)*NB
+                    cells=set(range(route[1],route[1]+route[2])); assert cells<=set(range(64)) and not (cells & occupation[family])
+                    occupation[family]|=cells
+            for e in q['local_programs'][c['orientation']]:
+                if e[0]==0 and e[4]: hist[e[4]]+=1
+                if e[0]==2: hist[e[5]]+=1
+        assert calls=={(s,r) for s in range(9) for r in range(8)}
+        assert set(occupation)==set(range(7680,LIVE)) and all(s==set(range(64)) for s in occupation.values())
+        levels=[-1]*4; scalar=[1<<i for i in range(8)]; seen=[]; br=0; exchanged=False
+        for e in q['schedule']:
+            if e['kind']=='local_cover_sweep':
+                s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1 and not exchanged
+                src,dst=(2*p+1,2*p) if rev else (2*p,2*p+1)
+                scalar[dst]^=scalar[src]; levels[p]=s; seen.append(s)
+            elif e['kind']=='idle':
+                p,src,dst,r=e['pair'],e['source_level'],e['target_level'],e['rank']
+                assert levels[p]==src and src<=dst<=8
+                assert r==7*(dst-src); levels[p]=dst
+                if r: hist[r]+=1920
+            elif e['kind']=='bridge':
+                d,s=e['dst'],e['src']; assert levels[d]==levels[s] and e['coefficient'] in (-1,1)
+                scalar[2*d]^=scalar[2*s]; scalar[2*s+1]^=scalar[2*d+1]; br+=1
+            else:
+                assert e['kind']=='exchange' and levels==[8]*4 and not exchanged
+                for p in range(4): scalar[2*p],scalar[2*p+1]=scalar[2*p+1],scalar[2*p]
+                exchanged=True
+        assert exchanged and scalar==[1<<i for i in range(8)] and seen==list(range(9)) and br==9
+        assert 64*LIVE-sum(r*n for r,n in hist.items())==2496
+        if check_profile: assert hist==Counter({int(k):v for k,v in g['profile'].items()})
+        return hist
+    hist=validate(t)
+    controls=[]
+    def rejects(name,mutator):
+        q=copy.deepcopy(t); mutator(q)
+        try: validate(q)
+        except (AssertionError,KeyError,IndexError): controls.append(name)
+        else: raise AssertionError('mutation accepted: '+name)
+    rejects('omit an idle child',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='idle')))
+    rejects('omit a bridge',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='bridge')))
+    rejects('omit terminal exchange',lambda q:q['schedule'].pop())
+    rejects('remove a local invocation',lambda q:q['calls'].pop())
+    rejects('re-use a helper bank slot',lambda q:q['calls'][0]['owners'].__setitem__(241,q['calls'][0]['owners'][240]))
+    rejects('understate live stock',lambda q:q.__setitem__('live',LIVE-1))
+    rejects('omit a local paid move',lambda q:q['local_programs']['forward'].pop(next(i for i,e in enumerate(q['local_programs']['forward']) if e[0]==0)))
+    rejects('wrong reflected copy charge',lambda q:q['local_programs']['reverse'][next(i for i,e in enumerate(q['local_programs']['reverse']) if e[0]==2)].__setitem__(5,0))
+    rejects('alter residual orthogonal basis',lambda q:q['residual_isometries'][0]['orthogonal_rows_numerator'][0].__setitem__(0,99))
+    rejects('wrong residual frame',lambda q:q['calls'][0]['owners'][240][1].__setitem__(3,-1))
+    rejects('omit a residual route factor',lambda q:next(r for r in q['residual_isometries'] if r['gaussian_reduction'])['gaussian_reduction'].pop())
+    result=dict(status='PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT',template_sha256=g['template_sha256'],
+                source_frames=len(proj),exact_nested_frame_pairs=len(pairs),exact_reflected_pairs=len(pairs),
+                orthogonal_lift_argument='Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.',
+                exact_bank_families=LIVE-7680,mixed_width_slots=True,entrance_rank_total=ENT,residual_isometries=len(t['residual_isometries']),mutations_rejected=controls,
+                profile=dict(sorted(hist.items())),seconds=time.monotonic()-start)
+    (out/'AUDIT.json').write_text(json.dumps(result,indent=2)+'\n'); print(json.dumps(result),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-joint-frame-retiming/code/bit_construct.py b/research/e8-joint-frame-retiming/code/bit_construct.py
new file mode 100644
index 0000000000..ffabc19e3b
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/bit_construct.py
@@ -0,0 +1,26 @@
+"""Rebuild pinned PR436's R740 word from its producer parameters, reuse, and retiming.
+PR436: eumemic with Anthropic Claude assistance; this integration: OpenAI Codex.
+"""
+import gzip, hashlib, json, os, subprocess, sys
+from pathlib import Path
+P=Path(__file__).resolve().parent.parent
+D=Path(os.environ['E8_OUTPUT'])/'bit426-source-centres'; D.mkdir(exist_ok=True)
+B=P/'vendor/pr436'
+subprocess.run([sys.executable,'-B',str(B/'code/reuse/regen.py'),str(B/'data/params/params-r740.json'),
+ str(D/'pr436-raw.json.gz'),str(D/'pr436-reused.json.gz'),str(D/'pr436-final.json.gz'),str(D/'pr436-ledger.json')],check=True)
+w=json.loads(gzip.decompress((D/'pr436-final.json.gz').read_bytes()))
+pinned=json.loads(gzip.decompress((B/'data/bit/bitE8-r740.json.gz').read_bytes()))
+assert w==pinned
+assert json.loads((D/'pr436-ledger.json').read_text())==json.loads((B/'data/bit/reuse-ledger.json').read_text())
+raw=json.dumps(w,sort_keys=True,separators=(',',':')).encode()
+assert hashlib.sha256(raw).hexdigest()=='d6ec8811541d6ab59a3bbbaaa15bccc8918b3b43b23d9f593198cfe90826fd20'
+assert w['R']==740 and len(w['ret'])==9
+(D/'bit-source-centres.json').write_bytes(raw)
+sys.path.insert(0,str(P/'vendor/kernel417'))
+from e8core import replay
+r=replay(w,span_mode='z');assert not r['viol'],r['viol'][:5]
+res=dict(status='PASS_PINNED_PR436_RECONSTRUCTION',R=w['R'],content_sha256=hashlib.sha256(raw).hexdigest(),
+ all_columns=r['n'],local_histogram=dict(sorted(r['H'].items())),
+ construction='Pinned #370 producer with #436 parameters, elimination reuse and six retiming sweeps; exact frozen #436 word and ledger equality')
+(D/'bit-source-centres-receipt.json').write_text(json.dumps(res,indent=2)+'\n')
+print(json.dumps(res))
diff --git a/research/e8-joint-frame-retiming/code/bit_global.py b/research/e8-joint-frame-retiming/code/bit_global.py
new file mode 100644
index 0000000000..95c1b2dd7d
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/bit_global.py
@@ -0,0 +1,275 @@
+# Adapted for the PR426/source-centre composition by icekylinx with Codex assistance.
+"""Source-bound compressed nine-stage bit template and exact scalar audits.
+
+Prepared by Zhihao Chen with OpenAI Codex assistance, Apache-2.0.
+The local E8 bit word is Dylan Crow's pinned PR #370 contribution.
+"""
+import argparse, gzip, hashlib, json, struct, time
+from collections import Counter
+from pathlib import Path
+from residual_routes import generate
+
+import sys as _sys
+H,V,L,K,T,M=8,120,9,4,8,64
+R=json.loads((Path(_sys.argv[_sys.argv.index('--source')+1])/'bit-source-centres.json').read_bytes())['R']
+LOCAL=2*V+R; DATA=2*K*V*T
+
+def tile_banks(width):
+    """exact width-64 bank tiling of the per-stage helper slots (8 replicas x R helpers, slot width = 8 - entrance rank);
+    returns {(replica, helper): (bank, offset)} and the bank count; every bank is filled exactly (no padding)."""
+    slots=sorted(((width[h],rep,h) for rep in range(T) for h in range(R)),key=lambda x:(-x[0],x[1],x[2]))
+    bins=[]; place={}
+    by={}
+    for w_,rep,h in slots: by.setdefault(w_,[]).append((rep,h))
+    def take(w_):
+        return by[w_].pop(0) if by.get(w_) else None
+    # Exact mixed widths: eight width-7 slots plus one width-8; divisor-width remainders filled with width-8 slots.
+    for w_ in sorted(by,reverse=True):
+        if w_==8: continue
+        while by.get(w_):
+            b=len(bins); off=0; cont=[]
+            if w_==7:
+                for _ in range(8): rep,h=take(7); cont.append((rep,h,off,7)); off+=7
+                rep,h=take(8); cont.append((rep,h,off,8)); off+=8
+            else:
+                assert 64%w_==0
+                for _ in range(min(64//w_,len(by[w_]))): rep,h=take(w_); cont.append((rep,h,off,w_)); off+=w_
+                assert (64-off)%8==0
+                while off<64: rep,h=take(8); cont.append((rep,h,off,8)); off+=8
+            assert off==64; bins.append(cont)
+    while by.get(8):
+        cont=[]; off=0
+        for _ in range(8): rep,h=take(8); cont.append((rep,h,off,8)); off+=8
+        bins.append(cont)
+    for b,cont in enumerate(bins):
+        for rep,h,off,w_ in cont: place[rep,h]=(b,off,w_)
+    assert len(place)==T*R
+    return place,len(bins)
+
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+def write(p,x): p.write_text(json.dumps(x,indent=2)+'\n')
+
+def recipe():
+    out=[dict(kind='local',stage=0,pair=0,reverse=False)]; stage=1
+    for j in range(K):
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=True)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=1))
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=False)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=-1))
+    for j in reversed(range(K-1)): out.append(dict(kind='bridge',dst=j+1,src=j,coefficient=1))
+    out.append(dict(kind='exchange'))
+    return out
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--source',type=Path,required=True)
+    ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out; out.mkdir(parents=True,exist_ok=True)
+    wp=a.source/'bit-source-centres.json'; w=json.loads(wp.read_bytes())
+    inherited=Path('inherited/bit-geometry.json.gz')
+    geo=json.loads(gzip.decompress(inherited.read_bytes()))
+    base=Path('work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz')
+    original=json.loads(gzip.decompress(base.read_bytes()))
+    assert geo['word_sha256']==sha(base)
+    assert w['lines']==original['lines'] and w['form']==original['form']
+    # PR436 regenerates the same root-closed frame family in a different order.
+    # Bind every actual frame by its exact root set; all record IDs remain actual IDs.
+    original_ids={tuple(sorted(fr)):i for i,fr in enumerate(original['frames'])}
+    actual_keys=[tuple(sorted(fr)) for fr in w['frames']]
+    assert len(original_ids)==len(original['frames'])==len(actual_keys)==len(set(actual_keys))
+    assert set(actual_keys)==set(original_ids)
+    frame_map=[original_ids[k] for k in actual_keys]
+    assert sorted(frame_map)==list(range(len(original['frames'])))
+    geo['actual_frame_to_pinned_frame']=frame_map
+    geo['frame_binding']='Exact bijection of root sets; frame IDs in emitted records are those of the reconstructed PR436 word.'
+    kr=json.loads((a.source/'bit-kernel-receipt.json').read_text()); assert kr['output_sha256'] and len(w['frames'])==len(original['frames'])+kr['new_frames']
+    geo['inherited_geometry_sha256']=sha(inherited);geo['word_sha256']=sha(wp)
+    geo['reuse_scope']='Unchanged ports and compressed windows; nonzero helper entrances use mixed-width residual slots, with every owner and coordinate checked independently.'
+    write(out/'GEOMETRY.json',geo)
+    rp=a.local_check/'records/249-records.bin';raw=rp.read_bytes();rec=list(struct.iter_unpack('<6i',raw))
+    state=json.loads((a.local_check/'records/249-states.json').read_text())
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    dims={int(f):z['dim'] for f,z in fs.items()}
+    assert (state['v'],state['n'])==(V,LOCAL)
+    expected_adds=sum(e[0]==1 for e in rec)
+    initial=[state['initial'][str(i)] for i in range(LOCAL)]
+    final=[state['final'][str(i)] for i in range(LOCAL)]
+    assert all(dims[final[i]]==H for i in range(2*V,LOCAL))
+    width={i-2*V:H-dims[initial[i]] for i in range(2*V,LOCAL)}; ENT=sum(H-x for x in width.values()); assert ENT%8==0
+    place,NB=tile_banks(width); assert NB==(8*R-ENT)//8
+    isometries=generate(w,dims)
+    LIVE=DATA+L*NB
+    streams={}; checks={}; localH=None
+    for reverse in (False,True):
+        cur=(final if reverse else initial)[:]+[-1]; val=[1<<i for i in range(LOCAL)]+[0]
+        norm=[1]*LOCAL+[0]; maxnorm=1; center=None; hist=Counter(); events=[]; copies=0; adds=0
+        dim=lambda f:H-dims[f] if reverse else dims[f]
+        for op,x,y,c,f,z in (reversed(rec) if reverse else rec):
+            if op==0:
+                oldf,newf=(c,y) if reverse else (y,c)
+                assert cur[x]==oldf and dim(newf)-dim(oldf)==f>=0
+                cur[x]=newf
+                if f: hist[f]+=1
+                events.append([0,x,oldf,newf,f,int(reverse)])
+            elif op==1:
+                assert cur[x]==cur[y]==f and x!=y and x<LOCAL
+                if center is not None: assert x!=center
+                if y==LOCAL: assert center is not None
+                if c&1: val[x]^=val[y]
+                norm[x]+=abs(c)*norm[y]; maxnorm=max(maxnorm,norm[x]); adds+=1
+                events.append([1,x,y,-c if reverse else c,f,int(reverse)])
+            elif op==(3 if reverse else 2):
+                assert center is None and y==LOCAL and cur[x]==c and val[LOCAL]==0
+                copy_rank=abs(dim(c)-dim(f)); assert copy_rank==8
+                assert z==(0 if reverse else copy_rank)
+                center=x; cur[LOCAL]=f; val[LOCAL]=val[x]; norm[LOCAL]=norm[x]
+                hist[copy_rank]+=1; copies+=1; events.append([2,x,LOCAL,c,f,copy_rank,int(reverse)])
+            else:
+                assert op==(2 if reverse else 3)
+                assert center==x and y==LOCAL and cur[x]==c and cur[LOCAL]==f
+                assert val[LOCAL]==val[x]
+                val[LOCAL]=0; norm[LOCAL]=0; cur[LOCAL]=-1; center=None
+                events.append([3,x,LOCAL,c,f,z,int(reverse)])
+        assert center is None and copies==9 and adds==expected_adds
+        assert cur[:LOCAL]==(initial if reverse else final)
+        for i in range(LOCAL):
+            want=(1<<i) ^ ((1<<(i-V)) if V<=i<2*V else 0)
+            assert val[i]==want
+        assert val[LOCAL]==0
+        if localH is None: localH=hist
+        else: assert localH==hist
+        key='reverse' if reverse else 'forward'; streams[key]=events
+        checks[key]=dict(copies=copies,adds=adds,records=len(events),all_columns=LOCAL,
+                         cancellation_free_row_l1=maxnorm,profile=dict(sorted(hist.items())),
+                         sha256=hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest())
+    assert sum(r*n for r,n in localH.items())==H*R-ENT+72+2*V*(H-1)
+
+    events=recipe(); levels=[-1]*K; schedule=[]; bridge_controls=[]
+    # Full scalar replay on separate dirty helpers for all nine stages.
+    # Physical banking then uses the separately checked injective cover owners.
+    n=2*K*V+L*R; vals=[1<<i for i in range(n)]+[0]; temp=n
+    stages=[]
+    for e in events:
+        if e['kind']=='local':
+            s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1
+            def mapper(i):
+                if i==LOCAL: return temp
+                if i<2*V:
+                    side=i//V; side=1-side if rev else side
+                    return (2*p+side)*V+i%V
+                return 2*K*V+s*R+i-2*V
+            before=vals[:]; opened=False
+            for z in streams['reverse' if rev else 'forward']:
+                if z[0]==0: continue
+                x,y=mapper(z[1]),mapper(z[2])
+                if z[0]==1:
+                    if z[3]&1: vals[x]^=vals[y]
+                elif z[0]==2:
+                    assert not opened; vals[temp]=vals[x]; opened=True
+                else:
+                    assert opened and vals[temp]==vals[x]; vals[temp]=0; opened=False
+            assert not opened
+            d=(2*p+(0 if rev else 1))*V; src=(2*p+(1 if rev else 0))*V
+            for t in range(V): before[d+t]^=before[src+t]
+            assert vals==before
+            levels[p]=s; schedule.append(dict(kind='local_cover_sweep',**{k:v for k,v in e.items() if k!='kind'}))
+            if s in (1,3,5):
+                j=(s+1)//2; assert levels[j]==-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7*(s+1),source_level=-1,target_level=s))
+            elif s in (2,4,6):
+                j=s//2; assert levels[j]==s-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7,source_level=s-1,target_level=s))
+            elif s==8:
+                for j in range(4):
+                    oldlevel=levels[j]; assert oldlevel==2*j+2
+                    schedule.append(dict(kind='idle',pair=j,rank=7*(8-oldlevel),source_level=oldlevel,target_level=8))
+                    levels[j]=8
+            stages.append(dict(stage=s,all_columns=n,helper_columns=L*R,reverse=rev))
+        elif e['kind']=='bridge':
+            d,s=e['dst'],e['src']; assert levels[d]==levels[s]
+            for t in range(V): vals[2*d*V+t]^=vals[2*s*V+t]; vals[(2*s+1)*V+t]^=vals[(2*d+1)*V+t]
+            schedule.append(e)
+        else:
+            assert levels==[8]*4
+            for j in range(K):
+                for t in range(V):
+                    x=2*j*V+t; y=(2*j+1)*V+t; vals[x],vals[y]=vals[y],vals[x]
+            schedule.append(e)
+    assert vals==[1<<i for i in range(n)]+[0]
+    # Integer scalar eight-bank matrix, with each individual bridge shear omitted.
+    def small(skip=-1):
+        z=[[int(i==j) for j in range(8)] for i in range(8)]; count=0
+        def add(d,s,c): z[d]=[x+c*y for x,y in zip(z[d],z[s])]
+        for e in events:
+            if e['kind']=='local':
+                p=e['pair']; add(2*p,2*p+1,-1) if e['reverse'] else add(2*p+1,2*p,1)
+            elif e['kind']=='bridge':
+                d,s,c=e['dst'],e['src'],e['coefficient']
+                for x,y,sgn in [(2*d,2*s,c),(2*s+1,2*d+1,-c)]:
+                    if count!=skip: add(x,y,sgn)
+                    count+=1
+            else:
+                for j in range(4): z[2*j],z[2*j+1]=z[2*j+1],[-x for x in z[2*j]]
+        return z,count
+    ident=[[int(i==j) for j in range(8)] for i in range(8)]
+    z,nb=small(); assert z==ident and nb==18
+    for skip in range(nb): assert small(skip)[0]!=ident; bridge_controls.append(skip)
+
+    paid=Counter(); calls=[]; assignment=set(); expanded=hashlib.sha256(); full_event_count=0
+    for e in events:
+        if e['kind']!='local': continue
+        s,p,rev=e['stage'],e['pair'],e['reverse']; ori='reverse' if rev else 'forward'
+        for rep in range(T):
+            owners=[]
+            for i in range(2*V):
+                side=i//V; side=1-side if rev else side
+                owners.append([rep*(2*K*V)+(2*p+side)*V+i%V, ['data',s,i%V]])
+            for r in range(R):
+                bank,off,w_=place[rep,r]
+                owners.append([DATA+s*NB+bank,['bank',off,w_,initial[2*V+r]]])
+                assignment.add((s,rep,r,bank,off))
+            assert len({(f,tuple(route)) for f,route in owners})==LOCAL
+            assert all(0<=f<LIVE for f,route in owners)
+            # Stream one full renamed instruction program into a source-bound
+            # digest, including exact owner route descriptors and reflection.
+            for z in streams[ori]:
+                op=z[0]
+                if op==0: paid[z[4]]+=bool(z[4]); mapped=[op,owners[z[1]],*z[2:]]
+                else:
+                    ox=owners[z[1]]; oy=owners[z[2]] if z[2]<LOCAL else [LIVE,['private',0]]
+                    mapped=[op,ox,oy,*z[3:]]
+                    if op==2: paid[z[5]]+=1
+                expanded.update((json.dumps(mapped,separators=(',',':'))+'\n').encode()); full_event_count+=1
+            calls.append(dict(stage=s,replica=rep,pair=p,orientation=ori,owners=owners,local_hash=checks[ori]['sha256']))
+    paid.pop(0,None)
+    assert len(assignment)==L*T*R and len(calls)==72
+    for e in schedule:
+        if e['kind']=='idle' and e['rank']: paid[e['rank']]+=2*V*T
+    mass=sum(r*c for r,c in paid.items()); assert M*LIVE-mass==2496
+    cf=checks['forward']['cancellation_free_row_l1']; cb=checks['reverse']['cancellation_free_row_l1']
+    prefix=(1<<nb)*cf**5*cb**4; charged_prefix=64*((prefix.bit_length()+63)//64);assert prefix<1<<charged_prefix
+    print('Fresh prefix bits',prefix.bit_length(),'charged',charged_prefix,flush=True)
+    template=dict(version='compressed-nine-e8-bit-v1',m=M,h=H,stages=L,replicas=T,live=LIVE,private_centre_reserve=9,
+                  cover='O(I_64/2,F_q) for admitted odd address primes q',loop_order='Each recipe phase: replicas then all cover classes; finish every local invocation before the next.',
+                  schedule=schedule,local_programs=streams,calls=calls,bank_padding=None,
+                  helper_route='Exact listed residual coordinate isometry, extended by identity on exterior coordinates and permuted to the assigned bank interval.',banks_per_stage=NB,entrance_rank_total=ENT,residual_isometries=isometries,
+                  data_route='owner (replica*960 + (2*pair+side)*120+port, d*rho_stage,port)',
+                  bit_operator='D_U exchanges the two address halves on projector U; D_I D_P = D_(I-P) exactly.',
+                  geometry_sha256=sha(out/'GEOMETRY.json'),source_record_sha256=sha(rp))
+    blob=json.dumps(template,separators=(',',':'),sort_keys=True).encode(); (out/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+    result=dict(status='PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE',h=H,m=M,v=V,R=R,replicas=T,live=LIVE,physical=LIVE+9,
+                word_sha256=sha(wp),source_records_sha256=sha(rp),local_checks=checks,scalar_stages=stages,
+                independent_unbanked_scalar_columns=n,all_scalar_columns_restored=True,
+                geometry_sha256=sha(out/'GEOMETRY.json'),template_sha256=hashlib.sha256(blob).hexdigest(),
+                emitted_program_sha256=expanded.hexdigest(),emitted_events=full_event_count,local_invocations=len(calls),
+                bank_assignments=len(assignment),banks_per_stage=NB,entrance_rank_total=ENT,mixed_width_slots=True,padding_calls=0,residual_isometries=len(isometries),extra_helper_route_factor_bound=144,
+                profile=dict(sorted(paid.items())),paid_calls=sum(paid.values()),rank_mass=mass,deficit=2496,
+                maxchild=max(paid),halving_depth=2,halving_integer_inequality=[64**2,2*42**2],
+                local_additions=expected_adds,bridge_additions=18*V*T,copy_erase_episodes=9*72,
+                global_prefix_bound=str(prefix),global_prefix_bits=prefix.bit_length(),charged_prefix_bits=charged_prefix,
+                omitted_bridge_shears_rejected=bridge_controls,
+                scope='Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.',
+                seconds=time.monotonic()-start)
+    write(out/'GLOBAL.json',result)
+    print(json.dumps({k:v for k,v in result.items() if k not in ('local_checks','scalar_stages','global_prefix_bound')}),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-joint-frame-retiming/code/bit_kernel.py b/research/e8-joint-frame-retiming/code/bit_kernel.py
new file mode 100644
index 0000000000..891ba85707
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/bit_kernel.py
@@ -0,0 +1,62 @@
+"""Shared-donor response kernel on the pinned PR436 R740 bit word (bitE8/1), from a frozen selection.
+Mechanism and code: chafreaky's #417 (vendor/kernel417: stages.kernel and the e8core exact replay with the source-span rule;
+#320/#329 kernel lineage); selection re-derived on this word with #417's discovery tools (ILS, chi scored at m = 64).
+Each entry: pivot p starts at entrance E (inside the first frame of p and of every donor), leaves the frame-0 completion
+gates; each donor pays d += p at E at the start of A and again at FULL after C (F2: response(p) = XOR responses(donors)).
+Checks here: selection bound to the exact input word, kernel applied, full exact replay (legality, F2 on all columns,
+source spans), output bound to the frozen hash, every new frame root-closed with Gram determinant (form <x,y>/2) a power
+of two (no new bad primes), total entrance rank = 0 mod 8 (exact width-64 bank tiling, checked in bit_global/bit_audit).
+Original kernel integration by rohanarun, with Anthropic Claude assistance. This R740 selection and integration by OpenAI Codex; Apache-2.0."""
+import json, os, sys, hashlib
+from fractions import Fraction as Q
+from pathlib import Path
+HERE = Path(__file__).resolve().parent.parent
+sys.path.insert(0, str(HERE / 'vendor/kernel417'))
+from stages import kernel, content_sha
+from e8core import replay, Lat
+D = Path(os.environ['E8_OUTPUT']) / 'bit426-source-centres'
+src = D / 'bit-source-centres.json'; pre = D / 'bit-source-centres-prekernel.json'
+c = json.loads(src.read_bytes()); pre.write_bytes(src.read_bytes())
+sel = json.loads((HERE / 'stages/kernel-selection.json').read_text())
+assert sel['input_sha256'] == content_sha(c), 'selection bound to a different input word'
+w, ne, tot, nd = kernel(c, sel['entries'])
+assert tot % 8 == 0 and tot == sel['total_entrance_rank']
+r = replay(w, span_mode='z'); assert not r['viol'], r['viol'][:5]
+assert content_sha(w) == sel['output_sha256'], 'output differs from the frozen selection output'
+L = Lat(w['lines']); n0 = len(c['frames']); newdets = []
+assert w['frames'][:n0] == c['frames']
+def det(M):
+    M = [[Q(x) for x in r] for r in M]; d = Q(1); k = len(M)
+    for i in range(k):
+        p = next((j for j in range(i, k) if M[j][i]), None)
+        if p is None: return Q(0)
+        if p != i: M[i], M[p] = M[p], M[i]; d = -d
+        d *= M[i][i]
+        for j in range(i + 1, k):
+            f = M[j][i] / M[i][i]; M[j] = [a - f * b for a, b in zip(M[j], M[i])]
+    return d
+for fr in w['frames'][n0:]:
+    m = sum(1 << i for i in fr); assert L.close(m) == m, 'new frame not root-closed'
+    vs = [w['lines'][i] for i in fr]
+    # basis of the span: greedy independent roots
+    B = []
+    for x in vs:
+        if len(B) < 8 and abs(det([[sum(a * b for a, b in zip(u, v)) for v in B + [x]] for u in B + [x]])) != 0: B.append(x)
+    G = [[Q(sum(a * b for a, b in zip(u, v)), 2) for v in B] for u in B]; g = det(G); assert g > 0
+    num, den = g.numerator, g.denominator
+    for x in (num, den):
+        while x % 2 == 0: x //= 2
+        assert x == 1, ('new frame Gram determinant has an odd prime factor', fr, g)
+    newdets.append(str(g))
+D.joinpath('bit-source-centres-pre-retime.json').write_bytes(json.dumps(w, sort_keys=True, separators=(',', ':')).encode())
+# The kernel output is followed by a source-bound joint A/B retime with the same scalar operands.
+from primitive_retime import apply
+rt=json.loads((HERE / 'stages/retime-selection.json').read_text())
+w=apply(w,rt)
+D.joinpath('bit-source-centres.json').write_bytes(json.dumps(w, sort_keys=True, separators=(',', ':')).encode())
+assert json.loads((HERE/'stages/final-word.json').read_text())==w
+r2 = replay(w, span_mode='z'); assert not r2['viol'], r2['viol'][:5]
+res = dict(status='PASS_KERNEL_AND_PRIMITIVE_RETIME_STAGE', entries=ne, total_entrance_rank=tot, donor_slots=nd, new_frames=len(w['frames']) - n0,
+           new_frame_gram_determinants=sorted(set(newdets)), kernel_histogram=dict(sorted(r['H'].items())), local_histogram=dict(sorted(r2['H'].items())), columns=r2['n'],
+           input_sha256=sel['input_sha256'], kernel_output_sha256=sel['output_sha256'], output_sha256=rt['output_sha256'], primitive_retime_moves=len(rt['gates']))
+(D / 'bit-kernel-receipt.json').write_text(json.dumps(res, indent=2) + '\n'); print(json.dumps(res))
diff --git a/research/e8-joint-frame-retiming/code/bit_price.py b/research/e8-joint-frame-retiming/code/bit_price.py
new file mode 100644
index 0000000000..005da012a3
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/bit_price.py
@@ -0,0 +1,18 @@
+"""Exact price of the emitted bit program; no histogram supplied by discovery."""
+import json,importlib.util
+from fractions import Fraction as Q
+from pathlib import Path
+
+def load(name):
+ p=Path('work/pr361/code/engines')/(name+'.py');sp=importlib.util.spec_from_file_location('price_'+name,p);m=importlib.util.module_from_spec(sp);sp.loader.exec_module(m);return m
+p=Path('bit426-source-centres/global');g=json.loads((p/'GLOBAL.json').read_text());a=json.loads((p/'AUDIT.json').read_text())
+assert a['template_sha256']==g['template_sha256']
+H={int(r):n for r,n in a['profile'].items()};m,W=g['m'],g['live']
+M,B=load('moment'),load('base_two_moment');root=M.certify(H,m,W,True);lo,hi=Q(root['lower']),Q(root['upper'])
+fb=32*m*m*sum(H.values())
+def other(x):
+ l,u=B.moment(m,W,list(H.items()),x);a,b=B.moment(m,W,[(1,fb)],x);return l+a/10**16,u+b/10**16
+assert other(lo)[1]<1<other(hi)[0]
+root.update(source_template_sha256=g['template_sha256'],two_exact_engines=True)
+Path('BIT-PRICE.json').write_text(json.dumps(root,indent=2)+'\n')
+print('PASS two rational bit moments',root['lower'])
diff --git a/research/e8-joint-frame-retiming/code/combined.py b/research/e8-joint-frame-retiming/code/combined.py
new file mode 100644
index 0000000000..6ec68dfdcc
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/combined.py
@@ -0,0 +1,56 @@
+"""Fresh bit finite invoice and joint strict arithmetic for two changed suppliers.
+icekylinx, with Codex assistance. Inherited all-size interfaces remain conditional.
+"""
+import json,hashlib,importlib.util
+from pathlib import Path
+from fractions import Fraction as Q
+import os
+ROOT=Path(os.environ['E8_OUTPUT']);D=ROOT/'bit426-source-centres/global';C=ROOT/'split-centres'
+read=lambda p:json.loads(p.read_text())
+g=read(D/'GLOBAL.json');geo=read(D/'GEOMETRY.json');audit=read(D/'AUDIT.json')
+cx=read(C/'INTEGRATION.json');ca=read(C/'INDEPENDENT-REPLAY.json')
+assert audit['template_sha256']==g['template_sha256'] and ca['template_sha256']==cx['global_template_sha256']
+assert len(audit['mutations_rejected'])==11 and len(ca['mutation_controls_rejected'])==7
+P={int(r):z for r,z in audit['profile'].items()};m,W=64,g['live'];E=sum(P.values());T,L,R,V,K=8,9,g['R'],120,4
+mass=sum(r*z for r,z in P.items());assert m*W-mass==2496 and g['live']==W
+physical=g['physical'];d=m*m;N=2*m
+unit=L*T*g['local_additions']+g['bridge_additions']
+J=8*T*L*(2*V+R)+8*(2*K*V*T)+2*g['bank_assignments']+2*g['copy_erase_episodes']
+high=16*(d+1)**2;good=8*m*m+8;compiler=128*N**3
+selectors=2*L*T*((W-1)+R*m*(geo['max_route_factors']+144+(m-1)+m))
+prefix=int(g['global_prefix_bound']);charged_prefix=64*((prefix.bit_length()+63)//64);assert prefix<1<<charged_prefix<=1<<256
+assert g['extra_helper_route_factor_bound']==144 and audit['residual_isometries']==g['residual_isometries']
+coefficient=unit+J*high+J*physical+E*(good+compiler)+16*m**3+g['copy_erase_episodes']+selectors+prefix+1
+two=(coefficient+1)**2*(E+1)**2
+assert two<1<<512 and 2*max(P)**2<m*m
+row=2*(m*m+1)+9909+252;assert row==18355<20161
+assert geo['bad_prime_factors']==[2] and geo['route_denominators']==[1,2,4]
+def load(name):
+ p=ROOT/'work/pr361/code/engines'/(name+'.py');sp=importlib.util.spec_from_file_location('joint_'+name,p);mod=importlib.util.module_from_spec(sp);sp.loader.exec_module(mod);return mod
+M,Other,Outer=load('moment'),load('base_two_moment'),load('outer')
+root=M.certify(P,m,W,True);c=Q(root['lower']);grid=Q(1,10**18);b=Q(ca['complex_b'])
+fb=32*m*m*E
+lo,hi=Other.moment(m,W,list(P.items()),c);bl,bh=Other.moment(m,W,[(1,fb)],c)
+assert hi+bh/10**16<1
+eta=beta=Q(1,10**18);s=min(c,(1-beta)*b)-Q(1,10**24)
+assert 0<s<c and s<(1-beta)*b
+chain=[Q(384599,10**10)];cutoffs=[]
+def ceil(x):return -((-x.numerator)//x.denominator)
+for j in range(6):
+ old=chain[-1];a=(1-s)*s+s*old
+ gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+ cutoff=max(ceil(36/gap**2),ceil(2*(4+512)/gap))
+ assert cutoff*gap**2>=36 and cutoff*gap>=2*(4+512)
+ cutoffs.append(dict(gap=str(gap),cutoff_log2=str(cutoff)));chain.append(a)
+q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin/grid;k=grid*((ticks.numerator-1)//ticks.denominator)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}
+a=Outer.assembly(chain[-1],b,bridge,k,eta=eta,beta=beta)
+assert len(a['strict_constraints'])==47 and all(x>0 for x in a['strict_constraints'].values())
+controls=[]
+for name,kk,ee,bb in [('next_grid',k+grid,eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]:
+ try:Outer.assembly(chain[-1],b,bridge,kk,eta=ee,beta=bb)
+ except AssertionError:controls.append(name)
+ else:raise AssertionError(name)
+result=dict(status='PASS_CONDITIONAL_SPLIT_CENTRE_ASSEMBLY',kappa=str(k),kappa_decimal=format(float(k),'.18f'),bit_lower=str(c),complex_lower=str(b),binding_component='bit',gain_over_pr425_percent=float(100*(k/Q(1048005508028206,10**18)-1)),bit_invoice=dict(prefix_bits=prefix.bit_length(),charged_prefix_bits=charged_prefix,extra_helper_route_factor_bound=144,selector_charge=selectors,full_counted_coefficient=str(coefficient),two_level_coefficient=str(two),coefficient_bits=coefficient.bit_length(),two_level_coefficient_bits=two.bit_length(),charged_two_level_coefficient_bits=512,row_coefficient=row,live=W,physical=physical),strict_outer_constraints={n:str(x) for n,x in a['strict_constraints'].items()},outer_controls=controls,bootstrap=cutoffs,bit_template_sha256=g['template_sha256'],complex_template_sha256=cx['global_template_sha256'],scope='Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim.')
+(ROOT/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n')
+print(result['status'],result['kappa_decimal'],result['gain_over_pr425_percent'],result['bit_invoice'])
diff --git a/research/e8-joint-frame-retiming/code/complex_audit.py b/research/e8-joint-frame-retiming/code/complex_audit.py
new file mode 100644
index 0000000000..ba6789a3a6
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/complex_audit.py
@@ -0,0 +1,168 @@
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Read-back audit, independent of the Hamming producer and its row state."""
+import copy,gzip,hashlib,importlib.util,json,math,time
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');p=OUT/'FULL-WORD.json.gz'
+word=json.load(gzip.open(p));v=120;n=240+word['report']['R'];start=time.monotonic()
+def apply(e,rows):
+    if e[0]=='scale':
+        _,t,a,b,*_=e;q=Q(a,b);assert q
+        rows[t]={j:q*x for j,x in rows[t].items()}
+    else:
+        _,t,s,a,b,*_=e;q=Q(a,b);assert t!=s
+        for j,x in list(rows[s].items()):
+            z=rows[t].get(j,Q(0))+q*x
+            if z:rows[t][j]=z
+            else:rows[t].pop(j,None)
+def ident():return [{r:Q(1)} for r in range(n)]
+def inv(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    return e
+def dual(e):
+    e=inv(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1]
+    return e
+
+main=word['A']+word['cut']+word['B']
+assert all(not 120<=e[2]<240 for e in word['A']+word['B'] if e[0]=='add' and not 120<=e[1]<240)
+matrix=ident()
+for e in main:apply(e,matrix)
+print('full main columns',n,'replayed',flush=True)
+# Compute -A_Y^-1 B_S using only rows of the explicit main operator.
+dirty=[{} for r in range(n)]
+for r in range(v,2*v):dirty[r]={j:x for j,x in matrix[r].items() if j>=2*v}
+for e in word['precondition']:apply(e,dirty)
+comp=[]
+for r in range(v,2*v):
+    for j,q in sorted(dirty[r].items()):comp.append(['add',r,j,-q.numerator,q.denominator,[]])
+
+cleanup=[inv(e) for e in reversed(word['A']+word['B']) if not v<=e[1]<2*v]
+assert [e[:-1] for e in cleanup]==[e[:-1] for e in word['cleanup']]
+program=word['precondition']+comp+main+cleanup
+actual=ident()
+for e in program:apply(e,actual)
+expected=ident()
+for t in range(v):expected[v+t][t]=Q(1)
+assert actual==expected
+print('PASS exact arbitrary dirt and restored sources/helpers',flush=True)
+back=ident()
+for e in program:apply(dual(e),back)
+expected_back=ident()
+for t in range(v):expected_back[t][v+t]=Q(-1)
+assert back==expected_back
+print('PASS exact inverse-transpose on every column',flush=True)
+# Independent sparse vector controls avoid repeating a dense full replay.
+def vector(es,x):
+    x=list(map(Q,x))
+    for e in es:
+        if e[0]=='scale':x[e[1]]*=Q(e[2],e[3])
+        else:x[e[1]]+=Q(e[3],e[4])*x[e[2]]
+    return x
+sample=[((i*137+13)%101)-50 for i in range(n)]
+want=vector(program,sample)
+controls={
+    'missing_dirty_compensation':word['precondition']+main+cleanup,
+    'missing_Y_inverse_basis':comp+main+cleanup,
+    'missing_source_cleanup':word['precondition']+comp+main,
+    'wrong_dual_event_order':[dual(e) for e in reversed(program)],
+}
+for name,es in controls.items():
+    expected_sample=vector([dual(e) for e in program],sample) if name=='wrong_dual_event_order' else want
+    assert vector(es,sample)!=expected_sample,name
+
+# Orthogonal transvection and a port permutation bring the new geometry onto
+# the already fixed 120-port routing family. Every incidence is transformed.
+old=json.load(gzip.open('work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz'))
+def tau(x):return x^(43 if (x&43).bit_count()%2 else 0)
+assert 43 .bit_count()%2==0
+assert set(map(tau,word['ports']))==set(old['ports'])
+mapping={i:old['ports'].index(tau(q)) for i,q in enumerate(word['ports'])}
+mapping.update({v+i:v+mapping[i] for i in range(v)})
+mapping.update({r:r for r in range(2*v,n)})
+def basis(vs):
+    b={}
+    for x in vs:
+        for k in sorted(b,reverse=True):
+            if x>>k&1:x^=b[k]
+        if x:
+            k=x.bit_length()-1
+            for j in b:
+                if b[j]>>k&1:b[j]^=x
+            b[k]=x
+    return tuple(b[k] for k in sorted(b,reverse=True))
+def perp(x):return basis([z for z in range(1,512) if not (x&z).bit_count()%2])
+full=tuple(1<<i for i in range(8,-1,-1));frames=[(),full];fi={f:i for i,f in enumerate(frames)}
+def fid(f):
+    f=basis(f)
+    if f not in fi:fi[f]=len(frames);frames.append(f)
+    return fi[f]
+def canonical(e):
+    e=copy.deepcopy(e);e[1]=mapping[e[1]]
+    if e[0]=='add':e[2]=mapping[e[2]]
+    if e[-1] is not None:e[-1]=fid([tau(x) for x in e[-1]])
+    return e
+can={key:[canonical(e) for e in word[key]] for key in ('A','B','cut','cleanup','precondition')}
+can['compensation']=[canonical(e) for e in comp]
+can['start']=[fid([q]) for q in old['ports']]+[0]*(v+word['report']['R'])
+can['final']=[1]*v+[fid(perp(q)) for q in old['ports']]+[1]*word['report']['R']
+can['ports']=old['ports'];can['centers']=[mapping[r] for r in word['centers']]
+can['center_frames']=[fid([tau(x) for x in f]) for f in word['center_frames']]
+can['h']=9;can['v']=v;can['R']=word['report']['R'];can['frames']=frames
+cur=list(can['start']);paid=Counter();edges=set();incidences=0
+def climb(r,f):
+    old=cur[r]
+    assert basis(frames[old]+frames[f])==frames[f]
+    if old!=f:
+        delta=len(frames[f])-len(frames[old]);assert delta>0
+        edges.add((old,f));paid[delta]+=1;cur[r]=f
+for part in ('A','B'):
+    if part=='B':
+        assert all(cur[r]==f for r,f in zip(can['centers'],can['center_frames']))
+        assert all(cur[r]==0 for r in range(v,2*v))
+        for f in can['center_frames']:paid[len(frames[f])]+=1
+    for e in can[part]:
+        rs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        for r in rs:climb(r,e[-1]);incidences+=1
+for r,f in enumerate(can['final']):climb(r,f)
+assert dict(paid)=={int(r):x for r,x in word['report']['local_profile'].items()}
+assert sum(r*x for r,x in paid.items())==9*can['R']+240*8+72
+can['local_profile']=dict(sorted(paid.items()));can['edges']=sorted(edges)
+cp=OUT/'CANONICAL-WORD.json.gz';cp.write_bytes(gzip.compress(json.dumps(can,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+
+def engine(name):
+    p=Path('work/pr361/code/engines')/(name+'.py');s=importlib.util.spec_from_file_location('hamming_'+name,p)
+    m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,M2=engine('moment'),engine('base_two_moment');m,W=73,12720
+HG={int(r):z for r,z in word['report']['global_profile'].items()}
+root=M.certify(HG,m,W,True);b=Q(int(Q(root['lower'])*10**18),10**18);grid=Q(1,10**18)
+assert M.moment(HG,m,W,b,True)[1]<1<M.moment(HG,m,W,b+grid,True)[0]
+fallback=32*m*m*sum(HG.values())
+def second(a):
+    lo,hi=M2.moment(m,W,list(HG.items()),a)
+    l2,h2=M2.moment(m,W,[(1,fallback)],a)
+    return lo+l2/10**16,hi+h2/10**16
+assert second(b)[1]<1<second(b+grid)[0]
+coeff=Counter(str(Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])) for e in program)
+report={'status':'PASS_EXACT_SCALAR_AND_FRAME_RESEARCH_CANDIDATE_NOT_YET_ADMITTED',
+        'full_word_sha256':hashlib.sha256(p.read_bytes()).hexdigest(),
+        'canonical_word_sha256':hashlib.sha256(cp.read_bytes()).hexdigest(),
+        'live_columns_each_orientation':n,'arbitrary_helper_columns':can['R'],
+        'all_live_source_and_helper_rows_restored':True,'all_target_rows_correct':True,
+        'negative_controls_rejected':list(controls),'old_response_additions':len(comp),
+        'complete_forward_scalar_operations':len(program),'coefficient_histogram':dict(coeff),
+        'frames':len(frames),'nested_directed_edges':len(edges),'common_frame_incidences':incidences,
+        'orthogonal_transport_vector':43,'transported_ports_exactly_match_fixed_routes':True,
+        'local_profile':dict(sorted(paid.items())),
+        'prospective_complex_b':str(b),'prospective_b_float':float(b),
+        'prospective_gain_percent':float(100*(b/Q(999388595603943,10**18)-1)),
+        'two_rational_moment_engines':True,'next_b_grid_rejected':True,
+        'remaining':['new general scalar-interface proof integration','exact phase and emitted local/global program','finite invoice and outer assembly'],
+        'scope':'Substantial new scalar-network candidate. All parameter values remain prospective until the expanded scalar interface and complete phase-aware supplier are admitted.',
+        'seconds':time.monotonic()-start}
+(OUT/'SCALAR-FRAME-AUDIT.json').write_text(json.dumps(report,indent=2)+'\n')
+print('PASS prospective b',float(b),'gain',report['prospective_gain_percent'],'percent; seconds',report['seconds'],flush=True)
diff --git a/research/e8-joint-frame-retiming/code/complex_construct.py b/research/e8-joint-frame-retiming/code/complex_construct.py
new file mode 100644
index 0000000000..bbc61e57dc
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/complex_construct.py
@@ -0,0 +1,278 @@
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+INPUT=Path('work/complex-network/hamming');OUT=Path('split-centres');OUT.mkdir(exist_ok=True);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+def alloc():
+    n=len(cur);cur.append(());rows.append({});return n
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# All original-source loads precede source borrowing.
+own={};fl={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines']
+    for s in ids:
+        own[s]=alloc();add(own[s],s,1,(P[s],))
+
+packets={};retired={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)})
+    for e,F in zip(z['events'],z['event_frames']):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    keys=[(p,epsilon) for p in it.combinations(c,2) for epsilon in (-1,1)]
+    for key,(reg,alpha) in zip(keys,z['outputs']):
+        a=mp[reg];alpha=Q(alpha);F=cur[a]
+        b=alloc();add(b,a,1,F)
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,rr in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(rr,alpha)
+    retired[c]=[mp[r] for r in z['dead_registers']]
+
+# Four coordinate sums per code block, reconstructed in the retired register
+# stock at its legal rank-four frame. The remaining eight rows retain a basis.
+block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];regs=retired[c];F=basis([P[s] for s in ids])
+    assert len(regs)==12 and len(F)==4
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    assert all(not rows[r] for r in regs[8:])
+    for i,reg in zip(c,regs[8:]):
+        for j,s in enumerate(ids):add(reg,regs[j],R[s][i],F)
+        block_totals[c,i]=reg
+
+# Eight global coordinate sums, with a single copy each for the centers. The
+# other copy is exactly the correction needed by the eight frame-line targets.
+global_totals={};centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    global_totals[i]=a
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+
+# Own-block and coordinate-frame corrections, one stream per code target.
+own_out={};tetrads={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines']
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        sources=tet[1-parity];xs=[own[s] for s in sources]
+        F=basis([P[s] for s in sources]);linear(xs,[[G[t][s] for s in sources] for t in targets],F)
+        for t,x in zip(targets,xs):own_out[t]=x
+
+# Cross-block M packets, shared by four targets, then two-output pair transforms.
+Ms={};consumers=defaultdict(list);pairs=[]
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for epsilon in (-1,1):
+            (a,alpha),(b,beta)=[packets[d,p,epsilon,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,epsilon]=(a,alpha)
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    for parity,tet in enumerate(tetrads[c]):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in tet:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                assert len(ts)==2;a,b=sorted(ts)
+                e2=R[a][q[0]]*R[a][q[1]]
+                assert e2==R[b][q[0]]*R[b][q[1]]
+                keys=[(c,p,eps),(c,q,e2)];pid=len(pairs)
+                selected=(pi==parity)  # different first partitions in the two tetrads
+                pairs.append({'targets':(a,b),'keys':keys,'selected':selected,
+                              'matrix':[[R[t][p[0]],R[t][q[0]]] for t in (a,b)]})
+                for key in keys:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    a,alpha=Ms[key];ordinary=[i for i in uses if not pairs[i]['selected']]
+    for j,pid in enumerate(ordinary):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+
+assert len(cur)-240==560,(len(cur)-240)
+
+# The selected target pairs borrow Y as the first packet destination. Their
+# two-shear output basis is compensated at frame zero and in the scatter table.
+phase=B;selected=[];output_basis=[]
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=Ms[key1],Ms[key2]
+    add(v+t,a,-Q(mat[0][0],2)*alpha,cur[a])
+    add(v+u,b,-Q(mat[0][1],2)*beta,cur[b])
+    selected.append((pid,t,u,mat))
+for pid,t,u,mat in selected:
+    F=basis(cur[v+t]+cur[v+u]);assert all((P[s]&p).bit_count()%2==0 for s in (t,u) for p in F)
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F)
+    output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+for t,r in own_out.items():add(v+t,r,-Q(1,2),hyper(P[t]))
+
+side=[dict(rows[v+t]) for t in range(v)]
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert side[t]==expected,('side identity',t)
+
+# Correct the eight-center scatter through the inverse two-output basis.
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8;by['c'][8]+=8;by['c'][1]+=8
+n=len(cur);Rcount=n-240
+assert sum(r*z for r,z in H.items())==9*Rcount+240*8+72
+
+def apply(event,matrix):
+    if event[0]=='add':
+        _,t,s,a,b,*_=event;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=event;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e,F=None):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    if F is not None:e[-1]=list(F)
+    return e
+cut=[]
+for t,rr in enumerate(scatter):
+    for i,q in enumerate(rr):
+        if q:cut.append(['add',v+t,centers[i],q.numerator,q.denominator,None])
+cleanup=[inverse(e,FULL) for e in reversed(A+B) if not v<=e[1]<2*v]
+
+# Exact clean replay checks the changed decoder and restored source basis.
+matrix=[{r:Q(1)} if r<v else {} for r in range(n)]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(n))
+
+m=73;T=8;L=9;W=7680+L*Rcount;globalH=Counter({r:z*L*T for r,z in H.items()})
+for r in (16,8,32,8,48,8,48,32,16):globalH[r]+=240*T
+globalH[1]+=L*Rcount
+assert m*W-sum(r*z for r,z in globalH.items())==2496
+low,high=0.,.003
+for _ in range(60):
+    q=(low+high)/2
+    moment=sum(r*z/(m*W)*(m/r)**q for r,z in globalH.items())+32*m*sum(globalH.values())/(10**16*W)*m**q
+    if moment<1:low=q
+    else:high=q
+report={'status':'EXACT_CLEAN_FULL_WORD_DISCOVERY_NOT_ADMITTED',
+        'h':9,'v':120,'R':Rcount,'cst':72,'local_profile':dict(sorted(H.items())),
+        'global_profile':dict(sorted(globalH.items())),'m':m,'W':W,
+        'complex_coarse_float':(low+high)/2,'baseline_b':0.000999388595603943,
+        'gain_percent_float':100*((low+high)/2/0.000999388595603943-1),
+        'scalar_operations_A':len(A),'scalar_operations_B':len(B),
+        'borrowed_output_pairs':len(output_basis),'centre_ranks':list(map(len,center_frames)),'source_columns_exact':120,
+        'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'retained_center_rows_exact':True,
+        'remaining':['full arbitrary-dirt program and independent replay','exact complex phases and global template','finite invoice and coefficient lowering','two rational prices and outer assembly']}
+full={'report':report,'ports':P,'root_lines':R,'A':A,'B':B,'centers':centers,'scatter':[[str(x) for x in r] for r in scatter],
+      'cut':cut,'cleanup':cleanup,'precondition':precondition,'center_frames':center_frames}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(full,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'FULL-DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/e8-joint-frame-retiming/code/complex_emit.py b/research/e8-joint-frame-retiming/code/complex_emit.py
new file mode 100644
index 0000000000..e5fe7b3489
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/complex_emit.py
@@ -0,0 +1,136 @@
+# Adapted from PR425 by icekylinx with Codex assistance.
+"""Emit both local programs, integrate the fixed nine-stage geometry, and bill.
+
+The expanded scalar interface is justified in PROOF.txt. This script does not
+claim a Lean proof or discharge the inherited all-size/analytic interfaces.
+"""
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp))
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R
+def digest(x):return hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+def basis(vs):
+    b={}
+    for x in vs:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def dual(e):
+    e=list(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1];e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    return e
+def scalar(e,back):
+    e=dual(e) if back else list(e)
+    if e[0]=='add':return ['add',['L',e[1]],['L',e[2]],e[3],e[4]]
+    return ['scale',['L',e[1]],e[2],e[3]]
+def primitive_bound(e):
+    if e[0] in ('clear','copy'):return 1
+    q=Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])
+    a,b=abs(q.numerator),q.denominator
+    assert b&(b-1)==0
+    if e[0]=='scale':
+        assert a&(a-1)==0
+        return abs(a.bit_length()-b.bit_length())+int(q<0)
+    # Exact binary Horner multiplication on a cleared private stream, repeated
+    # halving, signed accumulation into the target, then clear the private stream.
+    return 3+(a.bit_length()-1)+a.bit_count()+(b.bit_length()-1)
+
+def emit(back):
+    out=[];cur=c['start'].copy()
+    def event(e):out.append(e)
+    def scal(e,f):event(['scalar',e,f])
+    event(['phase','zero_frame_precondition'])
+    for e in c['precondition']+c['compensation']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['start'][r]==0 for r in regs)
+        scal(scalar(e,back),0)
+    event(['phase','entry_adapters'])
+    for r,f in enumerate(c['start']):event(['adapter','old_to_new',r,f])
+    def climb(r,f,part):
+        old=cur[r]
+        if old==f:return
+        assert basis(frames[old]+frames[f])==tuple(frames[f])
+        rank=len(frames[f])-len(frames[old]);assert rank>0
+        event(['climb',part,r,old,f,rank]);cur[r]=f
+    for part in ('A','centers','B','final'):
+        event(['phase',part])
+        if part in ('A','B'):
+            for e in c[part]:
+                regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+                for r in regs:climb(r,e[-1],part)
+                scal(scalar(e,back),e[-1])
+        elif part=='centers':
+            assert all(cur[r]==0 for r in range(v,2*v))
+            for k,r in enumerate(c['centers']):
+                cf=c['center_frames'][k];rank=len(frames[cf]);assert cur[r]==cf
+                C=['C',k];scal(['clear',C],0 if back else cf)
+                terms=[e for e in c['cut'] if e[2]==r]
+                if back:
+                    for e in terms:scal(['add',C,['L',e[1]],e[3],e[4]],0)
+                else:scal(['copy',C,['L',r]],cf)
+                event(['center',k,0 if back else cf,cf if back else 0,rank])
+                if back:scal(['add',['L',r],C,-1,1],cf)
+                else:
+                    for e in terms:scal(['add',['L',e[1]],C,e[3],e[4]],0)
+                scal(['clear',C],cf if back else 0)
+        else:
+            for r,f in enumerate(c['final']):climb(r,f,part)
+    event(['phase','exit_adapters'])
+    for r,f in enumerate(c['final']):event(['adapter','new_to_old',r,f])
+    event(['phase','full_frame_cleanup'])
+    for e in c['cleanup']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['final'][r]==1 for r in regs)
+        scal(scalar(e,back),1)
+    event(['phase','done'])
+    return out
+
+def check_local(events,back):
+    # Literal scalar replay of the emitted stream, including center lifetimes.
+    state={('L',r):{r:Q(1)} for r in range(n)};live=[];paid=Counter();prims=0;macros=0
+    for e in events:
+        if e[0]=='climb':assert not live;paid[e[5]]+=1
+        elif e[0]=='center':assert live==[e[1]];paid[e[4]]+=1
+        elif e[0]=='scalar':
+            op=e[1];tag=op[0];t=tuple(op[1]);macros+=1;prims+=2*primitive_bound(op)
+            if tag=='clear':
+                state[t]={}
+                if t[0]=='C' and t[1] in live:live.remove(t[1])
+            elif tag=='copy':state[t]=dict(state.get(tuple(op[2]),{}));live.append(t[1])
+            elif tag=='scale':state[t]={j:Q(op[2],op[3])*x for j,x in state[t].items()}
+            else:
+                s=tuple(op[2]);q=Q(op[3],op[4]);row=state.setdefault(t,{})
+                if t[0]=='C' and t[1] not in live:live.append(t[1])
+                for j,x in list(state.get(s,{}).items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+    assert not live and all(not row for r,row in state.items() if r[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert state['L',r]==expected,('emitted column mismatch',back,r)
+    assert dict(paid)=={int(r):z for r,z in c['local_profile'].items()}
+    return {'sha256':digest(events),'events':len(events),'scalar_macros':macros,
+            'real_component_primitive_bound':prims,'paid_profile':dict(sorted(paid.items())),
+            'all_columns':n,'private_centers_cleared':True,'private_coefficient_stream_cleared_after_each_macro':True}
+
+programs={};checks={}
+for name,back in [('forward',False),('backward',True)]:
+    programs[name]=emit(back);checks[name]=check_local(programs[name],back)
+    print('PASS emitted',name,checks[name]['events'],'events',flush=True)
+
+
+(OUT/'LOCAL-PROGRAMS.json.gz').write_bytes(gzip.compress(json.dumps(programs,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'LOCAL-CHECKS.json').write_text(json.dumps(checks,indent=2)+'\n')
diff --git a/research/e8-joint-frame-retiming/code/complex_integrate.py b/research/e8-joint-frame-retiming/code/complex_integrate.py
new file mode 100644
index 0000000000..ffa5c036d7
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/complex_integrate.py
@@ -0,0 +1,109 @@
+# Adapted from PR425 for heterogeneous centres by icekylinx, with Codex assistance.
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+OUT=Path('split-centres');cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp));audit=json.loads((OUT/'SCALAR-FRAME-AUDIT.json').read_text())
+phase=json.loads((OUT/'CLIFFORD-REVIEW.json').read_text());sha=lambda p:hashlib.sha256(Path(p).read_bytes()).hexdigest()
+assert phase['canonical_word_sha256']==audit['canonical_word_sha256']==sha(cp)
+assert phase['all_child_equalities_include_global_phase']
+programs=json.load(gzip.open(OUT/'LOCAL-PROGRAMS.json.gz'));checks=json.loads((OUT/'LOCAL-CHECKS.json').read_text())
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R;private_centres=len(c['centers'])
+for z in checks.values():z['paid_profile']={int(r):n for r,n in z['paid_profile'].items()}
+old=Path('work/complex-nine-native');template=json.load(gzip.open(old/'GLOBAL-TEMPLATE.json.gz'))
+data_phase=json.loads((old/'DATA-PHASES.json').read_text())
+assert template['exact_data_phase_recipe_sha256']==sha(old/'DATA-PHASES.json')
+assert data_phase['status']=='PASS_EXACT_Z4_DATA_ROUTE_IDLE_AND_TERMINAL_PHASES'
+m,T,L,k=73,8,9,4;W=2*v*k*T+L*R;physical=W+R+private_centres+2
+template['version']='hamming-mutable-basis-nine-v1';template['live']=W;template['physical']=physical
+template['local_programs']=programs;paid=Counter();assignments=set();event_count=0;scalar_primitives=0
+for call in template['calls']:
+    stage,rep,pair=call['stage'],call['replica'],call['pair'];ori=call['orientation']
+    owners=[[rep*2*k*v+(2*pair+r//v)*v+r%v,[1,stage,r%v]] for r in range(2*v)]
+    for r in range(R):
+        z=rep*R+r;bank,slot=divmod(z,T);owners.append([2*v*k*T+stage*R+bank,[2,slot]])
+        assignments.add((stage,rep,r,bank,slot))
+    assert len(owners)==n and len({(f,tuple(route)) for f,route in owners})==n
+    assert all(f<W for f,route in owners)
+    call['owners']=owners;call['local_program_sha256']=checks[ori]['sha256']
+    for r,z in checks[ori]['paid_profile'].items():paid[r]+=z
+    event_count+=checks[ori]['events'];scalar_primitives+=checks[ori]['real_component_primitive_bound']
+assert len(assignments)==L*T*R and len(template['calls'])==72
+for item in template['idle_children']:paid[item['rank']]+=item['replicas']
+paid[1]+=L*R
+assert dict(paid)=={int(r):z for r,z in json.load(gzip.open(OUT/'FULL-WORD.json.gz'))['report']['global_profile'].items()}
+mass=sum(r*z for r,z in paid.items());assert m*W-mass==2496
+template['bank_padding']['families']=list(range(7680,W))
+template['cover_final_correction']['families']=[0,W]
+template['cover_final_correction']['charged_calls_per_cover']=W
+for e in template['execution_schedule']:
+    if e['kind']=='bank_padding_cover_sweep':e['families']=[7680,W]
+    elif e['kind']=='translate_every_live_family':e.update(template['cover_final_correction'])
+template['private_namespace']={'centers':[W,W+private_centres],'reserved_tableau':[W+private_centres,W+private_centres+R],
+                               'coefficient':[physical-2,physical]}
+template['exact_local_clifford_recipe_sha256']=sha(OUT/'CLIFFORD-RECIPES.json')
+template['expanded_scalar_interface']='See PROOF.txt: mutable source basis, frame-zero output preconditioner, explicit dirty compensator, and full-frame inverse source/helper cleanup.'
+blob=json.dumps(template,sort_keys=True,separators=(',',':')).encode()
+(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+
+# Fresh finite overcharge, with the changed stock, scalar counts, coefficient
+# lowering, and private work reserve. No unchanged local invoice is assumed.
+compiler=64*(m+1)**3;macros=max(z['scalar_macros'] for z in checks.values());children=sum(checks['forward']['paid_profile'].values())
+adapters=16*(macros+children+n+private_centres)+64*m
+local_bound=max(z['real_component_primitive_bound'] for z in checks.values())+adapters*compiler
+bridges=[e for e in template['recipe'] if e['kind']=='bridge'];bridge_adds=2*v*T*len(bridges)
+terminal_shifts=k*v*T;terminal_moves=2*k*v*T
+nonlocal_items=4*v*T*L+2*v*T*L+2*L*T*R+sum(e['replicas'] for e in template['idle_children'])+L*R+bridge_adds+terminal_shifts+terminal_moves+W+physical
+outside=8*nonlocal_items+64*m
+pervertex=scalar_primitives+bridge_adds+terminal_shifts+terminal_moves+W+(72*adapters+outside)*compiler+64*physical
+r=m//2;group=2**(r*r)*math.prod(2**(2*i)-1 for i in range(1,r+1));stock=group*physical
+smass=group*mass;logical=group*pervertex+64;router=compiler*(logical+1)*(stock+1)**2
+GG,EE,C0=1<<30000,1<<100000,1<<210000;BB=smass+EE
+literal=2*GG*stock**2+8*smass+4*stock+4+32*m
+maxchild=max(paid);depth=2;assert m**depth>2*maxchild**depth
+assert local_bound<1<<48 and logical<1<<6050 and router<GG and literal<EE and BB<1<<100001
+assert 32*m*BB*BB<C0 and 2*BB+18<C0
+row=depth*stock.bit_length()+9909+252;assert row<20161
+
+def load(name):
+    sp=importlib.util.spec_from_file_location('hamming_integrate_'+name,Path('work/pr361/code/engines')/(name+'.py'))
+    mod=importlib.util.module_from_spec(sp);sp.loader.exec_module(mod);return mod
+Outer=load('outer');b=Q(audit['prospective_complex_b']);bit=Q(json.loads(Path('BIT-PRICE.json').read_text())['lower'])
+eta=Q(1,10**12);beta=Q(1,10**9);grid=Q(1,10**18)
+s=Q(int(((1-beta)*min(b,bit)-grid)*10**18),10**18);assert s<bit
+chain=[Q(384599,10**10)];cutoffs=[]
+for _ in range(3):
+    a=chain[-1];z=(1-s)*s+s*a;gap=min(s-z,1-z-s,1-z-s*(1-a),1-s)
+    assert a<z<s<1-z and gap>0
+    bound=max(math.ceil(36/gap**2),math.ceil(2*(4+512)/gap))
+    assert bound*gap**2>=36 and bound*gap>=2*(4+512)
+    cutoffs.append(str(bound));chain.append(z)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},
+        'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}
+q=chain[-1]*(1-2*eta);ticks=(1-eta)*q/(1+q)/grid;kap=Q((ticks.numerator-1)//ticks.denominator,10**18)
+assembly=Outer.assembly(chain[-1],b,bridge,kap,eta=eta,beta=beta)
+try:Outer.assembly(chain[-1],b,bridge,kap+grid,eta=eta,beta=beta)
+except AssertionError:pass
+else:raise AssertionError('next kappa grid accepted')
+result={'status':'PASS_NEW_STRUCTURAL_PROGRAM_AND_FINITE_ASSEMBLY_PENDING_REPLAY',
+        'canonical_word_sha256':sha(cp),'scalar_audit_sha256':sha(OUT/'SCALAR-FRAME-AUDIT.json'),
+        'exact_phase_receipt_sha256':sha(OUT/'CLIFFORD-REVIEW.json'),'global_template_sha256':hashlib.sha256(blob).hexdigest(),
+        'local_program_checks':checks,'R':R,'m':m,'live':W,'physical':physical,
+        'bank_assignments':len(assignments),'rank_mass':mass,'deficit':2496,
+        'global_profile':dict(sorted(paid.items())),'emitted_local_events_all_calls':event_count,
+        'finite_invoice':{'local_primitive_bound':local_bound,'local_adapters':adapters,
+                          'pervertex':pervertex,'physical_stock_bits':stock.bit_length(),
+                          'router_bits':router.bit_length(),'literal_bits':literal.bit_length(),
+                          'physical_row_coefficient':row,'retained_row_coefficient':20161,
+                          'compiler':compiler,'G_exponent':30000,'E_exponent':100000,'C0_exponent':210000,
+                          'required_C0_bits':(32*m*BB*BB).bit_length(),'halving_degree':depth,
+                          'halving_integer_inequality':[m**depth,2*maxchild**depth]},
+        'complex_b':str(b),'bit_c':str(bit),'prospective_kappa':str(kap),'kappa_float':float(kap),
+        'log2_kappa':math.log2(float(kap)),
+        'kappa_gain_percent':float(100*(kap/Q(998390813251625,10**18)-1)),
+        'strict_outer_constraints':{name:str(z) for name,z in assembly['strict_constraints'].items()},
+        'next_kappa_grid_rejected':True,'bootstrap_cutoffs_log2':cutoffs,
+        'scope':'New finite scalar interface with a written conjugation proof, conditional on inherited all-size compiler, precision/tape and analytic transfer. Independent emitted-program replay and fresh package replay still required before final promotion.'}
+(OUT/'INTEGRATION.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS prospective kappa',float(kap),'gain',result['kappa_gain_percent'],'percent',flush=True)
diff --git a/research/e8-joint-frame-retiming/code/complex_phases.py b/research/e8-joint-frame-retiming/code/complex_phases.py
new file mode 100644
index 0000000000..127a042ea7
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/complex_phases.py
@@ -0,0 +1,29 @@
+"""Bind unchanged exact phase evidence, or regenerate all selected phase pairs."""
+import gzip,hashlib,json,os,subprocess,sys
+from pathlib import Path
+P=Path(__file__).resolve().parent.parent;O=Path('split-centres')
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+c=json.load(gzip.open(O/'CANONICAL-WORD.json.gz'))
+r=json.loads((P/'inputs/complex-phase-receipt.json').read_text())
+raw=gzip.decompress((P/'inputs/complex-phase-recipes.json.gz').read_bytes());recipes=json.loads(raw)
+# Bind the canonical payload to the original frozen envelope. Python 3.11/3.12
+# and 3.14 emit different gzip OS bytes for identical contents.
+reference=P/'inputs/complex-canonical-reference.json.gz'
+assert sha(reference)==r['canonical_word_sha256']
+assert gzip.decompress((O/'CANONICAL-WORD.json.gz').read_bytes())==gzip.decompress(reference.read_bytes())
+r['frozen_canonical_envelope_sha256']=r['canonical_word_sha256']
+r['canonical_word_sha256']=sha(O/'CANONICAL-WORD.json.gz')
+r['canonical_payload_sha256']=hashlib.sha256(gzip.decompress(reference.read_bytes())).hexdigest()
+assert hashlib.sha256(raw).hexdigest()==r['recipe_sha256']
+edges=set(map(tuple,c['edges']))|{(a,b) for f in c['center_frames'] for a,b in ((f,0),(0,f))}
+assert {(z['old'],z['new']) for z in recipes['children']}==edges
+assert len(recipes['children'])==len(edges) and len(recipes['endpoint_adapters'])==240
+for z in recipes['children']:assert z['rank']==abs(len(c['frames'][z['old']])-len(c['frames'][z['new']]))
+if os.environ.get('E8_REPLAY_PHASES')=='1':
+ subprocess.run([sys.executable,'-B',str(P/'code/complex_phases_full.py')],check=True)
+ assert (O/'CLIFFORD-RECIPES.json').read_bytes()==raw
+else:
+ (O/'CLIFFORD-RECIPES.json').write_bytes(raw)
+ r['validation_mode']='Reuse exact phase evidence bound to the unchanged canonical word and recipe hashes'
+ (O/'CLIFFORD-REVIEW.json').write_text(json.dumps(r,indent=2)+'\n')
+print('PASS source-bound phase recipes',len(edges))
diff --git a/research/e8-joint-frame-retiming/code/complex_phases_full.py b/research/e8-joint-frame-retiming/code/complex_phases_full.py
new file mode 100644
index 0000000000..b5a5bd64b4
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/complex_phases_full.py
@@ -0,0 +1,39 @@
+# Adapted from PR425 for heterogeneous centres by icekylinx with Codex assistance.
+"""Exact phase-aware lowering of every used edge of the new structural word."""
+import gzip,hashlib,json,sys,time
+from collections import Counter
+from pathlib import Path
+sys.path.insert(0,str(Path('work/odd-stages').resolve()))
+from clifford_exact import *
+
+OUT=Path('split-centres');P=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(P));n=c['h'];frames=c['frames'];start=time.monotonic();ops=[]
+for U in frames:
+    op=canonical_frame(n,U)
+    L=[u|(u<<n) for u in U]+[v<<n for v in nullspace(U,n)]
+    pre=[x|(z<<n) for x,z,p in inverse(op.tab)[n:]]
+    assert rank(L)==n and rank(L+pre)==n
+    assert rank([x for x,z,p in op.tab[n:]])==len(U)
+    ops.append(op)
+edges=set(map(tuple,c['edges']))|{(a,b) for f in c['center_frames'] for a,b in ((f,0),(0,f))};recipes=[];hist=Counter()
+for i,(a,b) in enumerate(sorted(edges)):
+    op=ops[a].adjoint().then(ops[b]);rec,compiled=lower_child(op)
+    assert rec['rank']==abs(len(frames[a])-len(frames[b]))
+    hist[rec['rank']]+=1;recipes.append({'old':a,'new':b,**rec})
+    if i%200==0:print('exact phase edges',i,'/',len(edges),'seconds',time.monotonic()-start,flush=True)
+adapters=[];F=fourier(n)
+for i,q in enumerate(c['ports']):
+    for role,old,f in [('source',cgate(n,q),c['start'][i]),
+                       ('target',cgate(n,q).adjoint().then(F),c['final'][c['v']+i])]:
+        rec,compiled=lower_child(old.adjoint().then(ops[f]));assert rec['rank']==0
+        adapters.append({'port':i,'role':role,'frame':f,**rec})
+raw=json.dumps({'children':recipes,'endpoint_adapters':adapters},sort_keys=True,separators=(',',':')).encode()
+(OUT/'CLIFFORD-RECIPES.json').write_bytes(raw)
+result={'status':'PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES',
+        'canonical_word_sha256':hashlib.sha256(P.read_bytes()).hexdigest(),
+        'frames':len(frames),'directed_edges':len(edges),'ranks':dict(hist),
+        'endpoint_adapters':len(adapters),'all_child_equalities_include_global_phase':True,
+        'recipe_sha256':hashlib.sha256(raw).hexdigest(),'seconds':time.monotonic()-start,
+        'scope':'Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations.'}
+(OUT/'CLIFFORD-REVIEW.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS exact local phases',result['seconds'],'seconds',flush=True)
diff --git a/research/e8-joint-frame-retiming/code/complex_replay.py b/research/e8-joint-frame-retiming/code/complex_replay.py
new file mode 100644
index 0000000000..e9f0490478
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/complex_replay.py
@@ -0,0 +1,177 @@
+# Adapted for heterogeneous centres by icekylinx with Codex assistance.
+"""Independent read-back of the serialized local/global instruction stream."""
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');P=OUT/'GLOBAL-TEMPLATE.json.gz'
+ir=json.load(gzip.open(P));c=json.load(gzip.open(OUT/'CANONICAL-WORD.json.gz'))
+integration=json.loads((OUT/'INTEGRATION.json').read_text())
+assert hashlib.sha256(gzip.decompress(P.read_bytes())).hexdigest()==integration['global_template_sha256']
+assert c['ports']==json.load(gzip.open('work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz'))['ports']
+v,R,h=c['v'],c['R'],c['h'];n=2*v+R;frames=c['frames']
+def contains(a,b):
+    for x in a:
+        for y in b:
+            if x>>(y.bit_length()-1)&1:x^=y
+        if x:return False
+    return True
+def local(events,back):
+    rows={('L',r):{r:Q(1)} for r in range(n)}
+    norm={('L',r):Q(1) for r in range(n)};prefix=Q(1);cur=c['start'].copy();private={}
+    hist=Counter();phases=[];entry=[];exit=[];centers=[];matrix_hash=hashlib.sha256()
+    allowed=['zero_frame_precondition','entry_adapters','A','centers','B','final','exit_adapters','full_frame_cleanup','done']
+    for event in events:
+        tag=event[0]
+        if tag=='phase':
+            phases.append(event[1]);assert phases==allowed[:len(phases)]
+            if event[1]=='A':assert entry==list(enumerate(c['start']))
+            if event[1]=='centers':assert all(cur[r]==0 for r in range(v,2*v))
+            if event[1]=='full_frame_cleanup':assert cur==c['final'] and exit==list(enumerate(c['final']))
+            assert not private
+        elif tag=='adapter':
+            assert event[3]==(c['start'] if event[1]=='old_to_new' else c['final'])[event[2]]
+            (entry if event[1]=='old_to_new' else exit).append((event[2],event[3]))
+        elif tag=='climb':
+            _,part,r,a,b,rank=event
+            assert not private and phases[-1]==part and cur[r]==a
+            assert contains(frames[a],frames[b]) and rank==len(frames[b])-len(frames[a])>0
+            hist[rank]+=1;cur[r]=b
+        elif tag=='center':
+            _,k,a,b,rank=event
+            assert phases[-1]=='centers' and private=={('C',k):a}
+            cf=c['center_frames'][k];cr=len(frames[cf])
+            assert (a,b,rank)==((0,cf,cr) if back else (cf,0,cr))
+            private['C',k]=b;hist[rank]+=1;centers.append(k)
+        elif tag=='scalar':
+            _,e,f=event;op=e[0];target=tuple(e[1]);source=tuple(e[2]) if op in ('copy','add') else None
+            if target[0]=='C' and op=='clear':
+                assert private.get(target,f)==f
+                private.pop(target,None)
+            else:
+                for r in (target,source):
+                    if r is None:continue
+                    if r[0]=='L':assert cur[r[1]]==f,('common frame',r,cur[r[1]],f)
+                    else:
+                        if r==target and r not in private:private[r]=f
+                        assert private[r]==f
+            if op=='clear':rows[target]={};norm[target]=Q(0)
+            elif op=='copy':rows[target]=dict(rows[source]);norm[target]=norm[source]
+            elif op=='scale':
+                q=Q(e[2],e[3]);a,b=abs(q.numerator),q.denominator
+                assert a&(a-1)==0 and b&(b-1)==0
+                rows[target]={j:q*x for j,x in rows[target].items()};norm[target]*=abs(q)
+            else:
+                q=Q(e[3],e[4]);a,b=abs(q.numerator),q.denominator
+                assert source!=target and b&(b-1)==0
+                # Independent symbolic replay of the cleared coefficient work.
+                w=0
+                for bit in bin(a)[2:]:w=2*w+int(bit)
+                assert Q(w,b)*(1 if q>0 else -1)==q
+                prefix=max(prefix,Q(a)*norm[source])
+                norm[target]=norm.get(target,Q(0))+abs(q)*norm[source]
+                row=rows.setdefault(target,{})
+                for j,x in list(rows[source].items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+            prefix=max(prefix,norm[target])
+        else:raise AssertionError(tag)
+    assert phases==allowed and centers==list(range(len(c['centers']))) and not private
+    assert all(not row for reg,row in rows.items() if reg[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert rows['L',r]==expected
+    # A 192-bit local payload allowance vastly dominates even coefficient work.
+    assert prefix<2**192
+    return hist,{'all_exact_columns':n,'prefix_l1_upper':str(prefix),
+                 'prefix_bits_upper':prefix.numerator.bit_length()-prefix.denominator.bit_length()+1,
+                 'charged_payload_bits':192,'private_work_erased':True}
+
+profiles={};checks={}
+for name in ('forward','backward'):
+    profiles[name],checks[name]=local(ir['local_programs'][name],name=='backward')
+    assert dict(profiles[name])=={int(r):z for r,z in c['local_profile'].items()}
+    print('independent emitted replay PASS',name,flush=True)
+controls=[]
+for name,mut in [
+    ('wrong_scale',lambda es:next(e for e in es if e[0]=='scalar' and e[1][0]=='scale')[1].__setitem__(2,3)),
+    ('missing_center',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center'))),
+    ('wrong_common_frame',lambda es:next(e for e in es if e[0]=='scalar' and e[2]!=0).__setitem__(2,0)),
+    ('wrong_child_rank',lambda es:next(e for e in es if e[0]=='climb').__setitem__(5,99)),
+]:
+    es=copy.deepcopy(ir['local_programs']['forward']);mut(es)
+    try:local(es,False)
+    except (AssertionError,KeyError):controls.append(name)
+    else:raise AssertionError('mutation accepted: '+name)
+
+def global_check(t):
+    assert t['live']==12720 and t['physical']==13298
+    # Eight data-wire scalar columns, independently recomposed.
+    matrix=[[int(i==j) for j in range(8)] for i in range(8)]
+    for e in t['recipe']:
+        if e['kind']=='local':
+            a=2*e['pair'];b=a+1;dst,src,q=(a,b,-1) if e['reverse'] else (b,a,1)
+            matrix[dst]=[x+q*y for x,y in zip(matrix[dst],matrix[src])]
+        elif e['kind']=='bridge':
+            i,j,q=e['dst'],e['src'],e['coefficient']
+            matrix[2*i]=[x+q*y for x,y in zip(matrix[2*i],matrix[2*j])]
+            matrix[2*j+1]=[x-q*y for x,y in zip(matrix[2*j+1],matrix[2*i+1])]
+        else:
+            assert e['kind']=='terminal';old=copy.deepcopy(matrix)
+            for i in range(4):matrix[2*i]=old[2*i+1];matrix[2*i+1]=[-x for x in old[2*i]]
+    assert matrix==[[int(i==j) for j in range(8)] for i in range(8)]
+    seen=set();hist=Counter();pairs={e['stage']:e for e in t['recipe'] if e['kind']=='local'}
+    for call in t['calls']:
+        stage,rep,pair=call['stage'],call['replica'],call['pair']
+        assert (stage,rep) not in seen;seen.add((stage,rep))
+        assert pair==pairs[stage]['pair']
+        assert call['orientation']==('backward' if pairs[stage]['reverse'] else 'forward')
+        assert len(call['owners'])==800
+        for r,(fam,route) in enumerate(call['owners']):
+            if r<240:assert fam==rep*960+(2*pair+r//120)*120+r%120 and route==[1,stage,r%120]
+            else:
+                z=rep*560+r-240;assert fam==7680+stage*560+z//8 and route==[2,z%8]
+        assert len(set((f,tuple(r)) for f,r in call['owners']))==800
+        for r,z in profiles[call['orientation']].items():hist[r]+=z
+    assert seen=={(s,r) for s in range(9) for r in range(8)}
+    for child in t['idle_children']:hist[child['rank']]+=child['replicas']
+    assert t['bank_padding']=={'families':list(range(7680,12720)),'axis':72,'child_rank':1}
+    hist[1]+=5040
+    assert t['cover_final_correction']['families']==[0,12720]
+    assert t['cover_final_correction']['charged_calls_per_cover']==12720
+    assert t['execution_schedule'][-1]=={'kind':'translate_every_live_family',**{k:v for k,v in t['cover_final_correction'].items() if k!='kind'}}
+    assert 73*12720-sum(r*z for r,z in hist.items())==2496
+    return hist
+H=global_check(ir)
+for name,mut in [('missing_padding',lambda t:t['bank_padding']['families'].pop()),
+                 ('aliased_owner',lambda t:t['calls'][0]['owners'][241].__setitem__(1,[2,0])),
+                 ('missing_cover_phase',lambda t:t['cover_final_correction'].__setitem__('charged_calls_per_cover',0))]:
+    t=copy.deepcopy(ir);mut(t)
+    try:global_check(t)
+    except (AssertionError,KeyError):controls.append(name)
+    else:raise AssertionError('global mutation accepted: '+name)
+assert dict(H)=={int(r):z for r,z in integration['global_profile'].items()}
+
+def load(name):
+    sp=importlib.util.spec_from_file_location('replay_hamming_'+name,Path('work/pr361/code/engines')/(name+'.py'))
+    m=importlib.util.module_from_spec(sp);sp.loader.exec_module(m);return m
+M,B=load('moment'),load('base_two_moment');b=Q(integration['complex_b']);grid=Q(1,10**18)
+assert M.moment(H,73,12720,b,True)[1]<1<M.moment(H,73,12720,b+grid,True)[0]
+def other(a):
+    lo,hi=B.moment(73,12720,list(H.items()),a)
+    l2,h2=B.moment(73,12720,[(1,32*73**2*sum(H.values()))],a)
+    return lo+l2/10**16,hi+h2/10**16
+assert other(b)[1]<1<other(b+grid)[0]
+result={'status':'PASS_INDEPENDENT_NEW_STRUCTURAL_IR_REPLAY',
+        'template_sha256':integration['global_template_sha256'],'local':checks,
+        'mutation_controls_rejected':controls,'all_eight_global_scalar_columns':True,
+        'bank_owners_and_padding_exact':True,'paid_profile':dict(sorted(H.items())),
+        'two_rational_moment_engines':True,'complex_b':str(b),
+        'next_b_grid_rejected':True,
+        'scope':'Independent finite replay; retains the written generic scalar-interface lemma and inherited all-size/analytic assumptions.'}
+(OUT/'INDEPENDENT-REPLAY.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS independent local/global replay and two exact moments',flush=True)
diff --git a/research/e8-joint-frame-retiming/code/independent_audit.py b/research/e8-joint-frame-retiming/code/independent_audit.py
new file mode 100644
index 0000000000..67367d6df4
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/independent_audit.py
@@ -0,0 +1,345 @@
+"""Independent R740-kernel audit: source word, emitted banks, invoice and exact outer arithmetic.
+Usage: python independent_audit.py PACKAGE REPLAY_OUTPUT AUDIT_JSON
+Python standard library only. No construction, discovery or pricing imports.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+import sys,json,gzip,hashlib,math,copy
+
+def audit_local(base_path,word_path,selection_path,retime_path=None):
+ base=json.loads(gzip.decompress(base_path.read_bytes()));w=json.loads(word_path.read_bytes());s=json.loads(selection_path.read_bytes())
+ sha=lambda x:hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+ assert sha(base)==s['input_sha256']=='d6ec8811541d6ab59a3bbbaaa15bccc8918b3b43b23d9f593198cfe90826fd20';assert retime_path is not None or sha(w)==s['output_sha256']
+ n=2*w['v']+w['R'];v=w['v'];h=w['h'];full=set(range(v));lines=w['lines']
+ assert w['frames']==base['frames'] and w['lines']==base['lines']
+ def primitive(x):
+  g=math.gcd(*x)
+  return [a//g for a in x] if g else x
+
+ def basis(vectors):
+  B={}
+  for x in vectors:
+   x=list(x)
+   for p,b in B.items():
+    if x[p]:
+     q=x[p];x=primitive([b[p]*a-q*c for a,c in zip(x,b)])
+   p=next((j for j,z in enumerate(x) if z),None)
+   if p is not None:B[p]=primitive(x)
+  return B
+
+ def contained(x,B):
+  x=list(x)
+  for p,b in B.items():
+   if x[p]:
+    q=x[p];x=primitive([b[p]*a-q*c for a,c in zip(x,b)])
+  return not any(x)
+ F=[set(x) for x in w['frames']];B=[basis(lines[i] for i in f) for f in F];dims=list(map(len,B))
+ for f,b in zip(F,B):assert f=={i for i,x in enumerate(lines) if contained(x,b)},'frame closure'
+ resp=defaultdict(int)
+ for f,t,src in base['D']:
+  assert not F[f] and v<=t<2*v
+  for q in src:resp[q]^=1<<(t-v)
+ first={q:None for q in range(2*v,n)}
+ for ph in ('D','A','B','C'):
+  for f,d,src in base[ph]:
+   if F[f]:
+    for q in [d]+src:
+     if q in first and first[q] is None:first[q]=F[f]
+ for q in first:
+  if first[q] is None:first[q]=F[base['final'][q]]
+ piv={};donors={};bydon=defaultdict(list);rank=0
+ for ef,p,ds in s['entries']:
+  E=set(ef);assert E and E in F and len(ds)==len(set(ds));assert 2*v<=p<n and p not in piv and p not in donors and p not in base['ret']
+  z=resp[p]
+  for d in ds:
+   assert 2*v<=d<n and d not in piv and d not in base['ret'];assert donors.setdefault(d,E)==E;bydon[d,tuple(ef)].append(p);z^=resp[d]
+  assert z==0,('response relation',p)
+  assert all(E<=first[q] for q in [p]+ds),('first frame',p)
+  piv[p]=E;rank+=len(basis(lines[i] for i in E))
+ assert not (set(piv)&set(donors));assert rank==s['total_entrance_rank'] and rank%8==0
+ assert len(piv)==s['entries_count'];assert len(bydon)==s['donor_slots']
+ # Reconstruct exactly using our own indices and sorted grouping.
+ r=copy.deepcopy(base)
+ for p,E in piv.items():r['start'][p]=next(i for i,f in enumerate(F) if f==E)
+ r['D']=[[f,t,[q for q in src if q not in piv]] for f,t,src in base['D']]
+ pre=[[next(i for i,f in enumerate(F) if f==set(E)),d,sorted(ps)] for (d,E),ps in sorted(bydon.items(),key=lambda kv:(kv[0][0],sum(1<<i for i in kv[0][1])))]
+ post=[[next(i for i,f in enumerate(F) if f==full),d,sorted(ps)] for (d,E),ps in sorted(bydon.items(),key=lambda kv:(kv[0][0],sum(1<<i for i in kv[0][1])))]
+ r['A']=pre+base['A'];r['C']=base['C']+post
+ assert sha(r)==s['output_sha256'],'independent kernel reconstruction differs'
+ retiming_changes=0
+ if retime_path is not None:
+  rs=json.loads(retime_path.read_bytes());assert rs['input_sha256']==sha(r)
+  primitive=copy.deepcopy(r)
+  for ph in ('D','A','B','C'):primitive[ph]=[[f,d,[src]] for f,d,ss in r[ph] for src in ss]
+  expanded_input_sha=sha(primitive)
+  assert expanded_input_sha=='cb2afa377baeb8578e867ecda0f81caa68b2dac9cca805f41247754cfe91deb5'
+  if 'primitive_input_sha256' in rs:assert rs['primitive_input_sha256']==expanded_input_sha
+  for ph in ('D','A','B','C'):
+   assert [(d,src) for f,d,ss in primitive[ph] for src in ss]==[(d,src) for f,d,ss in w[ph] for src in ss],'primitive scalar sequence changed'
+   assert all(len(ss)==1 for f,d,ss in w[ph])
+  done=set()
+  for ph,k,old,new in rs['gates']:
+   assert ph in ('A','B') and (ph,k) not in done;done.add((ph,k));f,d,ss=primitive[ph][k]
+   assert primitive['frames'][f]==old and set(old)!=set(new)
+   nf=next(i for i,fr in enumerate(primitive['frames']) if fr==new);primitive[ph][k]=[nf,d,ss]
+  assert primitive==w and sha(w)==rs['output_sha256'];retiming_changes=len(done)
+ else:assert r==w,'independent reconstruction differs'
+
+ # Independent scalar expansion and forward chronology.
+ cur=w['start'][:];ev=[];hist=Counter();coeff=[{i:1} if i<v else {} for i in range(n)];spanchecks=0
+ for phase in ('D','A','scatter','B','C'):
+  if phase=='scatter':
+   for k,q in enumerate(w['ret']):
+    assert dims[cur[q]]==8
+    ev.append(('copy',q));hist[8]+=1
+    for t,sc in enumerate(w['scatter']):
+     for kk in sc:
+      if kk==k:ev.append(('add',v+t,n))
+    ev.append(('erase',q))
+   continue
+  for f,d,src in w[phase]:
+   assert d not in src and len(set(src))==len(src)
+   for q in [d]+src:
+    if cur[q]!=f:
+     assert F[cur[q]]<=F[f];delta=dims[f]-dims[cur[q]];assert delta>=0
+     ev.append(('move',q,cur[q],f,delta));hist[delta]+=bool(delta);cur[q]=f
+   for q in src:
+    if q<v or q>=2*v:assert set(coeff[q])<=F[f];spanchecks+=1
+    for x,c in coeff[q].items():coeff[d][x]=coeff[d].get(x,0)+c
+    ev.append(('add',d,q))
+   if d<v or d>=2*v:assert set(coeff[d])<=F[f];spanchecks+=1
+ for q,f in enumerate(w['final']):
+  if cur[q]!=f:
+   assert F[cur[q]]<=F[f];delta=dims[f]-dims[cur[q]];assert delta>=0
+   ev.append(('move',q,cur[q],f,delta));hist[delta]+=bool(delta);cur[q]=f
+ hist.pop(0,None)
+ assert cur==w['final']
+ def scalar(events,rev=False,omit=None):
+  vals=[1<<q for q in range(n)]+[0];current=(w['final'] if rev else w['start'])[:];hs=Counter();copies=0
+  for idx,e in enumerate(reversed(events) if rev else events):
+   if omit is not None and omit(e,idx):continue
+   if e[0]=='move':
+    _,q,a,b,d=e
+    if rev:a,b=b,a
+    assert current[q]==a;delta=(h-dims[b])-(h-dims[a]) if rev else dims[b]-dims[a]
+    assert delta==d and delta>=0;current[q]=b
+    if d:hs[d]+=1
+   elif e[0]=='add':vals[e[1]]^=vals[e[2]]
+   elif e[0]==('erase' if rev else 'copy'):
+    assert vals[n]==0;vals[n]=vals[e[1]];hs[8]+=1;copies+=1
+   else:
+    assert e[0]==('copy' if rev else 'erase') and vals[n]==vals[e[1]];vals[n]=0
+  assert current==(w['start'] if rev else w['final']);assert copies==len(w['ret'])
+  assert all(vals[q]==((1<<q)^((1<<(q-v)) if v<=q<2*v else 0)) for q in range(n)) and vals[n]==0,'scalar/dirty failure'
+  assert hs==hist
+  return dict(all_columns=n,dirty_columns=w['R'],copies=copies,paid_profile=dict(sorted(hs.items())))
+ forward=scalar(ev);reverse=scalar(ev,True)
+ # Negative controls must break the actual scalar computation.
+ controls=[]
+ first_event=next(i for i,e in enumerate(ev) if e==('add',pre[0][1],pre[0][2][0]))
+ last_event=max(i for i,e in enumerate(ev) if e==('add',post[-1][1],post[-1][2][0]))
+ for name,pred in [('omitted_first_basis',lambda e,i:i==first_event),('omitted_final_basis',lambda e,i:i==last_event)]:
+  try:scalar(ev,omit=pred)
+  except AssertionError:controls.append(name)
+  else:raise AssertionError(name)
+ for name,entries in [('missing_donor',copy.deepcopy(s['entries']))]:
+  E,p,ds=entries[0];z=resp[p]
+  for d in ds[1:]:z^=resp[d]
+  assert z!=0;controls.append(name)
+ result=dict(retiming_changes=retiming_changes,status='PASS_INDEPENDENT_R740_KERNEL_AND_RETIMING' if retiming_changes else 'PASS_INDEPENDENT_R740_KERNEL',source_sha256=sha(base),candidate_sha256=sha(w),entries=len(piv),donor_slots=len(bydon),total_entrance_rank=rank,root_closed_frames=len(F),source_span_checks=spanchecks,forward=forward,reflected=reverse,negative_controls=controls,events=len(ev),scope='Independent reconstruction, every F2 scalar column and dirty restoration, exact source span/first-frame relations and both complementary dimension ledgers; global banking and pricing audited separately.')
+ return dict(w=w,ev=ev,hist=hist,dims=dims,sha=sha,receipt=result)
+
+P=Path(sys.argv[1]);O=Path(sys.argv[2]);out=Path(sys.argv[3])
+retime_path=next((p for p in (P/'stages/retime-selection.json',P/'stages/retiming-selection.json') if p.exists()),None)
+a=audit_local(P/'vendor/pr436/data/bit/bitE8-r740.json.gz',O/'bit426-source-centres/bit-source-centres.json',P/'stages/kernel-selection.json',retime_path)
+local_receipt=a['receipt']
+w,ev,localH,dims=a['w'],a['ev'],a['hist'],a['dims'];R=w['R'];N=240+R;D=O/'bit426-source-centres/global'
+read=lambda p:json.loads(p.read_bytes());sha=lambda b:hashlib.sha256(b).hexdigest()
+g=read(D/'GLOBAL.json');geo=read(D/'GEOMETRY.json');result=read(O/'RESULT.json');blob=gzip.decompress((D/'GLOBAL-TEMPLATE.json.gz').read_bytes());t=json.loads(blob)
+assert g['word_sha256']==a['sha'](w) and sha(blob)==g['template_sha256']==result['bit_template_sha256']
+assert t['geometry_sha256']==sha((D/'GEOMETRY.json').read_bytes())
+assert t['source_record_sha256']==sha((O/'bit426-source-centres/records/249-records.bin').read_bytes())
+# Compare both emitted scalar streams with the independently expanded source word.
+def normalize(prog):
+ out=[]
+ for e in prog:
+  if e[0]==0:out.append(('move',e[1],e[2],e[3],e[4]))
+  elif e[0]==1:assert abs(e[3])==1;out.append(('add',e[1],e[2]))
+  elif e[0]==2:assert e[5]==8;out.append(('copy',e[1]))
+  else:out.append(('erase',e[1]))
+ return out
+assert normalize(t['local_programs']['forward'])==ev
+rev=[]
+for e in reversed(ev):
+ if e[0]=='move':rev.append(('move',e[1],e[3],e[2],e[4]))
+ elif e[0]=='copy':rev.append(('erase',e[1]))
+ elif e[0]=='erase':rev.append(('copy',e[1]))
+ else:rev.append(e)
+assert normalize(t['local_programs']['reverse'])==rev
+width=[8-dims[f] for f in w['start'][240:]];ENT=sum(8-x for x in width);NB=R-ENT//8;W=7680+9*NB
+assert ENT%8==0 and (NB,W)==(723,14187)
+assert (t['live'],t['banks_per_stage'],t['private_centre_reserve'],t['replicas'],t['stages'],t['entrance_rank_total'])==(W,NB,9,8,9,ENT)
+assert g['physical']==W+9 and t['bank_padding'] is None
+# Explicit isometries from E-perp to coordinate blocks, checked independently.
+def validate_routes(routes):
+ byframe={}
+ for r in routes:
+  f=r['frame'];rank=r['entrance_rank'];matrix=r['orthogonal_rows_numerator']
+  assert f not in byframe and rank==dims[f] and r['denominator']==2
+  indices=r['entrance_basis']+r['residual_basis'];assert len(indices)==8 and len(r['entrance_basis'])==rank
+  assert matrix==[w['lines'][i] for i in indices] and len(matrix)==8 and all(len(row)==8 for row in matrix)
+  assert all(type(x) is int and x%2==0 for row in matrix for x in row)
+  dot=lambda u,v:sum(x*y for x,y in zip(u,v))
+  assert all(dot(u,v)==4*int(i==j) for i,u in enumerate(matrix) for j,v in enumerate(matrix))
+  assert all(sum(dot(w['lines'][i],row)**2 for row in matrix[:rank])==4*dot(w['lines'][i],w['lines'][i]) for i in w['frames'][f])
+  reduced=[[Q(x,2) for x in row] for row in matrix];ops=r['gaussian_reduction'];assert len(ops)<=7
+  for op,i,j,c in ops:
+   assert op=='swap' and c is None and i in range(8) and j in range(8);reduced[i],reduced[j]=reduced[j],reduced[i]
+  assert reduced==[[int(i==j) for j in range(8)] for i in range(8)];byframe[f]=r
+ assert set(byframe)==set(w['start'][240:])
+ return byframe
+isometries=validate_routes(t['residual_isometries']);route_controls=[]
+for name in ('altered_basis','missing_factor','wrong_frame'):
+ damaged=copy.deepcopy(t['residual_isometries'])
+ if name=='altered_basis':damaged[0]['orthogonal_rows_numerator'][0][0]+=1
+ elif name=='missing_factor':next(r for r in damaged if r['gaussian_reduction'])['gaussian_reduction'].pop()
+ else:damaged[0]['frame']=damaged[1]['frame']
+ try:validate_routes(damaged)
+ except AssertionError:route_controls.append(name)
+ else:raise AssertionError(name)
+occ=defaultdict(int);seen=set();paid=Counter();events=0;assign=0;expanded=hashlib.sha256()
+for call in t['calls']:
+ st,rep,p,ori=call['stage'],call['replica'],call['pair'],call['orientation'];rv=ori=='reverse'
+ assert st in range(9) and rep in range(8) and (st,rep) not in seen;seen.add((st,rep));assert p==max(0,(st-1)//2) and rv==(st in (1,3,5,7))
+ owners=call['owners'];assert len(owners)==N
+ for q,(family,route) in enumerate(owners):
+  if q<240:
+   side=q//120
+   if rv:side=1-side
+   assert family==rep*960+(2*p+side)*120+q%120 and route==['data',st,q%120]
+  else:
+   assert len(route)==4 and route[3]==w['start'][q] and route[3] in isometries and route[0]=='bank' and route[2]==width[q-240] and 7680+st*NB<=family<7680+(st+1)*NB
+   bits=((1<<route[2])-1)<<route[1];assert 0<=route[1] and bits<1<<64 and not(occ[family]&bits);occ[family]|=bits;assign+=1
+ for e in t['local_programs'][ori]:
+  events+=1
+  if e[0]==0:
+   if e[4]:paid[e[4]]+=1
+   mapped=[0,owners[e[1]],*e[2:]]
+  else:
+   mapped=[e[0],owners[e[1]],owners[e[2]] if e[2]<N else [W,['private',0]],*e[3:]]
+   if e[0]==2:paid[e[5]]+=1
+  expanded.update((json.dumps(mapped,separators=(',',':'))+'\n').encode())
+assert seen=={(s,r) for s in range(9) for r in range(8)} and len(occ)==9*NB and all(z==(1<<64)-1 for z in occ.values())
+assert events==g['emitted_events']==72*len(ev) and expanded.hexdigest()==g['emitted_program_sha256'];assert assign==g['bank_assignments']==72*R
+# Every unbanked global basis column from the independently expanded source events.
+GN=960+9*R;values=[1<<q for q in range(GN)]+[0];global_stages=[]
+for schedule_event in t['schedule']:
+ kind=schedule_event['kind']
+ if kind=='local_cover_sweep':
+  st,p,rv=schedule_event['stage'],schedule_event['pair'],schedule_event['reverse'];before=values[:]
+  def owner(q):
+   if q==N:return GN
+   if q<240:
+    side=q//120
+    if rv:side=1-side
+    return (2*p+side)*120+q%120
+   return 960+st*R+q-240
+  for e in (rev if rv else ev):
+   if e[0]=='add':values[owner(e[1])]^=values[owner(e[2])]
+   elif e[0]=='copy':assert values[GN]==0;values[GN]=values[owner(e[1])]
+   elif e[0]=='erase':assert values[GN]==values[owner(e[1])];values[GN]=0
+  source,destination=(2*p+int(rv))*120,(2*p+int(not rv))*120
+  for q in range(120):before[destination+q]^=before[source+q]
+  assert values==before;global_stages.append(st)
+ elif kind=='bridge':
+  d,src=schedule_event['dst'],schedule_event['src']
+  for q in range(120):values[2*d*120+q]^=values[2*src*120+q];values[(2*src+1)*120+q]^=values[(2*d+1)*120+q]
+ elif kind=='exchange':
+  for p in range(4):
+   for q in range(120):x,y=2*p*120+q,(2*p+1)*120+q;values[x],values[y]=values[y],values[x]
+assert values==[1<<q for q in range(GN)]+[0] and global_stages==list(range(9))
+# Exact signed scalar 8-block assembly and its 18 bridge omission controls.
+def small(skip=-1):
+ z=[[int(i==j) for j in range(8)] for i in range(8)];level=[-1]*4;stages=[];bridge=0;exchange=0
+ def add(d,s,coef):z[d]=[x+coef*y for x,y in zip(z[d],z[s])]
+ for e in t['schedule']:
+  kind=e['kind']
+  if kind=='local_cover_sweep':
+   st,p,rv=e['stage'],e['pair'],e['reverse'];assert level[p]==st-1;level[p]=st;stages.append(st)
+   add(2*p,2*p+1,-1) if rv else add(2*p+1,2*p,1)
+  elif kind=='idle':
+   p,u,d,r=e['pair'],e['source_level'],e['target_level'],e['rank'];assert level[p]==u and u<=d<=8 and r==7*(d-u);level[p]=d
+  elif kind=='bridge':
+   d,s,c=e['dst'],e['src'],e['coefficient'];assert level[d]==level[s] and abs(c)==1
+   for x,y,coef in [(2*d,2*s,c),(2*s+1,2*d+1,-c)]:
+    if bridge!=skip:add(x,y,coef)
+    bridge+=1
+  else:
+   assert kind=='exchange' and level==[8]*4 and exchange==0;exchange+=1
+   for p in range(4):z[2*p],z[2*p+1]=z[2*p+1],[-x for x in z[2*p]]
+ assert stages==list(range(9)) and bridge==18 and exchange==1
+ return z
+identity=[[int(i==j) for j in range(8)] for i in range(8)];assert small()==identity
+assert all(small(i)!=identity for i in range(18))
+for e in t['schedule']:
+ if e['kind']=='idle' and e['rank']:paid[e['rank']]+=1920
+assert dict(sorted(paid.items()))=={int(k):v for k,v in g['profile'].items()};E=sum(paid.values());mass=sum(r*c for r,c in paid.items());assert 64*W-mass==2496
+# Derive scalar norm guards from actual source events, not stored summary counts.
+def norm(events):
+ z=[1]*N+[0];mx=1
+ for e in events:
+  if e[0]=='add':z[e[1]]+=z[e[2]];mx=max(mx,z[e[1]])
+  elif e[0]=='copy':z[N]=z[e[1]]
+  elif e[0]=='erase':z[N]=0
+ return mx
+cf,cb=norm(ev),norm(rev);prefix=2**18*cf**5*cb**4
+assert cf==g['local_checks']['forward']['cancellation_free_row_l1'] and cb==g['local_checks']['reverse']['cancellation_free_row_l1']
+assert prefix==int(g['global_prefix_bound']) and prefix<2**128
+localadds=sum(e[0]=='add' for e in ev);copies=sum(e[0]=='copy' for e in ev)
+assert localadds==g['local_additions'] and copies==9 and g['bridge_additions']==18*120*8 and g['copy_erase_episodes']==72*copies
+J=8*8*9*N+8*7680+2*assign+2*72*copies
+selectors=2*9*8*((W-1)+R*64*(geo['max_route_factors']+144+63+64))
+coefficient=72*localadds+18*120*8+J*(16*(4097)**2)+J*(W+9)+E*((8*64*64+8)+128*128**3)+16*64**3+72*copies+selectors+prefix+1
+two=(coefficient+1)**2*(E+1)**2;assert two<2**512 and 2*max(paid)**2<64**2
+invoice=dict(prefix_bits=prefix.bit_length(),charged_prefix_bits=128,coefficient_bits=coefficient.bit_length(),two_level_coefficient_bits=two.bit_length(),charged_two_level_coefficient_bits=512,row_coefficient=18355,live=W,physical=W+9)
+invoice.update(extra_helper_route_factor_bound=144,selector_charge=selectors,full_counted_coefficient=str(coefficient),two_level_coefficient=str(two))
+assert invoice==result['bit_invoice'];assert geo['bad_prime_factors']==[2] and geo['route_denominators']==[1,2,4]
+# Third rational moment enclosure: range-reduced atanh series + positive exponential series.
+GRID=10**70
+from functools import lru_cache
+@lru_cache(None)
+def log_bounds(x):
+ k=0
+ while x>2:x/=2;k+=1
+ def unit(y):
+  z=(y-1)/(y+1);s=Q(0);power=z
+  for j in range(100):s+=2*power/(2*j+1);power*=z*z
+  return s,s+2*power/(201*(1-z*z))
+ l,u=unit(x);l2,u2=unit(Q(2));return Q(((l+k*l2)*GRID).__floor__(),GRID),Q(((u+k*u2)*GRID).__ceil__(),GRID)
+def expo(x):
+ assert 0<=x<1;t=s=Q(1)
+ for j in range(1,25):t*=x/j;s+=t
+ return s,s+t*x/25/(1-x/26)
+def moment(c):
+ lo=hi=Q(0)
+ for r,count in list(paid.items())+[(1,Q(32*64*64*E,10**16))]:
+  l,u=log_bounds(Q(64,r));a,b=expo(c*l)[0],expo(c*u)[1];lo+=Q(r*count,64*W)*a;hi+=Q(r*count,64*W)*b
+ return lo,hi
+c=Q(result['bit_lower']);l,u=moment(c);assert u<1
+lup,uup=moment(c+Q(1,10**24));assert lup>1
+# Recompute finite bootstrap and every exact outer inequality without pricing imports.
+b=Q(result['complex_lower']);eta=beta=Q(1,10**18);s=min(c,(1-beta)*b)-Q(1,10**24);chain=[Q(384599,10**10)];cuts=[]
+for _ in range(6):
+ old=chain[-1];a=(1-s)*s+s*old;gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+ ceil=lambda x:-((-x.numerator)//x.denominator)
+ cut=max(ceil(36/gap**2),ceil(2*(4+512)/gap));assert cut*gap**2>=36 and cut*gap>=1032;cuts.append({'gap':str(gap),'cutoff_log2':str(cut)});chain.append(a)
+assert cuts==result['bootstrap'];a=chain[-1];q=a*(1-2*eta);tau,sigma=1-a,1-b;lp=1-q;lam=(tau+lp)/2;cc=q+eta/4;eps=(1-eta)/(1+q);minimum=eps*q;rr=(minimum+1-eps)/2;delta=eta/8;internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+margin={'balanced_prefix':1-eps,'coordinate_movement':a,'compact_phase_layer':minimum,'bulk_exposure':a,'Gaussian_arithmetic':min(1-eps-delta,rr-delta),'scalar_work':1-eps-delta,'dimension':eps}
+k=Q(((minimum*10**18).numerator-1)//(minimum*10**18).denominator,10**18);assert k==Q(result['kappa']) and k<minimum<=k+Q(1,10**18)
+slack=dict(bit_positive=a,complex_above_bit=b-a,complex_below_one_over32=Q(1,32)-b,beta_positive=beta,beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,c_positive=cc,c_below_one=1-cc,q_below_reservations=cc-q,lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,compact_leaf=lp-leaf,compact_reservations=lp-(1-cc),lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,guard_width=1-eps,K_geometry=1-eps*(1+cc),K_dominates_log=eps*cc,record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=rr-delta,gamma_sublinear=1-eps-rr,cell_above_band=eps-(1-rr)/2,prime_interval_packing=1-eps,alpha_positive=rr,alpha_below_one=1-rr,alpha_below_one_fourth=Q(1,4)-rr,delta_positive=delta,delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,small_field_exposure=1-eps-minimum,artificial_boundary=8-eps+rr-delta-minimum,literal_scalar_guard=Q(1),row_product_gap=Q(10**6)-Q(51*20161,25))
+slack.update({name+'_above_kappa':value-k for name,value in margin.items()});assert len(slack)==47 and min(slack.values())>0
+assert {name:str(value) for name,value in slack.items()}==result['strict_outer_constraints']
+r=dict(local_audit=local_receipt,status='PASS_INDEPENDENT_GLOBAL_INVOICE_AND_EXACT_ASSEMBLY',candidate_sha256=g['word_sha256'],global_template_sha256=g['template_sha256'],expanded_program_sha256=expanded.hexdigest(),events=events,global_scalar_columns=GN,global_dirty_columns=9*R,all_global_scalar_columns_restored=True,bank_assignments=assign,bank_families=len(occ),residual_isometries=len(isometries),route_corruption_controls=route_controls,extra_route_factors=144,banks_per_stage=NB,live=W,physical=W+9,paid_profile=dict(sorted(paid.items())),deficit=2496,source_bound_invoice=invoice,independent_moment='third rational enclosure; lower passes, adjacent upper fails',bit_lower=str(c),kappa=str(k),kappa_decimal=result['kappa_decimal'],strict_outer_constraints=len(slack),bridge_omission_controls=18,bootstrap_levels=6)
+out.write_text(json.dumps(r,indent=2)+'\n');print(json.dumps(r,indent=2))
diff --git a/research/e8-joint-frame-retiming/code/primitive_retime.py b/research/e8-joint-frame-retiming/code/primitive_retime.py
new file mode 100644
index 0000000000..e6e7317a14
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/primitive_retime.py
@@ -0,0 +1,27 @@
+"""Apply the pinned joint A/B primitive retiming to the V2 kernel word.
+Selection and output hashes are exact; scalar gate operands remain unchanged.
+OpenAI Codex integration, using the finite candidate found by search_r740_quad.
+"""
+import copy,hashlib,json
+from pathlib import Path
+
+def content(w): return hashlib.sha256(json.dumps(w,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+def apply(src,sel):
+ w=copy.deepcopy(src); frame_map={tuple(sorted(x)):i for i,x in enumerate(w['frames'])}
+ assert sel['input_sha256']==content(w)
+ for ph in ('D','A','B','C'):w[ph]=[[f,d,[x]] for f,d,ss in w[ph] for x in ss]
+ assert content(w)==sel['primitive_input_sha256']
+ prepared=copy.deepcopy(w)
+ changed=0
+ seen=set()
+ for ph,i,old_lines,new_lines in sel['gates']:
+  assert ph in ('A','B') and (ph,i) not in seen; seen.add((ph,i))
+  gate=w[ph][i]; old=tuple(sorted(w['frames'][gate[0]])); assert old==tuple(sorted(old_lines)),(ph,i,old,old_lines)
+  nf=tuple(sorted(new_lines)); assert nf in frame_map
+  gate[0]=frame_map[nf]; changed+=1
+ assert changed==len(sel['gates']) and all(g[1:]==prepared[ph][i][1:] for ph in ('D','A','B','C') for i,g in enumerate(w[ph]))
+ assert content(w)==sel['output_sha256']
+ return w
+if __name__=='__main__':
+ import sys
+ src=json.load(open(sys.argv[1])); sel=json.load(open(sys.argv[2])); out=apply(src,sel);json.dump(out,open(sys.argv[3],'w'),sort_keys=True,separators=(',',':')); print('PASS primitive retime',sel['gates'].__len__(),'moves',sel['output_sha256'])
diff --git a/research/e8-joint-frame-retiming/code/residual_routes.py b/research/e8-joint-frame-retiming/code/residual_routes.py
new file mode 100644
index 0000000000..04feccfe52
--- /dev/null
+++ b/research/e8-joint-frame-retiming/code/residual_routes.py
@@ -0,0 +1,26 @@
+"""Generate exact coordinate isometries for this kernel's residuals.
+OpenAI Codex. Route witness/check conventions follow chafreaky's PR439.
+"""
+import sys
+from pathlib import Path
+sys.path.insert(0,str(Path(__file__).resolve().parent.parent/'vendor/pr439'))
+from bank_routes import validate_isometries
+
+def generate(word,dimensions):
+    roots=word['lines'];index={tuple(r):i for i,r in enumerate(roots)};out=[]
+    for f in sorted(set(word['start'][240:])):
+        e=dimensions[f];rs=[roots[j] for j in word['frames'][f]]
+        axes=sorted({i for r in rs for i,x in enumerate(r) if x})
+        assert len(axes)==e, 'This finite selection must have coordinate entrances'
+        order=axes+[i for i in range(8) if i not in axes]
+        matrix=[[2*int(i==j) for j in range(8)] for i in order]
+        basis=[index[tuple(r)] for r in matrix]
+        assert set(basis[:e])<=set(word['frames'][f])
+        reduced=order[:];ops=[]
+        for i in range(8):
+            j=reduced.index(i)
+            if i!=j:reduced[i],reduced[j]=reduced[j],reduced[i];ops.append(['swap',i,j,None])
+        assert reduced==list(range(8)) and len(ops)<=7
+        out.append(dict(frame=f,entrance_rank=e,denominator=2,entrance_basis=basis[:e],residual_basis=basis[e:],orthogonal_rows_numerator=matrix,gaussian_reduction=ops))
+    assert validate_isometries(out,word['frames'],roots,dimensions)==set(word['start'][240:])
+    return out
diff --git a/research/e8-joint-frame-retiming/inputs/bit-geometry.json.gz b/research/e8-joint-frame-retiming/inputs/bit-geometry.json.gz
new file mode 100644
index 0000000000..19725bec46
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diff --git a/research/e8-joint-frame-retiming/inputs/complex-canonical-reference.json.gz b/research/e8-joint-frame-retiming/inputs/complex-canonical-reference.json.gz
new file mode 100644
index 0000000000..d604ec1ae8
Binary files /dev/null and b/research/e8-joint-frame-retiming/inputs/complex-canonical-reference.json.gz differ
diff --git a/research/e8-joint-frame-retiming/inputs/complex-data-phases.json.gz b/research/e8-joint-frame-retiming/inputs/complex-data-phases.json.gz
new file mode 100644
index 0000000000..22154a8c58
Binary files /dev/null and b/research/e8-joint-frame-retiming/inputs/complex-data-phases.json.gz differ
diff --git a/research/e8-joint-frame-retiming/inputs/complex-phase-receipt.json b/research/e8-joint-frame-retiming/inputs/complex-phase-receipt.json
new file mode 100644
index 0000000000..2a370225ea
--- /dev/null
+++ b/research/e8-joint-frame-retiming/inputs/complex-phase-receipt.json
@@ -0,0 +1,22 @@
+{
+  "status": "PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES",
+  "canonical_word_sha256": "79ff8e19335d5d5d1563ef0bc218106945d6a2b88ece53ee24bb3d88b2594ba3",
+  "fresh_edges": 248,
+  "reused_exact_edges": 2670,
+  "prior_recipe_sha256": "ecd793998109e76a139afcf5a3d83376cbc27f6364fd5fbc9e5645d129b2f791",
+  "frames": 956,
+  "directed_edges": 2918,
+  "ranks": {
+    "1": 1424,
+    "3": 168,
+    "8": 24,
+    "5": 294,
+    "2": 784,
+    "4": 224
+  },
+  "endpoint_adapters": 240,
+  "all_child_equalities_include_global_phase": true,
+  "recipe_sha256": "242fe77af077973e1933524fe5c7ff3b68bef14b1f6938e024827de78d954492",
+  "seconds": 17.302232877002098,
+  "scope": "Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations."
+}
diff --git a/research/e8-joint-frame-retiming/inputs/complex-phase-recipes.json.gz b/research/e8-joint-frame-retiming/inputs/complex-phase-recipes.json.gz
new file mode 100644
index 0000000000..03dc5fbe5e
Binary files /dev/null and b/research/e8-joint-frame-retiming/inputs/complex-phase-recipes.json.gz differ
diff --git a/research/e8-joint-frame-retiming/inputs/complex-ports.json.gz b/research/e8-joint-frame-retiming/inputs/complex-ports.json.gz
new file mode 100644
index 0000000000..ccbdc0596c
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diff --git a/research/e8-joint-frame-retiming/inputs/complex-template.json.gz b/research/e8-joint-frame-retiming/inputs/complex-template.json.gz
new file mode 100644
index 0000000000..975ce5c0df
Binary files /dev/null and b/research/e8-joint-frame-retiming/inputs/complex-template.json.gz differ
diff --git a/research/e8-joint-frame-retiming/inputs/e8-r865.json.gz b/research/e8-joint-frame-retiming/inputs/e8-r865.json.gz
new file mode 100644
index 0000000000..8bec1751f7
Binary files /dev/null and b/research/e8-joint-frame-retiming/inputs/e8-r865.json.gz differ
diff --git a/research/e8-joint-frame-retiming/local-evidence/KERNEL440-GROUP-FINAL-FRAME-SEARCH.json b/research/e8-joint-frame-retiming/local-evidence/KERNEL440-GROUP-FINAL-FRAME-SEARCH.json
new file mode 100644
index 0000000000..4cb2392125
--- /dev/null
+++ b/research/e8-joint-frame-retiming/local-evidence/KERNEL440-GROUP-FINAL-FRAME-SEARCH.json
@@ -0,0 +1,8 @@
+{
+  "status": "NOMINATION_NEEDS_EXACT_REPLAY",
+  "source_sha256": "00d8aa8608e40b53fd8752399de06cb730cc55caaadc528f88379cb31b8460a6",
+  "output_sha256": "00d8aa8608e40b53fd8752399de06cb730cc55caaadc528f88379cb31b8460a6",
+  "tested_gates": 14846,
+  "candidate_evaluations": 203,
+  "changes": []
+}
diff --git a/research/e8-joint-frame-retiming/local-evidence/KERNEL440-GROUP2-SEARCH.json b/research/e8-joint-frame-retiming/local-evidence/KERNEL440-GROUP2-SEARCH.json
new file mode 100644
index 0000000000..54751b966c
--- /dev/null
+++ b/research/e8-joint-frame-retiming/local-evidence/KERNEL440-GROUP2-SEARCH.json
@@ -0,0 +1,709 @@
+{
+  "status": "GROUP_NOMINATION_NEEDS_EXACT_REPLAY",
+  "source_sha256": "b443c9a7a03f35dc767841e736a3b64bcd115a4acaa5efeb80b4f4aa82517e91",
+  "output_sha256": "00d8aa8608e40b53fd8752399de06cb730cc55caaadc528f88379cb31b8460a6",
+  "groups_tested": 88774,
+  "positive": 42,
+  "selected": [
+    {
+      "gates": [
+        [
+          "B",
+          5
+        ],
+        [
+          "B",
+          6
+        ],
+        [
+          "B",
+          7
+        ]
+      ],
+      "old_frame": 458,
+      "new_frame": 515,
+      "delta": {
+        "5": 3,
+        "4": -3,
+        "1": 5,
+        "2": -4
+      },
+      "score": -0.0022336800848096333
+    },
+    {
+      "gates": [
+        [
+          "B",
+          15
+        ],
+        [
+          "B",
+          16
+        ],
+        [
+          "B",
+          17
+        ]
+      ],
+      "old_frame": 459,
+      "new_frame": 493,
+      "delta": {
+        "5": 3,
+        "4": -3,
+        "1": 5,
+        "2": -4
+      },
+      "score": -0.0022336800848096333
+    },
+    {
+      "gates": [
+        [
+          "B",
+          23
+        ],
+        [
+          "B",
+          24
+        ],
+        [
+          "B",
+          25
+        ]
+      ],
+      "old_frame": 460,
+      "new_frame": 492,
+      "delta": {
+        "5": 3,
+        "4": -3,
+        "1": 5,
+        "2": -4
+      },
+      "score": -0.0022336800848096333
+    },
+    {
+      "gates": [
+        [
+          "B",
+          31
+        ],
+        [
+          "B",
+          32
+        ],
+        [
+          "B",
+          33
+        ]
+      ],
+      "old_frame": 461,
+      "new_frame": 489,
+      "delta": {
+        "5": 3,
+        "4": -3,
+        "1": 5,
+        "2": -4
+      },
+      "score": -0.0022336800848096333
+    },
+    {
+      "gates": [
+        [
+          "B",
+          40
+        ],
+        [
+          "B",
+          41
+        ],
+        [
+          "B",
+          42
+        ]
+      ],
+      "old_frame": 462,
+      "new_frame": 488,
+      "delta": {
+        "5": 3,
+        "4": -3,
+        "1": 5,
+        "2": -4
+      },
+      "score": -0.0022336800848096333
+    },
+    {
+      "gates": [
+        [
+          "B",
+          48
+        ],
+        [
+          "B",
+          49
+        ],
+        [
+          "B",
+          50
+        ]
+      ],
+      "old_frame": 463,
+      "new_frame": 485,
+      "delta": {
+        "5": 3,
+        "4": -3,
+        "1": 5,
+        "2": -4
+      },
+      "score": -0.0022336800848096333
+    },
+    {
+      "gates": [
+        [
+          "B",
+          58
+        ],
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diff --git a/research/e8-joint-frame-retiming/local-evidence/first-group-full311.json b/research/e8-joint-frame-retiming/local-evidence/first-group-full311.json
new file mode 100644
index 0000000000..e9ceb5707a
--- /dev/null
+++ b/research/e8-joint-frame-retiming/local-evidence/first-group-full311.json
@@ -0,0 +1,126 @@
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+      "cutoff_log2": "6233134433230709243370204574243874436982430"
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+  "bit_template_sha256": "5172360df70765158c57c17aafa6bc80ee3f3a87a6a3f18c4d6b56d3904b4627",
+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f",
+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim.",
+  "verification_steps": [
+    "hamming_packets",
+    "complex_construct",
+    "complex_audit",
+    "complex_emit",
+    "complex_phases",
+    "bit_construct",
+    "bit_kernel",
+    "bit_export",
+    "bit_global",
+    "bit_audit",
+    "bit_price",
+    "complex_integrate",
+    "complex_replay",
+    "combined",
+    "independent_audit"
+  ],
+  "phase_mode": "full replay",
+  "manifest_sha256": "7e8f1c0f8bac1fdc82dd1f103cb08f75ce3daa21dc8b54a97eb1dc6885ab4bab"
+}
diff --git a/research/e8-joint-frame-retiming/local-evidence/first-group-full314.json b/research/e8-joint-frame-retiming/local-evidence/first-group-full314.json
new file mode 100644
index 0000000000..e9ceb5707a
--- /dev/null
+++ b/research/e8-joint-frame-retiming/local-evidence/first-group-full314.json
@@ -0,0 +1,126 @@
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+  "verification_steps": [
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diff --git a/research/e8-joint-frame-retiming/local-evidence/group-search.json b/research/e8-joint-frame-retiming/local-evidence/group-search.json
new file mode 100644
index 0000000000..2659e6956e
--- /dev/null
+++ b/research/e8-joint-frame-retiming/local-evidence/group-search.json
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diff --git a/research/e8-joint-frame-retiming/local-evidence/group-sweeps.json b/research/e8-joint-frame-retiming/local-evidence/group-sweeps.json
new file mode 100644
index 0000000000..9822dea63a
--- /dev/null
+++ b/research/e8-joint-frame-retiming/local-evidence/group-sweeps.json
@@ -0,0 +1,10 @@
+[
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diff --git a/research/e8-joint-frame-retiming/local-evidence/nonwinning-kernel-swaps.json b/research/e8-joint-frame-retiming/local-evidence/nonwinning-kernel-swaps.json
new file mode 100644
index 0000000000..eec983c561
--- /dev/null
+++ b/research/e8-joint-frame-retiming/local-evidence/nonwinning-kernel-swaps.json
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+{
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diff --git a/research/e8-joint-frame-retiming/local-evidence/source-span.json b/research/e8-joint-frame-retiming/local-evidence/source-span.json
new file mode 100644
index 0000000000..1e5b7ef6b7
--- /dev/null
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diff --git a/research/e8-joint-frame-retiming/local-evidence/upstream440/CERTIFICATE.json b/research/e8-joint-frame-retiming/local-evidence/upstream440/CERTIFICATE.json
new file mode 100644
index 0000000000..68ce443eb2
--- /dev/null
+++ b/research/e8-joint-frame-retiming/local-evidence/upstream440/CERTIFICATE.json
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+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim.",
+  "verification_steps": [
+    "hamming_packets",
+    "complex_construct",
+    "complex_audit",
+    "complex_emit",
+    "complex_phases",
+    "bit_construct",
+    "bit_kernel",
+    "bit_export",
+    "bit_global",
+    "bit_audit",
+    "bit_price",
+    "complex_integrate",
+    "complex_replay",
+    "combined",
+    "independent_audit"
+  ],
+  "phase_mode": "full replay"
+}
diff --git a/research/e8-joint-frame-retiming/local-evidence/upstream440/INDEPENDENT-AUDIT.json b/research/e8-joint-frame-retiming/local-evidence/upstream440/INDEPENDENT-AUDIT.json
new file mode 100644
index 0000000000..e75f4d081a
--- /dev/null
+++ b/research/e8-joint-frame-retiming/local-evidence/upstream440/INDEPENDENT-AUDIT.json
@@ -0,0 +1,100 @@
+{
+  "local_audit": {
+    "retiming_changes": 57,
+    "status": "PASS_INDEPENDENT_R740_KERNEL_AND_RETIMING",
+    "source_sha256": "d6ec8811541d6ab59a3bbbaaa15bccc8918b3b43b23d9f593198cfe90826fd20",
+    "candidate_sha256": "bae58f0692326f180ba49642360fd55557f59a93a96a8fa62bf7babd55d2384e",
+    "entries": 112,
+    "donor_slots": 100,
+    "total_entrance_rank": 136,
+    "root_closed_frames": 944,
+    "source_span_checks": 20652,
+    "forward": {
+      "all_columns": 980,
+      "dirty_columns": 740,
+      "copies": 9,
+      "paid_profile": {
+        "1": 2500,
+        "2": 990,
+        "3": 326,
+        "4": 389,
+        "5": 90,
+        "8": 9
+      }
+    },
+    "reflected": {
+      "all_columns": 980,
+      "dirty_columns": 740,
+      "copies": 9,
+      "paid_profile": {
+        "1": 2500,
+        "2": 990,
+        "3": 326,
+        "4": 389,
+        "5": 90,
+        "8": 9
+      }
+    },
+    "negative_controls": [
+      "omitted_first_basis",
+      "omitted_final_basis",
+      "missing_donor"
+    ],
+    "events": 19727,
+    "scope": "Independent reconstruction, every F2 scalar column and dirty restoration, exact source span/first-frame relations and both complementary dimension ledgers; global banking and pricing audited separately."
+  },
+  "status": "PASS_INDEPENDENT_GLOBAL_INVOICE_AND_EXACT_ASSEMBLY",
+  "candidate_sha256": "bae58f0692326f180ba49642360fd55557f59a93a96a8fa62bf7babd55d2384e",
+  "global_template_sha256": "b59a206d355bb257cb06966d15c8542cfc591bfee729b821e3efe30a7ba8cdd9",
+  "expanded_program_sha256": "2ab85ff14ea58042311334194b0fc4e17cf66cb375cd12af51adb8636c155828",
+  "events": 1420344,
+  "global_scalar_columns": 7620,
+  "global_dirty_columns": 6660,
+  "all_global_scalar_columns_restored": true,
+  "bank_assignments": 53280,
+  "bank_families": 6507,
+  "residual_isometries": 15,
+  "route_corruption_controls": [
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+    "missing_factor",
+    "wrong_frame"
+  ],
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+  "physical": 14196,
+  "paid_profile": {
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+    "14": 3840,
+    "28": 3840,
+    "42": 3840
+  },
+  "deficit": 2496,
+  "source_bound_invoice": {
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 282,
+    "charged_two_level_coefficient_bits": 512,
+    "row_coefficient": 18355,
+    "live": 14187,
+    "physical": 14196,
+    "extra_helper_route_factor_bound": 144,
+    "selector_charge": 2375347104,
+    "full_counted_coefficient": "8271410009661736653226855278395470361",
+    "two_level_coefficient": "7323242093316479963924177312150069573045566553609912891292783054664675728289084971684"
+  },
+  "independent_moment": "third rational enclosure; lower passes, adjacent upper fails",
+  "bit_lower": "284424154625755093061/250000000000000000000000",
+  "kappa": "142050466976941/125000000000000000",
+  "kappa_decimal": "0.001136403735815528",
+  "strict_outer_constraints": 47,
+  "bridge_omission_controls": 18,
+  "bootstrap_levels": 6
+}
diff --git a/research/e8-joint-frame-retiming/local-evidence/upstream440/VALIDATION.json b/research/e8-joint-frame-retiming/local-evidence/upstream440/VALIDATION.json
new file mode 100644
index 0000000000..f86efc07e8
--- /dev/null
+++ b/research/e8-joint-frame-retiming/local-evidence/upstream440/VALIDATION.json
@@ -0,0 +1,35 @@
+{
+  "status": "PASS_FRESH_COMPLETE_PHASE_AND_INDEPENDENT_REPLAY",
+  "runtime": {
+    "executable": "/private/tmp/moonshot/primitives/char0/venv/bin/python",
+    "version": "3.12.13 (main, May 10 2026, 19:20:41) [Clang 22.1.3 ]"
+  },
+  "command": "python3 -B research/r740-shared-donor-kernel/verify.py OUTPUT --replay-phases",
+  "observed_exit_code": 0,
+  "full_complex_phase_replay": true,
+  "independent_audit_no_producer_or_pricing_imports": true,
+  "independent_script_sha256": "b2d49af260d5d3482010da7986c9701f7a41ef8dcfb3bd8547c22bd25c26aeca",
+  "word_sha256": "bae58f0692326f180ba49642360fd55557f59a93a96a8fa62bf7babd55d2384e",
+  "kappa": "142050466976941/125000000000000000",
+  "bit_template_sha256": "b59a206d355bb257cb06966d15c8542cfc591bfee729b821e3efe30a7ba8cdd9",
+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f",
+  "verification_steps": [
+    "hamming_packets",
+    "complex_construct",
+    "complex_audit",
+    "complex_emit",
+    "complex_phases",
+    "bit_construct",
+    "bit_kernel",
+    "bit_export",
+    "bit_global",
+    "bit_audit",
+    "bit_price",
+    "complex_integrate",
+    "complex_replay",
+    "combined",
+    "independent_audit"
+  ],
+  "validation_code_manifest_sha256": "65fdaac82ca44618ffec5bdb9eb3112e792574a7d31f323e73ecde21575ca348",
+  "post_replay_packaging": "Documentation/attribution, exact template-hash expectations and static certificates added after successful full code replay; no construction, admission or independent-audit code changed. Two whitespace-only lines in the independent audit were trimmed at release; AST equality was checked, and the committed archive is replayed separately before publication."
+}
diff --git a/research/e8-joint-frame-retiming/notices/NOTICE-PR352.md b/research/e8-joint-frame-retiming/notices/NOTICE-PR352.md
new file mode 100644
index 0000000000..4f9a0194a3
--- /dev/null
+++ b/research/e8-joint-frame-retiming/notices/NOTICE-PR352.md
@@ -0,0 +1,33 @@
+# Attribution and provenance
+
+Prepared by DaysSky, assisted with Claude. Apache-2.0 (see `LICENSE`) applies to the new code and to the inherited Apache-2.0
+code below; third-party notices are preserved where files are vendored.
+
+- **Complex supplier: the E8 unit** (`code/complex/inputs/e8/`): Jacob Sussman, jacobalansussman/wht-power-saving-lean
+  at `9c94857bbaee886f8649edee0bc2d3c738f9555e` (Apache-2.0, Copyright 2026 Jacob Sussman; his `LICENSE` and `NOTICE`
+  are vendored beside the files). The certificate `tools/certificate/gcert1-e8-r783.json.gz`, the 24 Lean modules and
+  the comparator configuration of his kernel-checked theorem `wht_main_block_B2Ge8x`, his Lean-data generators
+  (`tools/gx/{gxgen,gxrate,gxbind,gxunit,gxcore,gsmirror,gxpaths,regen_check,regen_check_e8}.py`,
+  `tools/gen/{foldlib,foldgen,gen_rates,gen_sharp}.py` and templates) and his stand-alone `tools/e8/replay.py` are
+  vendored byte-identical and sha-pinned in `code/complex/inputs/complex/source-pins.json`. His README credits
+  devices from this repository in the unit: slot reuse with a compensating read (jamesyc #124, eumemic #143), late
+  pairing (Chafik Boukhalfa #200/#233), the in-place pair (icekylinx #184, carried in ikeboy's #191/#193).
+- **Bit word, Design T, twin condensation, checkers and engines** (`data/bit/`, `code/builders/`, `code/checkers/`,
+  `code/pricing/`, `code/export_p10.py`, `code/stage_cohort.py`): unchanged from LJH-217's PR #346 at
+  `11b4de5ff8ed5fccf55d4af1043358d257308e8e`, which builds on DreamingOfClouds' PR #325 p10b word and PR #315 engines
+  (#285/#276 gen5/gen4 lineage on eumemic's PR168 generator and source527 package, PR #200's physical rules, hcg890
+  and Jacob Sussman's five-stage architecture, Evan McKinney's completed banks), utcorvusvolat-dotcom's w3 Design T,
+  twin condensation and verifier (PR #310) and PR #266's official checkers. See PR #346's notice for detail.
+  `json.hpp`: Niels Lohmann, MIT license in its header.
+- **Complex checks** (`code/complex/portable_complex.py`, `code/complex/code/`, `code/complex/inputs/complex/`):
+  PR #315's portable complex checks as ported to p = 10 in PR #346 (#256/#233/#202/#200/#194/#184 lineage:
+  icekylinx, Chafik Boukhalfa, Avi Eisenberg, eumemic and others). Jacob Sussman's `gx.check1`, `gxcore` and pinned
+  Lean chain sources under `code/complex/inputs/complex/sources` are unchanged from PR #346 (byte-identical at
+  `9c94857` except his `ORIGIN.md`, kept at `f010392`).
+- **New here**: `code/complex/code/scatter.py` and the generalization of the label, scalar, splice and guard checks
+  from the paired-cube star scatter with h centres of rank h − 2 to any gx scatter (table or star) with any number
+  of retained totals of any rank (regression: on PR #346's p = 10 program the generalized checks give byte-identical
+  scalar schedules, splice programs, primitive expansions, ledger and precision guard); the generalized final-climb
+  partition; the E8 pins; the Lean-binding and replay steps of `certify_complex.py`; `verify.sh` changes.
+
+Credits do not imply endorsement or review by the credited authors.
diff --git a/research/e8-joint-frame-retiming/notices/NOTICE.md b/research/e8-joint-frame-retiming/notices/NOTICE.md
new file mode 100644
index 0000000000..c244e3f56a
--- /dev/null
+++ b/research/e8-joint-frame-retiming/notices/NOTICE.md
@@ -0,0 +1,47 @@
+# Attribution and provenance
+
+Prepared by Dylan Crow, with Anthropic Claude assistance. Apache-2.0 (see `LICENSE`) applies to the new code and to the
+inherited Apache-2.0 code. Third-party notices are preserved where files are vendored.
+
+## New in this package
+
+- The E8 bit word `bitE8-r865` and its producer (`code/bit/producer/`).
+- The record exporter.
+- The independent checker and the controls.
+- The centre-count CP-SAT proof.
+- The generalized bit-side checkers, each with a documented default that reproduces the original:
+  - `NCOPY` in `legality_h.cpp` and `columns_h.cpp`;
+  - the `--gram` parameter in `gram_frames.py`;
+  - the label-family parameters in `geometry_g.py`;
+  - h and replicas in `tile_g.py`;
+  - h and T in `certify_bit_g.py`;
+  - NCOPY and the route template in `finite_g.py`.
+- The receipt assembler.
+- The secondary `seven_stage.py`.
+
+## Vendored
+
+- **`code/complex/`, `code/pricing/`**: unchanged from PR #352 (DaysSky) at `04b4c3c478b5bd8797d2663d89d8db4dfd0ad9f2`. This
+  includes:
+  - Jacob Sussman's E8 unit, Lean data, generators and replay, from jacobalansussman/wht-power-saving-lean at `9c94857`
+    (Apache-2.0, Copyright 2026 Jacob Sussman; his `LICENSE`/`NOTICE` are beside the files);
+  - PR #315's engines (`moment.py`, `base_two_moment.py`, `outer.py`, `prime_witnesses.py`).
+  See `NOTICE-PR352.md`.
+- **`code/bit/regression/`**: unmodified from PR #352 / PR #346 (LJH-217):
+  - `legality_h_pr346.cpp` and `columns_h_pr346.cpp` (PR #266's official cohort checkers as generalized in h by #346);
+  - `stage_cohort.py`, `prime_new.py`, `tile_check.py`, `cost.py`, `certify_bit.py`.
+  The generalized checkers in `code/bit/checkers/` derive from these, and from the source527/p10 packages'
+  `finite_check.py`, `geometry527.py` and `global_lowering.py`, whose lineage is:
+  - eumemic's source527 package;
+  - PR #200 (Chafik Boukhalfa);
+  - PR234 (hcg890 / Henry Grant), on Jacob Sussman's five-stage architecture;
+  - Evan McKinney's completed banks;
+  - the p = 10 ports by DreamingOfClouds and Chafik Boukhalfa.
+- **`code/secondary/bridged.py`**: unchanged from PR #363 (DaysSky) at `9df55dad6ddd05c3458793dfd82d1c2fe0ddbbb4`.
+  See `NOTICE-PR363.md`.
+- **`data/regression-p10/BASE-*`**: PR #325's p10b word as exported in PR #352 (DreamingOfClouds; #352 `data/bit`).
+- **`data/regression-p10/receipts-loans/`**: verification receipts of agent G's p = 10 passive-loans package, used only as
+  regression input.
+- **`json.hpp`**: Niels Lohmann, MIT license in its header.
+
+The E8 label family on the bit side follows Jacob Sussman's introduction of the E8 family for the complex supplier.
diff --git a/research/e8-joint-frame-retiming/notices/PR386.txt b/research/e8-joint-frame-retiming/notices/PR386.txt
new file mode 100644
index 0000000000..28cfebeb08
--- /dev/null
+++ b/research/e8-joint-frame-retiming/notices/PR386.txt
@@ -0,0 +1,25 @@
+Prepared by Zhihao Chen with substantial OpenAI Codex assistance.
+New compressed nine-stage bit geometry, source-bound global template,
+independent audit, finite bill, combined certificate and documentation:
+Apache License 2.0, the repository LICENSE.
+
+Pinned dependency research/e8-bit is reproduced without modification from
+Dylan Crow (utcorvusvolat-dotcom), with Anthropic Claude assistance, PR #370:
+https://github.com/CrocSwap/integer-mult-bounds/pull/370
+commit b7fe9cdf2da009c947ff6b334c562bc190b30373.
+All LICENSE, NOTICE.md, NOTICE-PR352.md and NOTICE-PR363.md files are retained.
+The local E8 bit word and its producer are their contribution, not ours.
+
+Pinned dependency research/nine-stage-complex-e8 is the independently
+developed complex component from PR #377, commit
+d0a620fcc99ba012468d61d01f5bb14007076d50:
+https://github.com/CrocSwap/integer-mult-bounds/pull/377
+Its inherited sources, source notices and licenses remain unchanged.
+
+Jacob Sussman introduced the E8 family and complex unit. The preserved
+upstream notices credit source527/eumemic, PR234/hcg890, PR266, PR315,
+PR346/LJH-217, PR352/DaysSky, PR363/DaysSky, Chafik Boukhalfa,
+DreamingOfClouds, Evan McKinney and other original contributors.
+
+The portable bits/stdc++.h shim contains standard-library includes only;
+it changes neither inherited algorithms nor their verification checks.
diff --git a/research/e8-joint-frame-retiming/notices/PR426-SOURCE-PINS.json b/research/e8-joint-frame-retiming/notices/PR426-SOURCE-PINS.json
new file mode 100644
index 0000000000..24a25d4342
--- /dev/null
+++ b/research/e8-joint-frame-retiming/notices/PR426-SOURCE-PINS.json
@@ -0,0 +1,1116 @@
+{
+  "files": [
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+    },
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+      "source_path": "research/e8-shared-donor-chains/NOTICE.md"
+    },
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+      "source_path": "research/e8-shared-donor-chains/README.md"
+    },
+    {
+      "commit": "12f488264cdd74a3b60d0fb534f4955792384f5c",
+      "path": "vendor/source404/PROOF.md",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "5ab68880c7a72d909ced76074650908d3a9bd1e19bd9df0f8b7b9e924e1cc899",
+      "source_path": "research/e8-shared-donor-chains/PROOF.md"
+    },
+    {
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+      "path": "vendor/source412/repivot.py",
+      "repository": "chafreaky/integer-mult-bounds",
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+      "source_path": "research/e8-repivot-fusion/code/repivot.py"
+    },
+    {
+      "commit": "616d9d678c00d79693b869934464003ba5b8d1b1",
+      "path": "vendor/source412/seqenlarge.py",
+      "repository": "chafreaky/integer-mult-bounds",
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+      "source_path": "research/e8-sequential-enlarged/code/seqenlarge.py"
+    },
+    {
+      "commit": "616d9d678c00d79693b869934464003ba5b8d1b1",
+      "path": "vendor/source412/repivot-e8.json",
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+    },
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+      "sha256": "e1e0dfe35c4ccbd572e6ecdd5be855e2a2e73a34a05c4437e94b97ab22d8f7d2",
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+    },
+    {
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+    },
+    {
+      "commit": "616d9d678c00d79693b869934464003ba5b8d1b1",
+      "path": "vendor/source412/pr409/SELECTION.json",
+      "repository": "chafreaky/integer-mult-bounds",
+      "sha256": "55ed27fc7d202aac06b5c62e5822764b24283f2637b70c2ffa9b3ee3dc7f2a48",
+      "source_path": "research/e8-sequential-enlarged/data/pr409/SELECTION.json"
+    },
+    {
+      "commit": "616d9d678c00d79693b869934464003ba5b8d1b1",
+      "path": "vendor/source412/LICENSE",
+      "repository": "chafreaky/integer-mult-bounds",
+      "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+      "source_path": "LICENSE"
+    },
+    {
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+      "path": "vendor/source412/NOTICE.md",
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+      "source_path": "research/e8-sequential-enlarged/data/pr409/LICENSE-pr409"
+    },
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+      "commit": "616d9d678c00d79693b869934464003ba5b8d1b1",
+      "path": "vendor/source412/LICENSE-pr410",
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+    },
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+      "sha256": "8c7f4785def2bc39334aac618184bb4e3c6b11ee6f1c8b51edc89d7b8fddc2c0",
+      "source_path": "research/e8-repivot-fusion/NOTICE.md"
+    }
+  ],
+  "parent": {
+    "commit": "b3c45822ca847aec8c0c019bb04db30881fc2966",
+    "manifest_sha256": "389ac12de894730bd534f9a00d604866dd400175e32bd1204920dd98eafb8888",
+    "package": "research/e8-coupled-bit-retiming",
+    "scope": "Complete frozen source tree is retained beside this extension, without modifying any original bytes."
+  }
+}
diff --git a/research/e8-joint-frame-retiming/notices/PR426.md b/research/e8-joint-frame-retiming/notices/PR426.md
new file mode 100644
index 0000000000..2a7a8c0c6b
--- /dev/null
+++ b/research/e8-joint-frame-retiming/notices/PR426.md
@@ -0,0 +1,53 @@
+# Sources and attribution
+
+This extension preserves the full frozen PR389 package at b3c45822ca847aec8c0c019bb04db30881fc2966.
+All notices and licenses in that package continue to apply, including Jacob
+Sussman's original gx/E8 construction and Dylan Crow's bit word.
+
+applecrusher PR376 supplies the two exact equal-helper aliases, frame repairs,
+two subsequent rank-six to rank-five moves, and deterministic transport.
+Dugongue PR390 supplies target-prefix difference restoration and its sufficient
+main-only Y-to-Y compiler extension. Rohan Arun PR395 supplies the signed
+extension; its original source file and exact function bytes are retained.
+The fixed signed selection here is reconstructed on the R779 word, rather than
+claiming another contributor's selected witness as new discovery.
+
+ai-nanachi, with substantial OpenAI Codex assistance, supplies two further
+two-donor clean substitutions, 55 clean-reset bit helper reuses, 54 subsequent
+bit frame moves, changed complete supplier replays and exact composition.
+The first contribution's frame search and exact record are preserved separately.
+The headline gain comes from the changed complex supplier. The bit gain is
+reported separately because it does not change the binding complex ceiling.
+No worldwide priority or global optimality is claimed.
+
+Source byte identities and original commit paths are in SOURCE-PINS.json.
+New contributions are Apache-2.0; original source-specific notices and licenses
+are retained in the frozen parent and vendor directories.
+
+Dugongue [PR401](https://github.com/CrocSwap/integer-mult-bounds/pull/401)
+at 7844f72c6051a4408284c3092490687061675c1a supplies arbitrary entrance
+subspaces, exact even/degenerate two-sided normalization, mixed banks and
+independent readback. Dugongue
+[PR404](https://github.com/CrocSwap/integer-mult-bounds/pull/404)
+at 12f488264cdd74a3b60d0fb534f4955792384f5c supplies the expanded shared-donor
+selection and sufficient nested-donor construction. Our private nested-flag
+experiments ran independently around this public update; no priority over
+PR404 is claimed. applecrusher's PR376 at
+7aa9d9f0247bb60c0519704bbca18990011e2a37 supplies the additional rank-eight
+to rank-seven frame change, frozen through PR404's composition source.
+Our contribution is the explicitly mapped R779 composition, all-pair fresh
+phase replay, full changed supplier/bit checks, and independent clean-reset
+bit mechanism. PR404's incompatible overlapping target recovery is excluded.
+No source-specific numerical gains are added to the headline.
+
+Chafik Boukhalfa, with Anthropic Claude assistance, supplies the checker-clean
+re-pivoting from [PR412](https://github.com/CrocSwap/integer-mult-bounds/pull/412)
+at 616d9d678c00d79693b869934464003ba5b8d1b1. The four ordered groups originate
+in Rohan Arun's [PR409](https://github.com/CrocSwap/integer-mult-bounds/pull/409);
+the eight enlargements originate in eumemic's
+[PR410](https://github.com/CrocSwap/integer-mult-bounds/pull/410).
+Exact selected source bytes, commit paths and licenses are retained through
+the frozen PR412 composition in vendor/source412. This submission maps these
+relations onto R779, checks both unchanged original checker families,
+recomputes every chronological omission, and freshly admits every phase pair.
+No independently reported numerical savings are added together.
diff --git a/research/e8-joint-frame-retiming/notices/PR438-NOTICE.md b/research/e8-joint-frame-retiming/notices/PR438-NOTICE.md
new file mode 100644
index 0000000000..ee51ac2694
--- /dev/null
+++ b/research/e8-joint-frame-retiming/notices/PR438-NOTICE.md
@@ -0,0 +1,44 @@
+# Attribution
+
+Copyright 2026 icekylinx. New split-centre cancellation, reversible source-centre
+composition, integration and verification changes were prepared by icekylinx
+with substantial OpenAI Codex assistance. Apache-2.0 applies to these changes.
+Earlier private Pro exploration used GPT-6 Astra; the new construction and
+composition in this package were developed with Codex.
+
+## Direct sources
+
+- Zhihao Chen, with OpenAI Codex assistance: PR425's mutable-basis Hamming packet
+  producer, common-frame scalar interface, exact phase lowering and verification;
+  PR386's compressed nine-stage bit geometry, owner template, audit and finite
+  accounting. These supply the immediate complex and geometric baselines.
+- ai-nanachi, with OpenAI Codex assistance: PR426's R767 bit word, including 55
+  clean-reset helper reuses and 54 frame changes. The complete selected word is
+  imported unchanged before the nine source-centre replacements.
+- Dylan Crow (utcorvusvolat-dotcom), with Anthropic Claude assistance: PR370's
+  Hamming E8 bit producer, root table, record exporter and local format.
+- Jacob Sussman: the E8 family, complex unit and underlying interchange framework.
+- applecrusher, Dugongue, eumemic, Rohan Arun, Chafik Boukhalfa, DaysSky,
+  DreamingOfClouds, Henry Grant, Evan McKinney, LJH-217 and other contributors:
+  the source, frame, compiler, rational-pricing and analytic lineage detailed
+  in the preserved original notices.
+
+The current value is computed from the two actual resulting programs.
+Independently published improvements are not added numerically. `SOURCES.json`
+records original commits and file hashes; `notices/` preserves source notices.
+Files under `proofs/` describe their original packages and retain their original
+scope and attribution; the current statement is in `PROOF.md`.
+
+## Earlier contributions by icekylinx
+
+The earlier #10, #18, #24, #32 and #36 contributions developed projector batching,
+partial-swap frames, endpoint gauges and conditional analytic/tape integration.
+The subsequent #104, #115, #130 and #144 contributions covered stopped-product
+integration, partial gauges, three-stage covers and paired-cube/source chronology.
+These provide historical context, not additional savings in this ledger. The
+source-centre idea from the preceding local round is used here on PR426's bit
+word. Unselected research experiments and superseded submission candidates are
+not part of this package.
+
+
+Kernel stage (this package): code/bit_kernel.py, the bank-tiling and audit changes in code/bit_global.py / code/bit_audit.py, stages/kernel-selection.json - rohanarun with Anthropic Claude assistance, Apache-2.0. vendor/kernel417/ is chafreaky's PR #417 code (e8core.py, stages.py, engines/), Apache-2.0, with two marked assertion relaxations.
diff --git a/research/e8-joint-frame-retiming/notices/SUSSMAN-NOTICE b/research/e8-joint-frame-retiming/notices/SUSSMAN-NOTICE
new file mode 100644
index 0000000000..63aa295646
--- /dev/null
+++ b/research/e8-joint-frame-retiming/notices/SUSSMAN-NOTICE
@@ -0,0 +1,290 @@
+Walsh-Hadamard power saving (wht-power-saving-lean)
+Copyright 2026 Jacob Sussman
+
+Repository: https://github.com/jacobalansussman/wht-power-saving-lean
+
+This repository is not a project of OpenAI. OpenAI did not write, review or
+endorse it. The package name "OAI" and the namespace "OAI.PowerSaving" are
+those of openai/math and are kept only because the new files extend that
+development.
+
+This repository is not a project of CrocSwap/integer-mult-bounds either. Its
+authors did not write, review or endorse it. Section 6 says what is taken
+from their repository.
+
+This repository contains files from, and files derived from, the repository
+"openai/math" (https://github.com/openai/math), family 130, "Exact Fourier
+transforms below n log n", at commit fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.
+That repository is published under the Apache License, Version 2.0. A copy of
+the licence is in the file LICENSE. The upstream repository has no NOTICE file
+and its licence text names no copyright holder; the files are attributed here
+to the authors of openai/math (OpenAI).
+
+1. Unmodified upstream files.
+   The 89 files under OAI/Computability/ are byte-for-byte copies of the files
+   with the same paths under lean/ in openai/math at the commit above. They
+   have not been changed. Modified copies of some of them are under
+   Work/Fourier/ and are listed in section 7.
+   One more file of openai/math is here unchanged, outside the Lean build:
+   third-party/openai-math/lean/ComparatorChallenges/UniformFourier.lean is a
+   byte-for-byte copy of lean/ComparatorChallenges/UniformFourier.lean at the
+   commit above (the statement of OpenAI's Fourier challenge). It is included
+   so that the modified copy named in section 2 can be compared with it.
+
+2. Files that contain upstream text.
+   - Work/CarrierCheck/ChallengeB2Ke16x.lean,
+     Work/CarrierCheck/ChallengeB2Ke16xR.lean,
+     Work/GCert/Data/ChallengeB2Gp193x.lean and the text template
+     tools/gen/templates/ChallengeB2L16x.lean.txt each contain, as their
+     lines 22-270, lines 9-257 of
+     lean/ComparatorChallenges/UniformFourier.lean of openai/math (the RAM cost
+     model), unchanged. Everything else in these files was written for this
+     repository.
+   - Work/Fourier/UniformFourierChallenge.lean is a modified copy of
+     lean/ComparatorChallenges/UniformFourier.lean of openai/math (the
+     statement of OpenAI's Fourier challenge, 336 lines). Changes: a comment
+     was added at the top; the exponent 1 - 1/(10^(13:ℕ)) was replaced by
+     1 - 7474546/(10^(10:ℕ)); seven names received the suffix "Z"
+     (decimalExponent, decimalTime, TimeBounds, DFTGoal, ConvGoal,
+     transform_main, convolution_main). Everything else in the file is the
+     upstream text, unchanged. See section 7.
+   - Work/Scratch/Engine.lean and Work/Block/Engine.lean contain copies of
+     proofs of openai/math, changed for this repository: sections 1, 2 and 5
+     of Work/Scratch/Engine.lean are upstream proofs with the batch layout
+     renamed, and both files contain a copy of the private upstream theorem
+     "hills_project" (lean/OAI/Computability/FourierTransform/
+     TensorProgram.lean) with its envelope generalised. The comments in the
+     two files mark these places.
+   - lakefile.lean is adapted from lean/lakefile.lean of openai/math: the same
+     package name, toolchain, package option and Mathlib pin; every other
+     dependency was removed and the libraries of this repository were added.
+     lean-toolchain is a byte-for-byte copy of lean/lean-toolchain.
+     lake-manifest.json lists Mathlib and its dependencies at the revisions of
+     lean/lake-manifest.json.
+   - RELATED-WORK.md reproduces the BibTeX entries of two manuscripts of
+     openai/math.
+
+3. New files that build on upstream proofs.
+   The other files under WHTCheck/ and Work/ were written for this
+   repository. They import the upstream files, and several of them generalise
+   or adapt proofs of upstream files (for example Work/Block/Recursion.lean,
+   which says so in its header). They are changes and additions made for this
+   repository and are not part of openai/math.
+
+4. How the new files were made.
+   Jacob Sussman made the new files on 2026-10-08 and 2026-10-09 by directing
+   a team of AI agents (Claude). The agents wrote the new Lean files, the
+   certificate data and the generator scripts. See README.md, section 4.
+
+5. Ideas taken from other public work.
+   The network of the first result uses ideas published by others, among them
+   the helper circuit "NStar3" (Swapnil-jain/integer-mult-kappa, which credits
+   CrocSwap pull request #36 and Paureel for parts of it), its transfer to
+   family 130 (shea256/fourier-transform-below-nlogn), and "carrier links" and
+   "whole-residual batching" (pull requests to CrocSwap/integer-mult-bounds).
+   No file of Swapnil-jain/integer-mult-kappa or of
+   shea256/fourier-transform-below-nlogn is included here. One comment in
+   Work/Scratch/Engine.lean quotes three counts reported in
+   Swapnil-jain/integer-mult-kappa and names that source. The general frame
+   lemma that Work/GFrame proves is stated in
+   notes/general-clifford-frames.tex of CrocSwap/integer-mult-bounds; its Lean
+   proof was written for this repository. The credits, with links, are in
+   RELATED-WORK.md.
+
+6. Data derived from CrocSwap/integer-mult-bounds (second result).
+   The helper circuit of the second result is the paired-cube circuit of the
+   repository "CrocSwap/integer-mult-bounds"
+   (https://github.com/CrocSwap/integer-mult-bounds), in the state of its pull
+   request #193. It is the design of that community: icekylinx (pull requests
+   #144 and #184), eumemic (#168, and #117 behind its modules), ikeboy /
+   Avi Eisenberg (#191 and #193), with an664 (#128) credited there for the
+   workspace-sharing principle. That repository is published under the Apache
+   License, Version 2.0 (the same licence text as the file LICENSE). Its
+   NOTICE file begins "A sharper exponent for integer multiplication /
+   Copyright 2026 Douglas Colkitt" and says that the community release "is
+   not solely Douglas Colkitt's work". A complete copy of that NOTICE file, as
+   it is at the head of pull request #193, is in
+   third-party/CrocSwap-integer-mult-bounds/NOTICE.
+
+   The data were taken from these files of that repository. They were loaded
+   as data by programs written for this repository; no program of that
+   repository was run, and none is included here.
+   - at the head of pull request #168 (eumemic),
+     4a3c769e5c5430e7114c4d3e099ff34664677f17:
+       references/paired-cube/sources/local_L1.json
+       references/paired-cube/sources/tmod_TE_TD_TB3_1_1_4_full_6.0617964e-4.json
+       references/paired-cube/sources/pmod_J0_full_6.0666810e-4.json
+       references/paired-cube/sources/qmod_climb3u_best.json
+       references/paired-cube/selected-module/matching-arcs.json
+       references/paired-cube/physical/frames.json
+   - at the head of pull request #193 (ikeboy),
+     187e1010ac8b259af8e9b5166f68b64bc27b4b47:
+       research/source-assisted-v4/data/physical-pairs.json
+
+   Files of this repository that contain data derived from them:
+   tools/certificate/gcert1-p11-pr193.json.gz and the Lean data modules
+   generated from it, Work/GCert/Data/Gen/P193*.lean and the files they import
+   from Work/GCert/Data/Gen/P193/; its block counts are also in the generated
+   modules Work/GCert/Data/P193Price.lean, RateB2Gp193.lean, RateB2Gp193x.lean
+   and InstB2Gp193.lean.
+   Changes made: the circuit was rebuilt from those data as one explicit,
+   renumbered list of additions with a table of frames, in the certificate
+   format "gcert/1" of this repository; its 1,980 in-place steps were written
+   as pairs of additions with rescaled coefficients; the Lean data modules
+   were generated from that list. No file of that repository is included
+   unchanged, except the copy of its NOTICE file named above.
+
+   Notices of that NOTICE file that pertain to these data, quoted:
+
+     Paired-cube and shared-core extension, 9 October 2026
+     Copyright 2026 icekylinx
+
+     Source-assisted common-frame extension (2026-10-09)
+     Copyright 2026 icekylinx. Apache-2.0.
+     Substantial dependency: eumemic PR168,
+     fd25adb7fbaa12ee761d02c733c54d1d2a7687ee
+
+   The full text of both notices, and the notices of the work they build on,
+   are in the copy named above. The credits, with links and with the words of
+   pull request #193 about its own sources, are in README.md ("Whose circuit
+   this is") and in RELATED-WORK.md, section 1.
+
+7. Modified copies of upstream files (third result).
+   The files listed below are copies of files of openai/math at the commit
+   above, changed for this repository. Each begins with a comment that names
+   the upstream file it is derived from and states what was changed. The
+   upstream originals under lean/OAI/Computability/ are in this repository
+   as well, unchanged (section 1), and the copies import them. The upstream
+   challenge file lean/ComparatorChallenges/UniformFourier.lean is in this
+   repository in both forms: unchanged under third-party/openai-math/
+   (section 1) and modified (section 2).
+
+   - Work/Fourier/ArbitraryLength.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/ArbitraryLength.lean (224
+     lines; 159 of them unchanged in the copy). Changes: identifiers renamed
+     on 64 lines (18 names: 15 with the suffix Z, 3 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/Asymptotics.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/Asymptotics.lean (187 lines;
+     112 of them unchanged in the copy). Changes: identifiers renamed on 74
+     lines (32 names: 26 with the suffix Z, 6 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+   - Work/Fourier/Axioms.lean: written for this repository (not a copy of an
+     upstream file).
+   - Work/Fourier/ConvolutionProgram.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/ConvolutionProgram.lean (100
+     lines; 77 of them unchanged in the copy). Changes: identifiers renamed
+     on 22 lines (10 names: 9 with the suffix Z, 1 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/Goal.lean: written for this repository; contains lines of
+     upstream files: of its 7 code lines, 6 are lines of
+     lean/OAI/Computability/FourierTransform/Goal.lean (original lines 35,
+     75-77, 79, 81): unchanged: its lines 25; with identifiers renamed: its
+     lines 21, 24, 26, 28, 30.
+   - Work/Fourier/Main.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/Main.lean (151 lines; 90 of
+     them unchanged in the copy). Changes: identifiers renamed on 59 lines
+     (40 names: 35 with the suffix Z, 5 with Z inserted); 1 import line
+     replaced by 2; 24 comment lines added; other code lines changed: 1 of
+     the original, 1 of the copy (copy line 59).
+   - Work/Fourier/Seam.lean: written for this repository; contains lines of
+     upstream files: of its 122 code lines, 15 are lines of
+     lean/OAI/Computability/FourierTransform/TensorProgram.lean (original
+     lines 36-37, 95-96): unchanged: its lines 93-94, 113-114, 141-142,
+     163-164, 185-187, 194-196; with identifiers renamed: its lines 184; 3
+     are lines of lean/OAI/Computability/FourierTransform/TensorSaving.lean
+     (original lines 83-84, 114): with identifiers renamed: its lines 45-46,
+     59; 1 is a line of lean/OAI/Computability/FourierTransform/Main.lean
+     (original line 60): with identifiers renamed: its lines 213.
+   - Work/Fourier/SectorAlgorithm.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/SectorAlgorithm.lean (224
+     lines; 162 of them unchanged in the copy). Changes: identifiers renamed
+     on 61 lines (17 names: 13 with the suffix Z, 4 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/SynchronizedAlgorithm.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/SynchronizedAlgorithm.lean (126
+     lines; 94 of them unchanged in the copy). Changes: identifiers renamed
+     on 31 lines (12 names: 10 with the suffix Z, 1 with Z inserted, 1
+     other), the other being "canopy" to "Grove.canopy" (5 lines); 1 import
+     line replaced by 1; 16 comment lines added; no other change to the
+     code.
+   - Work/Fourier/TransformProgram.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/TransformProgram.lean (146
+     lines; 94 of them unchanged in the copy). Changes: identifiers renamed
+     on 51 lines (21 names: 19 with the suffix Z, 2 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/UniformBounds.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/UniformBounds.lean (183 lines;
+     115 of them unchanged in the copy). Changes: identifiers renamed on 67
+     lines (29 names: 25 with the suffix Z, 4 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+   - Work/Fourier/UniformFourierChallenge.lean: modified copy of
+     lean/ComparatorChallenges/UniformFourier.lean (336 lines; 328 of them
+     unchanged in the copy). Changes: identifiers renamed on 7 lines (7
+     names: 7 with the suffix Z); 12 comment lines added; other code lines
+     changed: 1 of the original, 1 of the copy (copy line 281).
+   - Work/Fourier/WorkingCompiler.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingCompiler.lean (153
+     lines; 104 of them unchanged in the copy). Changes: identifiers renamed
+     on 48 lines (14 names: 14 with the suffix Z); 1 import line replaced by
+     1; 15 comment lines added; no other change to the code.
+   - Work/Fourier/WorkingPreparation.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingPreparation.lean (212
+     lines; 156 of them unchanged in the copy). Changes: identifiers renamed
+     on 55 lines (30 names: 28 with the suffix Z, 2 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/WorkingTransform.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingTransform.lean (119
+     lines; 91 of them unchanged in the copy). Changes: identifiers renamed
+     on 27 lines (9 names: 8 with the suffix Z, 1 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+
+   Changes made to the eleven copied proof files: every declaration received
+   the letter "Z" in its name (as a suffix of its own name, or of the name
+   of the declaration it belongs to), so that it does not collide with the
+   upstream declaration of the same name; the upstream exponent "alpha"
+   (1 - 2/10^11) and the bound "hills" defined from it were replaced by
+   "alphaZ" (1 - 7474547/10^10) and "hillsZ", which are defined in
+   Work/Fourier/Seam.lean, and the single use of the upstream theorem
+   "hills_program" by "hillsZ_program"; the five definitions of the upstream
+   statement that contain its exponent (decimalExponent, decimalTime,
+   TimeBounds, DFTGoal, ConvGoal) were replaced by the versions of
+   Work/Fourier/Goal.lean, whose exponent is 1 - 7474546/(10^(10:ℕ));
+   the import lines point to the copies; a header comment was added.
+      Two further changes: in the copy of Main.lean the same constant stands
+   once as the literal 2/10^11 and was replaced there too, and the two
+   final theorems of that copy received a documentation comment; in the
+   copy of SynchronizedAlgorithm.lean the name "canopy" was written out as
+   "Grove.canopy" in 5 places, because the short name is shadowed in the
+   larger environment of the copy. The script also renamed three names
+   inside upstream comments; the comments are otherwise the upstream ones
+   and describe the upstream network.
+   The proofs are those of openai/math. The copies were made by the script
+   tools/fourier/mkchain.py of this repository.
+
+   Work/Fourier/Goal.lean contains copies of those five definitions of
+   lean/OAI/Computability/FourierTransform/Goal.lean, with the exponent
+   replaced and the suffix "Z" on the five names.
+
+   Work/Fourier/Seam.lean was written for this repository. It repeats the
+   statement of the upstream theorem "hills_program" (TensorProgram.lean) and
+   the definition of "hills" (TensorSaving.lean) with the two names replaced;
+   its header says so.
+
+   The work of others that the third result follows (danadran01, shea256,
+   eumemic) is credited in README.md ("Whose reduction this is") and in
+   RELATED-WORK.md, section 1. No file of their repositories is included
+   here.
+
+Not included in this repository and fetched by the build: Mathlib
+(https://github.com/leanprover-community/mathlib4, Apache License 2.0) and its
+dependencies. The comparator (https://github.com/leanprover/comparator) is a
+separate tool and is not included.
diff --git a/research/e8-joint-frame-retiming/proofs/INHERITED-COMPLEX-GEOMETRY.txt b/research/e8-joint-frame-retiming/proofs/INHERITED-COMPLEX-GEOMETRY.txt
new file mode 100644
index 0000000000..c4150cb693
--- /dev/null
+++ b/research/e8-joint-frame-retiming/proofs/INHERITED-COMPLEX-GEOMETRY.txt
@@ -0,0 +1,161 @@
+Independent compressed nine-stage complex component
+
+Claim and retained assumptions
+
+The fixed E8 local invocation has h=9, v=120, R=783 and copied rank loss
+cst=72. The construction below has m=73, live stock 14727 per complete
+orthogonal cover, and paid profile
+  1:157599, 2:43488, 3:37296, 4:10080, 5:15480, 6:23832,
+  7:3096, 8:7488, 9:576, 16:3840, 32:3840, 48:3840.
+It is a conditional complex component, not an integer multiplication bound.
+The local E8 invocation theorem, general Clifford rank-zero compiler,
+complete-stream tape primitives, common fine-grid precision, and retained
+analytic recurrence interfaces are assumptions retained from the fixed local
+source package. The new finite construction and its charges are supplied
+here. No new Lean kernel proof is asserted. Final bit-side admission and
+outer assembly are separate obligations.
+
+Exact operator convention
+
+For q in F2^m, let X_q be translation by q and
+  C_q = ((1+i) I + (1-i) X_q)/2.
+Then C_q^2=X_q and C_q fixes the uniform vector. Write C_all for the product
+over the coordinate vectors. An invertible binary matrix G acts by the
+literal address permutation P_G. All products of C_q are commuting exact
+Gaussian-dyadic operators. Their multiplier on Fourier character y is
+i^(sum epsilon_q * parity(q.y)). Modulo 4, parity expands as its linear sum
+minus twice its pair sum, so this multiplier is an exact Z4 quadratic form.
+Equality of these forms proves equality including the scalar phase.
+
+For arbitrary local subspaces U, including degenerate ones, use the
+deterministic canonical representative from clifford_exact.py. A basis G
+whose first columns span U gives K_G = D_Q P_G, with
+Q=I+G^(-T)G^(-1), and T_U=K_G C_[dim U] K_G^(-1).
+Its preimage Lagrangian is {(u,u+w): u in U, w in U^perp}. Thus a nested
+transition has Fourier rank equal to the dimension difference. The supplied
+compiler produces two explicit monomial operators around one rank-r C child.
+Its equality is checked both as a signed Pauli tableau and on a nonzero
+exact Gaussian state vector, which fixes the otherwise missing global phase.
+All 946 local frames, all 3120 used directed transitions, and all 240 old/new
+source/target adapters are checked. No rank-only replacement is made.
+
+Compressed window and data routes
+
+Use V=F2^9 direct_sum (F2^8)^8 with the ordinary dot product. Let E_s be the
+first s exterior eight-dimensional blocks, for 0<=s<=8. The exact window
+representative of local U is T_U tensor C_Es. A nested transition cancels
+the common exterior tensor factor exactly and keeps its original rank.
+Conjugating the whole window by any cover permutation preserves this fact.
+The old/new endpoint adapters are the checked local adapters tensored with
+identity, followed by the declared address conjugation. This proves the
+window lift directly; a divisibility assumption m=multiple_of_h is not used.
+
+Every supplied port q has odd weight and a zero coordinate. The explicit
+orthogonal matrix U_q in data_phases.py maps e0 to q: swap e0 with a zero
+coordinate e_j when necessary, then use the even-vector transvection
+x -> x + ((q+e_j).x)(q+e_j). Its remaining columns are an orthonormal basis
+of q^perp. For s>0, rho_s,q exchanges that complement in the local block
+with exterior block s and fixes q and all other exterior coordinates.
+It is a symmetric orthogonal involution. The stage data owners are
+g=d*rho_s,q, with rho_0,q=I, so the right factors are bijections of O(73,2).
+
+Use canonical data levels X_s=C_[0,9+8s), Y_s=X_s C_q^(-1), and initially
+X_(-1)=C_q, Y_(-1)=I. The routed stage starts at level s-1 and ends at level s.
+Their binary preimages agree with the window endpoints. Exact phase
+polynomials determine the translation that reconciles each endpoint, and
+the template applies that translation. There are 3840 nonzero such
+translations across the 120 port types and nine stages, before replica
+multiplicity. These operators are not silently identified from equal
+binary matrices.
+
+Four-pair scalar chain and idle children
+
+Starting with F_0 (Y_0 += X_0), for j=0,1,2,3 apply B_j (X_j -= Y_j),
+then for j<3 apply X_j += X_(j+1), Y_(j+1) -= Y_j, apply F_j, and undo
+that bridge. The last pair has B_3,F_3 without a following bridge.
+Afterwards apply, in descending j=2,1,0, X_(j+1)+=X_j and Y_j-=Y_(j+1).
+Finally exchange each pair by newX=oldY, newY=-oldX. The complete signed
+integer scalar matrix is the identity; omission of every bridge fails.
+
+Before a bridge, advance the idle pair to the active pair's level. The
+two advances for the newly used pairs have ranks (16,8), (32,8), (48,8).
+The final advances have ranks 48,32,16,0. Each rank occurs on both members
+of the pair, each of 120 ports, and each of eight replicas. A nested idle
+transition is factored in the explicit orthonormal basis U_q direct_sum I.
+Its exact Z4 phase is reconciled by the stored translation after that child.
+
+The final Y endpoint is C_all C_q^(-1). A source began at C_q, so its
+unadjusted exchange route would be C_all C_q^(-2)=C_all X_q. Applying the
+literal X_q to each final Y before the signed exchange removes this factor.
+The corresponding 120 omission controls fail. This correction is charged.
+
+Banks and arbitrary correlated dirt
+
+There are eight replicas of each of the four data pairs, hence 7680 data
+families. Each stage has 783 independent bank families. Number a local
+helper occurrence by z=783*replica+helper. It uses bank floor(z/8) and slot
+z mod 8, with its nine-dimensional residual assigned to coordinates
+[9*slot,9*slot+9). A paid coordinate C child at coordinate 72 completes
+each bank. All eight whole residuals and this padding fill dimension 73.
+Thus there are 9*783=7047 bank families and live stock 14727.
+
+Let Pi_slot swap the first nine coordinates with the assigned block. The
+local invocation at class d uses the bank class g=d*Pi_slot^(-1). Its
+residual at that owner is P_g C_block P_g^(-1). Right multiplication is a
+bijection. Local helpers sharing one bank have distinct slots, hence
+different right factors and different actual bank classes for every d.
+All data and private families are disjoint from banks. The checker verifies
+these injections for all 72 invocation/replica templates and 56376 residual
+assignments. A complete cover sweep for one replica finishes before the
+next begins. The local dirty invocation is block diagonal on helpers at
+its endpoint and permits arbitrary correlated helper values. Therefore
+overlap between different invocations does not impose a cleanliness or
+independence assumption. At each bank class, the eight residuals and the
+padding are coordinate factors in one common conjugated basis, and their
+exact product is P_g C_all P_g^(-1).
+
+One more exact correction is essential. Orthogonality alone does not imply
+that P_g commutes with C_all as an exact operator. In fact
+  P_g C_all P_g^(-1) = C_all X_delta(g),
+  delta(g)_i = (weight(row_i(g))-1)/2 mod 2.
+The quadratic terms cancel by row orthogonality and the remaining even
+linear terms give the displayed translation. Both sides fix the uniform
+vector, fixing the global scalar. Apply X_delta(g) to EVERY final live
+family in cover class g, after the bank padding and signed data exchange.
+The template includes and charges all 14727 corrections per cover. This
+identity is also checked on every orthogonal matrix in dimensions 1..5.
+
+Finite work and recurrence charges
+
+The source emitter is regenerated and revalidated in both orientations.
+It accounts for 1242936 local events over 72 invocations, with all copied
+center and dirty-tableau lifetimes intact. Forward and backward scalar
+words freshly replay all 1023 independent dirty live columns. Only the
+private work starts at zero. Work comprises 783 tableau streams, nine
+reserved center streams (eight used), and one coefficient stream. Each
+invocation completes and erases its private work before the next. Physical
+stock is therefore 15520 per cover; scalar-only work is excluded from the
+recursion-volume denominator.
+
+GLOBAL-REVIEW.json records the complete recomputed finite overcharge, with
+64*(73+1)^3 compiler groups per rank-zero adapter, source-counted scalar
+primitives, and overcharges for all data routes, bank selectors, phases,
+padding, bridges, exchanges and cover corrections. The O(73,2) order is
+2^(36^2)*product(2^(2i)-1,i=1..36); its bit length is 2628. The recomputed
+router fits 2^30000, the literal charge fits 2^100000, and the precision
+guard fits C0=2^210000. No even-dimensional orthogonal-order formula is used.
+
+Largest child 48 does not satisfy one-layer halving. Instead
+73^2=5329>2*48^2=4608, so two nested children have width strictly below
+half the parent, including floors. The general depth is bounded by
+2*ceil(log2 e), with direct small leaves. For B=s+E the completed-child
+semantic induction has 2B(73-48)-s-E=49B>0. The resulting conservative
+complete-row coefficient is 2*2642+9909+252=15445<20161, retaining the
+external bit/base-row allowance as an explicit interface assumption.
+The inherited bad-branch envelope is priced conservatively as before.
+
+Two independent rational moment engines admit
+b=999240641319551/10^18 and exclude b+10^-18 for the source-bound profile.
+The rank mass is 1072575, and 73*14727-1072575=2496=8*(8*120-9*72).
+This complex component exceeds 1/1024 but does not improve the current
+bit bottleneck. No improved final kappa or completed PR milestone follows.
diff --git a/research/e8-joint-frame-retiming/proofs/PR386-BIT-GEOMETRY.txt b/research/e8-joint-frame-retiming/proofs/PR386-BIT-GEOMETRY.txt
new file mode 100644
index 0000000000..31efe31268
--- /dev/null
+++ b/research/e8-joint-frame-retiming/proofs/PR386-BIT-GEOMETRY.txt
@@ -0,0 +1,191 @@
+Compressed nine-stage E8 bit supplier and combined conditional bound
+
+Claim and source assumptions
+
+The conditional combined value is
+  kappa = 998243154231047 / 10^18 = 0.000998243154231047 > 1/1024.
+It is approximately 2^-9.9683211064. This is a conditional finite construction
+in the inherited supplier framework, not a Lean proof of integer multiplication.
+No priority claim is made.
+
+The E8 bit word, its 120 root lines, all 865 helpers, and nine retained totals
+are taken without modification from Dylan Crow's PR #370, commit
+b7fe9cdf2da009c947ff6b334c562bc190b30373. Its raw word has SHA256
+1fb726ea3818fe0837cceb0dd22a71a0814f064e5e781628104610d6468e0e55.
+The original verification is rerun, including regeneration, independent
+1105-column F2 checking, official record legality/formal columns, all-frame
+Gram and prime witnesses, negative controls, and the original regression set.
+Its five-stage c is 904072820242522/10^18, insufficient by itself for -10.
+
+The complex supplier is the separately reconstructed compressed nine-stage
+component from PR #377, with b = 999240641319551/10^18. Its complete source,
+notices, exact Clifford and Z4 phase checks, global template and finite bill
+remain included. In particular, its terminal X_q and every-live-family
+X_delta(g) corrections are retained; equality of binary matrices is not
+substituted for equality of complex operators.
+
+The inherited all-size weighted bit compiler, tape/prime/precision and
+analytic transfer interfaces remain conditional. PR #370's explicit admission
+of nine copied totals at h=8 is retained. The complex local E8 theorem,
+Clifford compiler, common fine-grid, restored-row and analytic interfaces
+remain conditional exactly as stated in the companion component. The new
+window, banking and two-level finite charges are described below rather
+than inferred from a rank histogram.
+
+Exact bit operators and compressed ambient space
+
+Over an admitted odd address field, the E8 form is G=I_8/2. For a nondegenerate
+subspace U, write P_U for its orthogonal projector. On the doubled address
+space define
+  D_U = [[I-P_U, P_U], [P_U, I-P_U]].
+Thus D_U is an exact involution. If U is contained in V then
+D_V D_U = D_(V intersect U-perp), with rank dim(V)-dim(U). Also
+  D_I D_P = D_(I-P).
+These are literal address matrices. Unlike the complex C operators, they
+have no hidden scalar phase. The auditor reconstructs all 944 rational
+projectors and checks all 3289 used nested pairs, in both orientations.
+
+Set V_global = Q^8 direct_sum (Q^7)^8, m=64, with form I_64/2.
+Let E_s be the first s exterior 7-blocks, s=0,...,8. At stage s lift the
+entire local word by replacing U with U direct_sum E_s. Both ends of every
+local transition contain the same E_s, so it cancels exactly; the child
+projector and rank are unchanged. This holds for copied totals as well:
+the temporary transforms between the source and scatter frames, whose
+common E_s cancels. COPY/ERASE windows remain sequential and immutable.
+No assumption that m is a multiple of 9h is used.
+
+Port routes
+
+The reference root is q*=2e_0. For every root q, the checked product g_q
+of at most two E8 root reflections sends q* to plus or minus q. Let A_q be
+its last seven columns. They form an orthonormal basis of q-perp:
+  A_q^T A_q=I_7, A_q A_q^T=I_8-P_q, P_q=q q^T/4.
+For stage s>0 use, on the local block and exterior block s,
+  rho_(s,q) = [[P_q, A_q], [A_q^T, 0]],
+and fix all other coordinates. For s=0 use the identity. These matrices
+are orthogonal involutions. Conjugating the lifted endpoints gives
+  (P_q,E_s) -> (I_8,E_(s-1)),    (I_8,E_s) -> (I_8,E_s),
+  (0,E_s)   -> (I_8-P_q,E_(s-1)),
+  (I_8-P_q,E_s) -> (I_8-P_q,E_s).
+These equalities are checked as exact rational matrices for every port.
+Each nontrivial route has a replayed elementary factorization, at most
+77 factors, with denominators 1,2,4. Omitting a factor fails. Thus all
+routes remain defined at every odd address prime; there is no new odd
+exceptional prime. The existing local prime witnesses are rerun separately.
+
+Nine-stage scalar recipe and deferred endpoint completion
+
+Use four data pairs (X_j,Y_j). Start with F_0: Y_0 += X_0. For j=0,...,3,
+apply B_j: X_j -= Y_j; when j<3 insert the two shears
+  X_j += X_(j+1), Y_(j+1) -= Y_j;
+apply F_j; then undo those two shears. After all stages, for j=2,1,0 apply
+  X_(j+1) += X_j, Y_j -= Y_(j+1).
+Finally replace (X_j,Y_j) by (Y_j,-X_j). The complete signed integer
+8-by-8 scalar matrix is the identity. Omitting any of the eighteen
+individual bridge shears changes it.
+
+Each B_j is the reflected inverse of the actual local record stream:
+reverse the order, negate ADD coefficients, replace U by U-perp, and
+turn ERASE into a fresh COPY from the original unchanged center. No erase
+is inverted. PR #370 stores zero in the ERASE rank field; the reflected
+COPY rank is freshly derived from its two frames, giving rank 8. Both
+oriented streams replay all 1105 independent input columns and close work.
+
+Before each bridge the newly used pair is advanced to the active level.
+The two idle increments are (14,7), (28,7), (42,7). Endpoint completion of
+the earlier pairs is deferred to the final stage, with ranks 42,28,14,0.
+Every increment acts on both members of every port pair and every replica.
+The schedule checker requires equal complete frames at every bridge.
+The signed terminal exchange completes the data transform using the exact
+identity D_I D_P=D_(I-P). Scalar replay on 8745 independent columns includes
+960 data and 7785 separate stage-helper inputs. All are restored after
+the exchange; the reflected copy work closes to zero.
+
+Whole-block banks and arbitrary correlated dirt
+
+Use eight replicas. There are 4*2*120*8=7680 data families. For each stage,
+number a local helper occurrence by z=865*replica+helper, and assign it
+to bank floor(z/8), slot z mod 8. There are 865 banks at each of nine
+stages. Each slot is one whole 8-dimensional coordinate block in Q^64.
+The eight slots are mutually perpendicular and fill the ambient space;
+no padding child is needed. Live recursion stock is 7680+9*865=15465.
+Nine private center slots are reserved and excluded from recursion volume,
+so charged physical stock is 15474. Only one such slot is used at a time.
+
+Let Pi_slot exchange the first eight coordinates with its bank block.
+For a cover class d in O(I_64/2,F_q), the helper owner is the bank class
+g=d Pi_slot^-1, and a data owner is d rho_(s,q). Right multiplication is a
+bijection of the finite cover. Within every local invocation, helpers in
+the same bank have different slots, hence different actual cover classes;
+all data and work families are disjoint from banks. All 62280 assignments
+are checked, and every physical bank receives each of its eight slots once.
+
+The local all-column theorem permits arbitrary helper inputs, including
+correlations created by earlier invocations. After its endpoint each helper
+has only the known residual D_H. The common E_s cancels, so no cleanliness
+assumption is imposed by a previous bank action. Complete cover sweeps run
+sequentially. At a fixed bank owner g the residuals are D on the eight
+orthogonal coordinate blocks conjugated by g. They commute and multiply
+to D_I. Since diag(g,g) commutes with the literal head/tail exchange D_I,
+no complex-style cover phase correction is needed on the bit side.
+This is a symbolic finite cover proof, not an enumeration of O(64,F_q).
+
+Actual emitted ledger
+
+The source-bound template emits 72 local invocations and 1355328 events.
+All local COPY/ERASE and helper lifetimes are rechecked. Its paid profile is
+  1:149472, 2:67824, 3:32256, 4:30096, 5:22176, 6:144,
+  7:5760, 8:1296, 14:3840, 28:3840, 42:3840.
+There are 320544 paid children, rank mass 987264 and deficit
+  64*15465-987264 = 2496 = 8*(8*120-9*72).
+The independent auditor recomputes the profile from the emitted template
+and rejects missing idle/bridge/exchange/invocation events, bank-slot aliasing,
+understated stock, a missing local MOVE and a wrong reflected COPY charge.
+
+Finite cost, precision allowance and two-level halving
+
+The largest child is 42, so one-level halving is false. Two levels suffice:
+  2*42^2=3528 < 64^2=4096.
+Floors only reduce descendant widths. The exact one-level moment, including
+the inherited 10^-16 bad-branch envelope, is strictly below one; composing
+two levels squares this contraction. The finite composite may be used with
+the inherited halving-based compiler and direct small leaves.
+
+The old five-stage 104-bit payload-prefix guard is not reused. Fresh local
+cancellation-free row bounds are 742 forward and 6308 reverse. For five
+forward calls, four reflected calls and eighteen bridge shears, the bound
+  2^18 * 742^5 * 6308^4
+has 117 bits. We explicitly charge 192 bits per nine-stage block. The actual
+source operations, copy episodes, 77-factor routes, selectors, all owner
+adapters and this prefix bound enter certify.py's finite coefficient. It
+has 117 bits; the charged two-level coefficient has 269 bits and is bounded
+by 2^512. This deliberately increases the finite cutoff, rather than passing
+the old 104-bit assertion. The exact three bootstrap cutoff inequalities
+are checked using the changed coefficient.
+
+For cover/routing enumeration use the inherited coarse q^(m^2+1) bound;
+two levels and the retained additive row charges give
+  2*(64^2+1)+9909+252 = 18355 < 20161.
+The explicit rational bit routes introduce only powers of two. The new
+finite constants fit well below the companion bridge's 2^30000 reserve,
+and the common external C0=2^210000 and row allowance 20161 are retained.
+As for the companion complex component, the general compiler/common-grid
+interfaces are assumptions; no new Lean formalization is asserted.
+
+Exact price and combined assembly
+
+Two independent rational moment engines, both with the 10^-16 envelope,
+admit c=1057833103534317/10^18 and reject c+10^-18. The complex supplier
+therefore binds. With eta=10^-12 and beta=10^-9 choose
+  s=999240640320309/10^18 < (1-beta)*b < c.
+Start a0=384599/10^10 and apply a_(j+1)=(1-s)s+s*a_j three times. The retained
+outer assembly at (a3,b) admits kappa=998243154231047/10^18. All 47 strict
+constraints are positive; the next 10^-18 kappa grid point is rejected.
+The strict excess over 1/1024 is 21680654231047/10^18. Final kappa is about
+24.0286% above frozen #361, within the explicitly retained assumptions.
+
+Attribution: Dylan Crow / Anthropic Claude for PR #370's new local bit word;
+Jacob Sussman for E8 and the complex unit; the inherited source527, PR234,
+PR266, PR315, PR346, PR352 and PR363 contributors as listed in the preserved
+notices; Zhihao Chen with OpenAI Codex assistance for this compressed bit
+composition, its independent audit, and the combined nine-stage package.
diff --git a/research/e8-joint-frame-retiming/proofs/PR425-COMPLEX.txt b/research/e8-joint-frame-retiming/proofs/PR425-COMPLEX.txt
new file mode 100644
index 0000000000..41061757ce
--- /dev/null
+++ b/research/e8-joint-frame-retiming/proofs/PR425-COMPLEX.txt
@@ -0,0 +1,211 @@
+Hamming packets with mutable source and target bases
+Conditional finite extension of the complex E8 supplier
+
+1. What is new
+
+The old r783 word keeps source values fixed and does not read target registers.
+Those are sufficient restrictions on a scalar word, not necessary conditions
+for a common-frame linear program. The new word uses 680 helper registers:
+
+  * source registers themselves carry one branch of a simultaneous signed
+    packet computation;
+  * retired packet registers retain a full source basis, from which the eight
+    central coordinate sums are reconstructed;
+  * 56 pairs of targets carry a first two-output butterfly, with its input
+    basis explicitly compensated at frame zero and in the center decoder;
+  * an exact inverse on all source/helper registers is executed at their
+    common full frame after the last recursive climb.
+
+No recursive work is deleted from the ledger. A helper is counted for its
+entire lifetime, including unused final climbs. All 120 sources and targets
+retain their original line/full and zero/hyperplane endpoint ranks.
+
+The new local histogram is
+  {1:2248, 2:896, 3:168, 4:336, 5:392, 8:24, 9:8}.
+Its rank mass is 9*680 + 240*8 + 72 = 8112. There are 4072 local children.
+There are more local children than in the old r783 word, but substantially
+less helper rank mass; the complete moment, not a count proxy, decides gain.
+
+2. Exact Hamming geometry and signed packet algebra
+
+Use the pinned PR370 table of 120 E8 root lines in Construction-A coordinates:
+eight coordinate lines 2e_i and 112 sign lines on the 14 weight-four Hamming
+blocks. For integer representatives r_s, let G_st = r_s dot r_t / 2.
+The matrix C_st = 1 + G_st mod 2 has binary rank nine. The construction gives
+an explicit orthonormal realization p_s in F_2^9 with
+
+  p_s dot p_t = C_st,  and  p_s dot p_s = 1.
+
+Consequently the nonzero off-diagonal entries of G/2 occur only where a source
+line lies in the target hyperplane. The rank-eight central factorization is
+
+  (G/2)_ts = sum_i r_ti r_si / 4.
+
+For a source Hamming block d, a coordinate pair {i,j} in d, and epsilon=+-1,
+define the signed face packet
+
+  P(d,ij,epsilon) = sum_{s in d, r_si*r_sj=epsilon} r_si x_s.
+
+Each packet has four terms and its binary port span has rank three. Split
+the eight sign lines of a block into its two parity tetrads. Each tetrad pair
+occurs in two face packets with independent signed coefficient rows. The two
+rows are formed simultaneously by two determinant-one shears, rather than
+forming independent one-output sums. The packet factory uses its eight source
+registers and sixteen additional helpers. Its twelve retired registers can
+be oriented to retain a full rank-eight source basis. Exact elimination on
+that stock produces four coordinate sums without allocating more helpers.
+
+This comparison of an individual factory is not a claim that the whole old
+supplier used 48 helpers per block. The relevant complete counts are 783 and
+680, both charged with their full actual profiles.
+
+For two target/source blocks whose intersection is {i,j}, the contribution
+to target t is -r_ti P(d,ij,r_ti*r_tj)/2. The remaining within-block and
+coordinate-line contributions are explicit four-output signed transforms.
+Every one of the 14400 rational decoder entries is rechecked. Adding the
+eight coordinate centers leaves precisely the identity matrix on sources.
+
+The binary transvection x -> x+(x dot 43)*43 is orthogonal because 43 has
+even weight. It maps the constructed port set exactly to the old fixed E8
+port set. All frames and register indices are transported, so the old nine-
+window data routes and their global phase correction apply to exactly the
+same ordered ports, without introducing an unproved new covering geometry.
+
+3. General scalar-interface lemma
+
+Write z=(x,s) for the source and arbitrary dirty helper streams, and y for
+the targets. Permit scalar additions and invertible dyadic scalings between
+registers at the same current label. No target may feed a z register. The
+raw A/center/B word therefore has block form
+
+  z' = U z,
+  y' = V y + J x + K s,
+
+where U and V are invertible, and the retained-center operations are included
+in J and K. The actual word has J=I after its adjusted center scatter. The
+checks compute every coefficient over Q, rather than inferring it from a
+desired sparsity pattern.
+
+At frame zero, before entry adapters or recursive children, execute
+
+  y <- V^{-1} y - V^{-1} K s.
+
+Both y and s have label zero there. The code emits the literal inverse of
+the 56 disjoint two-output target bases and a direct, charged dyadic old-
+response matrix with 13216 additions. There is no uncharged oracle for K.
+It is computed from the explicit scalar word and serialized. All coefficient
+work is cleared immediately after its use.
+
+After the last main gate, finish every z register's climb to the full frame,
+then execute U^{-1} by reversing and inverting the non-target gates. These
+gates are legal at one common full frame, including helper-to-source gates.
+The result is exactly
+
+  (x,s,y) -> (x,s,y+x).
+
+The second orientation is the inverse transpose: negate and transpose every
+addition and invert every scale in the SAME event order. Each retained
+center is implemented by the transposed gather/child/scatter stream. The
+result is (x,s,y) -> (x-y,s,y). Both orientations are replayed on all 920
+independent live columns, including all 680 arbitrary helper columns.
+Missing compensation, missing output preconditioning, missing cleanup and
+the wrong inverse-transpose order are rejected.
+
+Why the scalar argument lifts to exact complex labels: for each binary
+subspace F use the exact canonical representative L(F). A climb from A to B
+acts as L(B)L(A)^{-1}. If two registers share F, a scalar addition commutes
+with their common L(F), as does a scalar scaling. Induction through the
+actual stream therefore gives the block-diagonal conjugation of its scalar
+matrix by the current labels. Center copies explicitly move from full to
+zero, or zero to full in the other orientation. The preconditioner uses
+only label-zero registers, and the z cleanup uses only full-label registers.
+Thus the proof never moves a scalar operation across unequal labels or
+identifies two frames merely because their ranks agree.
+
+Every used canonical frame, nested transition, center direction and endpoint
+adapter is independently lowered by the exact Gaussian Clifford compiler.
+Equalities include global phase. The old restricted gx gate-shape checker
+is not used to admit this new interface; the stronger explicit matrix and
+common-frame checks replace its source-immutability/target-read restrictions.
+This is a written finite algebraic extension, not a new Lean theorem.
+
+4. Complete programs and work lifetimes
+
+Each orientation emits 27537 events, including startup, entry/exit adapters,
+all recursive climbs, eight sequential center children, scalar operations
+and final cleanup. Temporary centers are initialized, used and erased one
+at a time. No center or coefficient work stream survives a live child.
+
+All added coefficients are dyadic. To apply a/2^j, compute |a| times the
+source by binary Horner additions on a cleared private stream, halve j
+times, accumulate with its sign, and clear the private stream. In-place
+scales are signed powers of two. Every such primitive is charged. This
+introduces no new denominator prime. Independent replay bounds the actual
+cancellation-free prefix norms, including coefficient work; a 192-bit local
+payload allowance is retained conservatively.
+
+5. Nine-window composition and finite bill
+
+Use the previously verified m=73 compressed nine-window geometry, four data
+pairs, eight replicas, and the original signed bridges, idle children,
+terminal exchange, terminal translations and full-cover phase correction.
+The source scalar identity and its negative inverse-transpose are exactly
+the two local interfaces consumed by that unchanged geometry.
+
+There are 680 whole-block banks per stage, each containing eight rank-nine
+helper blocks plus one paid rank-one padding child. The live width is
+
+  W = 240*4*8 + 9*680 = 13800.
+
+The conservative physical width is W+680+9+2=14491. The old-response matrix
+uses no persistent tableau, but the old-size reserve is still charged.
+The emitted owner table has 48960 distinct stage/replica/helper assignments.
+The new global profile is
+
+  {1:167976, 2:64512, 3:12096, 4:24192, 5:28224,
+   8:7488, 9:576, 16:3840, 32:3840, 48:3840}.
+
+Its rank deficit is 73*13800 - sum(r*H_r) = 2496. The maximum child is 48,
+and 73^2 > 2*48^2 supplies the same charged two-level halving argument.
+
+The finite bill is recomputed from the new scalar programs, bank owners,
+work stock and adapter counts. It is not asserted unchanged. The local
+primitive bound fits 2^48; the tape router fits 2^30000; the literal envelope
+fits 2^100000; the precision envelope fits 2^210000. The physical row
+coefficient is 15445, below the explicitly inherited external allowance
+20161. Full-cover corrections apply to all 13800 live families.
+
+6. Conditional numerical conclusion and retained assumptions
+
+Two independent rational moment engines, with the inherited 10^-16 bad-
+branch envelope, accept
+
+  b = 1049104978040580 / 10^18 = 0.001049104978040580
+
+and reject the next 10^-18 grid point. With the unchanged bit parameter
+c=0.001057833103534317, three bootstrap steps and all 47 strict outer
+conditions give the prospective finite-assembly value
+
+  kappa = 1048005508028206 / 10^18
+        = 0.001048005508028206, approximately 2^-9.898137985359.
+
+The finite statement is conditional on the same all-size weighted compiler,
+common fine grid, restored-row/base allowance, tape/prime/precision and
+analytic transfer interfaces as the retained nine-stage result. The new
+scalar-interface lemma above and its serialized program are additional
+reviewable material, not an appeal to gx accepting a program outside its
+grammar. No unconditional integer-multiplication theorem is claimed.
+The result is approximately +4.97% over the locally verified retimed bound,
+and remains well short of 2^-9. A fresh extracted-package replay is required
+by this research workflow before publication or final promotion.
+
+Attribution
+
+The root table and the motivation to use Hamming coordinates come from the
+already pinned PR370 bit package (Dylan Crow, with Anthropic Claude assistance).
+The E8 complex label family, original scalar word and gx interfaces are due
+to Jacob Sussman. The retained complex admission, pricing and global analytic
+interfaces are credited in the original package notices and PROOF.txt.
+The mutable-basis packet word, transported geometry, expanded scalar proof,
+new finite program and the present checks were developed in this local
+research session by Zhihao Chen with OpenAI Codex assistance.
diff --git a/research/e8-joint-frame-retiming/proofs/PR426.md b/research/e8-joint-frame-retiming/proofs/PR426.md
new file mode 100644
index 0000000000..e589cfbf50
--- /dev/null
+++ b/research/e8-joint-frame-retiming/proofs/PR426.md
@@ -0,0 +1,108 @@
+# Construction, dependencies and sufficient argument
+
+The fixed complex witness starts from Chafik Boukhalfa's far-retimed E8 word
+and applecrusher's two equal-helper substitutions and two frame refinements.
+It additionally replaces helper 556 by -2 times helpers 354 and 461, then
+helper 576 by -2 times helpers 402 and 478 after compaction. Exact clean
+linear forms agree at every substituted read. The backward upper-frame and
+forward nested repairs retain copied-total pins and final address caps.
+R is 779. The actual new dirty response and cleanup are regenerated: equality
+on clean values alone is not the arbitrary-dirt proof.
+
+The signed prefix restoration is the PR390/395 bracket. For 25 disjoint
+targets, subtract lambda times the donor before the prefix, emit the exact
+source/write-version/frame difference, and restore lambda times that donor
+at the common recovery frame. Lambda is +1 or -1. The full rational main
+operator and all retained totals agree with the explicit same-width R779
+baseline on all 1,019 independent columns. Source/helper subwords agree
+exactly, so the new baseline's explicit dirty response and cleanup remain
+valid. The changed compiler permits a main Y read only when its target is Y;
+helper-to-X remains forbidden. Both signed orientations and private lifetimes
+are freshly admitted, with all actual Clifford phases and physical incidences.
+
+The shared entrance construction follows PR401/404. Each pivot p satisfies
+K_p + sum_d a_pd K_d = 0 in the explicit baseline response. Four re-pivots
+from PR412 replace the basis of these same relations, including the
+half-valued donor that otherwise fails the original sixths-denominator
+condition. PR410 enlarges eight entrance subspaces. Removed original helpers
+556 and 577 are mapped explicitly onto our R779 word. The shared layer has
+192 pivots, rank mass 350, and 496 literal unit shears. Its pivots and donors
+are disjoint, so this layer alone has (S-I)^2=0.
+
+PR409's four ordered groups, with PR412's two additional re-pivots, prepend
+55 more shears and admit ten further pivots. The combined word has 202
+gauges of rank mass 360 and 551 entrance shears. The complete chronological
+prefix need not have (S-I)^2=0. We check its actual product M S, all retained
+totals, and that every gauged target-response column is zero. Every entrance
+source is read before any earlier entrance operation writes it.
+
+Every one of the 551 omission controls is recomputed from the suffix
+response. If shear t += q s is removed, its suffix response is multiplied
+by -q times the original independent s column: earlier operations leave s
+unchanged by the read-before-write condition. A nonzero response is required
+for each omission; the entire changed scalar schedule is also replayed for
+sampled omissions. No global donor/pivot disjointness is assumed here. Both
+unchanged original gx.check1 and gxcore.mirror checkers pass, including the
+native denominator conditions. Every actual nested transition is charged.
+
+PR376's additional target201/helper491 frame change from rank eight to seven
+is checked for full operator equality and nested paid paths before gauging.
+PR404's target125/124 overlapping-prefix recovery requires a different
+chronological input and is not imported. Its numerical gain is not included.
+
+Each entrance chart is normalized explicitly. Even and degenerate E_p use
+the full two-sided exact Clifford factorization of F T_E inverse. The right
+inverse adapter precedes the entire old-response invocation; the left inverse
+adapter follows all main and helper cleanup. Both orientations retain every
+unitary address operator in the inverse-adjoint chronology. Rank-zero adapters
+are costed. All old/new/reflected Gaussian child pairs are recomputed,
+including Pauli signs and global phase. Newly assigned mixed-bank coordinate
+permutations and inverse owners are emitted and independently decoded.
+Padding is an exact fixed integer witness, not a claim of solver optimality.
+
+The new bit operation differs from the preceding all-dirt reset: a retired
+helper only needs its clean X-content zeroed before a new logical helper is
+placed in the same slot. An arbitrary residual helper value is allowed. The
+new helper basis determines a newly computed initial D compensation. C is
+the reversed helper subword, restoring every physical helper, including its
+original independent dirt. Each reset is checked exactly before reuse; the
+retired slot has no later original use, the new helper has no earlier use,
+and copied totals are protected. The combined word is checked over every
+independent binary column. It uses 55 fewer helpers (822 to 767). The initial 27 reuses and 26 frame
+moves are followed by two fixed rounds of 14 reuses and 14 frame moves.
+The later resets use exact two- or three-parent clean forms; every parent
+and all rebuilt dirty compensation are charged and independently checked. Integer signed-prefix bounds, lifting,
+copied-center controls, routes and whole-bank packing are recomputed rather
+than inferred from the clean calculation.
+
+The complex assembly has dimension 73, 14,286 live and
+15,075 physical families, 734 banks per stage, deficit 2,496,
+maximum child rank 48 and halving degree two. The bit assembly has dimension
+56, 10,409 live families, deficit 1,512 and halving degree two. Actual row
+coefficients fit the common 20,161 reserve. Both finite invoices and both
+exact rational moment engines retain the positive 10^-16 fallback. Adjacent
+10^-24 complex coarse grid points are rejected; the unchanged bit coarse
+grid remains 10^-18. The exact outer assembly uses positive eta=10^-24,
+beta=10^-18, eight finite bootstrap continuations and a 10^-27 grid; it
+checks 47 strict constraints and invalid eta/beta/adjacent-point controls.
+
+The complex coefficient is 254951444354246755323/250000000000000000000000. The bit coefficient is
+104575879789097/100000000000000000. The resulting conditional kappa is 40750673324589432209923/40000000000000000000000000.
+Using the preceding unchanged bit supplier with this same complex coefficient
+gives 203354853562950029967497/200000000000000000000000000, where the bit side
+binds. The new clean-reuse bit supplier removes that bottleneck. Its exact
+additional kappa contribution is recorded as the difference from this fair
+control; the combined witness is limited by the new complex coefficient.
+
+All original files are manifest-bound and immutable. A copied supplier tree
+is changed only through asserted literal edits. DERIVATION.json records every
+old/new digest, changed pin and textual difference. Both full predecessor
+supplier suites run before the changed admission. Expected records are checked
+after recomputation, rather than used to obtain a PASS.
+
+This is a sufficient finite conditional construction. The inherited all-size
+recursive suppliers, canonical/rank-zero compiler, compressed Clifford windows,
+dirty banking/cover, routing, restored-row, fixed tape, common-grid, Gaussian
+precision/recovery and analytic interfaces remain assumptions. No new full
+Lean theorem or unconditional integer-multiplication exponent is asserted.
+The target kappa > 0.002 is not attained by this witness.
diff --git a/research/e8-joint-frame-retiming/proofs/PR438-PROOF.md b/research/e8-joint-frame-retiming/proofs/PR438-PROOF.md
new file mode 100644
index 0000000000..9f0346913c
--- /dev/null
+++ b/research/e8-joint-frame-retiming/proofs/PR438-PROOF.md
@@ -0,0 +1,198 @@
+# Split centres and a joint conditional exponent
+
+The finite construction gives
+
+$$
+T(n)=O\!\left(n(\log n)^{1-\kappa}\right),
+\qquad \kappa=0.001120864952258278,
+$$
+
+conditional on the retained all-size compiler, compressed-window, correlated
+bank-dirt, restored-work, fixed-tape/common-grid, precision and analytic
+interfaces. The changes below concern both finite suppliers. Original source
+proofs and notices are retained; they do not replace the changed checks.
+
+## 1. Cancel coordinate terms before lifting the complex decoder
+
+Partition the 120 Hamming E8 root lines into the 112 code lines C and the eight
+coordinate lines F, represented by 2e_i. Write r_s for a root representative and
+G_ts = r_t · r_s / 2. The parent decoder is the rank-eight centre factorization
+G/2 together with its negative off-diagonal entries.
+
+For each code target t, the coordinate-source centre contribution is
+r_ti x_(2e_i)/2. Its side contribution is its negative. Cancel this pair before
+constructing the lifted program. For code targets retain only
+
+$$
+Z_i=\sum_{s\in C}r_{si}x_s,
+\qquad
+\sum_i\frac{r_{ti}}4Z_i
+-\sum_{\substack{s\in C\\s\ne t}}\frac{G_{ts}}2x_s=x_t.
+$$
+
+For coordinate targets, implement the identity x_(2e_i) directly. Thus the
+entire 120-by-120 clean decoder is still the identity, including both cross
+blocks between C and F.
+
+In the parent's binary address realization,
+
+$$
+p_s\cdot p_t=1+G_{st}\pmod2.
+$$
+
+Every code source contributing to Z_i is orthogonal to p_(2e_i), because its
+ith root coordinate is ±1. The already constructed global sum Z_i lies in that
+rank-eight hyperplane. Copy it there, lower the private copy to frame zero with
+one rank-eight child, and scatter into the code targets. The eight coordinate
+identities copy their source lines with one rank-one child each. Each private
+copy has a sequential lifetime, and is erased before the next episode.
+
+The total copied rank is unchanged:
+
+$$
+8\cdot8+8\cdot1=72.
+$$
+
+The 112 coordinate-source helpers and eight dedicated full-centre helpers are
+removed. Own-block corrections use their original source-copy rows directly;
+all remaining signed packets and selected target butterflies are retained.
+The actual helper count is 560. No rank-four recovered row is substituted for
+a rank-three input.
+
+## 2. Arbitrary dirt and heterogeneous copy frames
+
+The explicit main word has block form z' = Uz and y' = Vy + x + Ks, where
+z=(x,s), and U,V are invertible. No target feeds z. At the common initial frame,
+apply V^-1 to the target basis and the literal correction -V^-1 Ks. Recompute K
+from the new word. After all main gates and final climbs, apply the literal
+inverse of the source/helper subword at the common full frame. This restores
+all sources and arbitrary helpers while adding x to y.
+
+The parent common-frame proof applies to each copy separately. A private copy
+created at label L(F) is lowered by the exact operator L(0)L(F)^-1, whether F
+has rank one or eight. Scalar operations occur only at equal labels. Adding
+the common exterior window to both labels cancels it exactly. The proof
+therefore does not require a full-frame centre, or infer an operator from rank
+alone. The inverse-transpose negates/transposes each scalar shear in the same
+order and reverses each private gather/child/scatter operation as emitted.
+
+Both scalar orientations and the serialized private-work programs replay all
+800 input columns. Both restore arbitrary source/helper inputs and erase private
+work. The changed exact Gaussian recipes include the heterogeneous centre
+transitions and their global phases. Of 2,918 selected directed pairs, 248 were
+newly computed; 2,670 were unchanged source-bound exact pairs already checked in
+the local phase run. The release optionally replays all selected pairs.
+
+The local paid profile is
+
+$$
+\{1:1912,\ 2:784,\ 3:168,\ 4:224,\ 5:392,\ 8:24\}.
+$$
+
+The compressed complex geometry uses m=73, eight replicas and nine stages.
+There are 560 banks per stage, each holding eight whole rank-nine residuals and
+one paid rank-one pad. Live width is 12,720; physical stock is 13,298, including
+16 centre slots, the conservative 560-row tableau reserve and two coefficient
+streams. The global rank deficit is 2,496. Explicit owner tables, padding,
+terminal translations and the cover correction are independently decoded.
+The largest child is 48; 73² > 2·48² gives two-level halving.
+
+The fresh invoice fits the retained 2^30000 router, 2^100000 literal and 2^210000
+precision reserves. Two exact rational engines certify
+
+$$
+b=0.001183986549206329.
+$$
+
+## 3. Source-centre bit composition
+
+Start with the exact R767 word from PR426. Its nine retained rows are written
+only by original sources at the full frame and are not read by ordinary A/B
+gates. Their nine independent binary forms have an invertible minor in source
+columns 0,1,2,4,8,9,16,32,64.
+
+Replace those rows of the 120-dimensional identity by the nine retained forms.
+Exact elimination produces an invertible source basis T, emitted as 559 XOR
+additions. Delete the nine retained helper rows and their old-dirt columns.
+After A apply T, perform the same nine sequential copies using the designated
+source rows, and immediately apply T^-1 before B. The copies have unchanged
+rank eight. All scalar operations of T and its inverse use the full frame.
+
+All 998 columns, arbitrary dirt, frame incidences and restoration pass. Omitting
+T^-1 or the remaining old-dirt correction fails. The actual exported record
+stream is reflected in reverse order with complementary frames. A reflected
+ERASE becomes a fresh COPY at that chronological point; the original source
+row remains unchanged within each copy episode. Both reflected programs and
+all nine composed invocations are replayed, rather than assuming that mutable
+source rows meet an old immutability restriction.
+
+Use the unchanged compressed bit windows in dimension 64: a local eight-space
+and eight exterior seven-spaces. The root data, rational frame family, form,
+port isometries and bank slots are source-bound to PR386. Every changed nested
+pair is checked by exact rational spans; positive definiteness gives the
+projector identity and its reflected version. There are 758 banks per stage,
+each filled by eight rank-eight residuals, with no padding. Live width is 14,502
+and physical stock is 14,511. All 54,576 owner assignments are checked. The
+unbanked global replay restores all 7,782 independent columns.
+
+The bit local profile is
+
+$$
+\{1:2367,\ 2:875,\ 3:475,\ 4:321,\ 5:164,\ 7:14,\ 8:9\}.
+$$
+
+Its global deficit is again 2,496. The maximum child is 42 and 64² > 2·42².
+The actual cancellation-free prefix bound needs 223 bits; the new charge is
+256 bits, replacing the parent's 192-bit allowance. The finite two-level
+coefficient needs 483 bits and fits the retained 2^512 allowance. The row
+coefficient is 18,355 < 20,161. These costs, including the basis operations,
+are recomputed from the emitted word. Two exact rational moment engines give
+
+$$
+c=0.001122122700265139220566.
+$$
+
+## 4. Joint strict assembly
+
+Both moments include the inherited 10^-16 bad-branch allowance. The bit supplier
+binds because c < b. Let eta=beta=10^-18 and
+
+$$
+s=\min\{c,(1-\beta)b\}-10^{-24}.
+$$
+
+Starting at a_0=384599/10^10, use six fixed ordinary bootstrap levels
+
+$$
+a_{j+1}=(1-s)s+sa_j.
+$$
+
+All bootstrap cutoff inequalities are checked with the actual charged finite
+coefficient. With q=a_6(1-2eta), choose the greatest 10^-18 grid point strictly
+below (1-eta)q/(1+q). It is
+
+$$
+\kappa=\frac{560432476129139}{500000000000000000}
+       =0.001120864952258278.
+$$
+
+All 47 retained strict outer inequalities pass. The next grid point, zero eta,
+zero beta and unit beta are rejected. The candidate is computed from both
+actual new templates; no independently reported savings are added together.
+
+The source-bound finite claims above do not discharge the inherited all-size
+interfaces or establish unconditional integer-multiplication complexity.
+
+
+## Addendum: shared-donor kernel entrances in the compressed bit geometry
+
+The kernel stage changes only helper chains: a pivot p starts at its entrance E (a root-closed frame inside the first frame
+of p and of every donor) instead of the zero frame and drops its frame-0 completion reads; every donor d of E adds p at E
+before the first A gate and again at FULL after the last C gate. Over F2 the completion responses satisfy
+resp(p) = XOR resp(D), so every target column is unchanged and every helper column is restored (checked by the exact replay
+on all 998 local columns, with arbitrary dirt, and by the global scalar replay). Frame nesting and the integer source-span
+rule are rechecked. In the compressed nine-stage construction a helper's residual is its endpoint dimension minus its
+entrance dimension; a helper of entrance rank e occupies a width-(8 − e) coordinate block of a 64-dimensional bank. The
+tiling places 8 × 758 slots per stage into 733 banks with every coordinate used exactly once, so the injective-owner and
+arbitrary-dirty-bank arguments apply with block isometries in place of whole rank-eight slots. The live stock drops by
+9·(200/8) = 225 families while the paid mass drops by 72·200, keeping the rank deficit 64·W − mass = 2,496.
diff --git a/research/e8-joint-frame-retiming/proofs/PR438-README.md b/research/e8-joint-frame-retiming/proofs/PR438-README.md
new file mode 100644
index 0000000000..872109a08e
--- /dev/null
+++ b/research/e8-joint-frame-retiming/proofs/PR438-README.md
@@ -0,0 +1,75 @@
+# Kernel + early resets on #433's bit word: conditional κ = 0.001133508328719775
+
+κ = 1133508328719775/10¹⁸ = 0.001133508328719775: **+0.414 % over #435** (0.001128832830332521, kernel on R758),
+**+0.465 % over #434** (0.001128250848293019, resets), +1.13 % over #433. The bit supplier binds; #433's split-centre complex
+supplier (b = 0.001183986549206329) is unchanged.
+
+Bit word: #433's R758 source-centre word → #434's eleven chronological clean resets (R747; #434's own reconstruction,
+`vendor/pr434/`, `code/bit_reset.py`) → #417's shared-donor response kernel re-derived on the R747 word (118 entries,
+total entrance rank 160, 119 donor slots, no new frames; `code/bit_kernel.py`, `stages/kernel-selection.json`) → #386's
+compressed nine-stage geometry with exact mixed-width bank tiling (727 banks per stage; live stock 14,223; deficit 2,496).
+Bit lower 0.001134794627881866 (R747 alone: 0.001129525236; R758 + kernel: 0.001130108534).
+
+Verify: `python3 -B research/split-centres-kernel-r747/verify.py /tmp/out` (~30 s) → `PASS conditional kappa 0.001133508328719775`.
+
+Credits: icekylinx (#433), rohanarun / OpenAI Codex (#434 resets), chafreaky (#417 kernel, vendored), ai-nanachi (#426),
+Zhihao Chen / jacklightChen (#425, #386), Dylan Crow (#370), J. Sussman (E8); this composition rohanarun with Anthropic Claude.
+
+---
+
+# Conditional κ = 0.001120864952258278
+
+This package combines a split-centre Hamming complex construction with a
+source-centre bit construction in compressed nine-stage windows. The resulting
+conditional exponent saving is
+
+$$
+\kappa=\frac{560432476129139}{500000000000000000}
+       =0.001120864952258278.
+$$
+
+This is approximately **6.9522% above PR425**. Both components change:
+
+| Component | Helpers | Ambient width | Certified saving |
+|---|---:|---:|---:|
+| Complex | 560 | 73 | 0.001183986549206329 |
+| Bit | 758 | 64 | 0.001122122700265139220566 |
+
+The bit component limits the final assembly. The complex construction removes
+coordinate contributions that cancel in the decoder, replacing eight full
+centres with eight rank-eight and eight rank-one copies. The bit construction
+starts from PR426's R767 word, computes its nine retained forms reversibly in
+source rows, and uses PR386's compressed windows.
+
+## Verification
+
+Python 3.11+ and its standard library suffice. Use a new output directory:
+
+```sh
+python3 -B research/split-centres-global/verify.py /tmp/split-centres-check
+```
+
+The default replays both changed words, reflected/inverse-transpose programs,
+bank ownership, costs, two rational moment engines and 47 strict outer
+inequalities. Exact complex phase evidence is reused only when the regenerated
+canonical word and complete recipe hashes match. To regenerate every selected
+Gaussian phase pair as well:
+
+```sh
+python3 -B research/split-centres-global/verify.py /tmp/split-centres-full-phases --replay-phases
+```
+
+The unchanged historical repository suite and PDF build are not required by
+this package. `EXPECTED.json` binds the result to both emitted global templates;
+`MANIFEST.json` binds the package files; `SOURCES.json` pins imported sources.
+
+## Scope
+
+[PROOF.md](PROOF.md) supplies the changed finite construction. The all-size
+compressed-window and correlated dirty-bank semantics, recursive compiler,
+restored-work/tape/common-grid precision, and analytic transfer interfaces remain
+conditional. This does not claim unchanged legacy gx/gxcore acceptance, a new
+Lean proof, or an unconditional multiplication theorem.
+
+Contributor history and AI assistance are recorded in [NOTICE.md](NOTICE.md).
+Original notices and the inherited proofs are retained separately.
diff --git a/research/e8-joint-frame-retiming/stages/final-word.json b/research/e8-joint-frame-retiming/stages/final-word.json
new file mode 100644
index 0000000000..38c454f38b
--- /dev/null
+++ b/research/e8-joint-frame-retiming/stages/final-word.json
@@ -0,0 +1 @@
+{"A":[[2,241,[787]],[2,241,[802]],[2,241,[816]],[2,241,[833]],[2,242,[746]],[2,242,[760]],[2,242,[773]],[2,244,[744]],[3,248,[743]],[3,248,[768]],[3,248,[860]],[3,248,[889]],[3,249,[754]],[3,249,[771]],[3,249,[846]],[3,249,[872]],[3,249,[887]],[3,251,[842]],[3,251,[857]],[4,256,[739]],[4,256,[798]],[4,256,[855]],[4,256,[908]],[4,257,[782]],[4,257,[797]],[4,257,[839]],[4,257,[852]],[5,261,[871]],[5,261,[897]],[5,261,[911]],[5,263,[738]],[5,263,[811]],[5,263,[825]],[5,263,[867]],[5,263,[881]],[5,263,[895]],[6,266,[757]],[6,266,[808]],[6,266,[875]],[6,266,[903]],[6,266,[931]],[6,268,[752]],[6,268,[785]],[6,268,[813]],[6,268,[841]],[6,268,[869]],[6,268,[923]],[6,269,[753]],[6,269,[781]],[6,269,[809]],[6,269,[837]],[6,269,[865]],[6,269,[893]],[8,278,[822]],[8,278,[915]],[8,278,[928]],[8,280,[921]],[8,281,[767]],[8,281,[821]],[8,281,[849]],[8,281,[907]],[9,283,[836]],[9,285,[794]],[9,285,[924]],[9,286,[766]],[9,287,[795]],[9,287,[879]],[5,736,[738]],[5,736,[866]],[5,736,[867]],[5,736,[880]],[5,736,[881]],[4,737,[739]],[4,737,[854]],[4,737,[855]],[3,742,[743]],[3,742,[768]],[3,742,[769]],[2,745,[744]],[2,747,[746]],[2,748,[788]],[2,748,[801]],[2,748,[818]],[2,748,[831]],[2,749,[789]],[2,749,[800]],[2,749,[818]],[2,749,[831]],[3,755,[754]],[3,755,[770]],[3,755,[771]],[6,756,[757]],[6,756,[902]],[6,756,[903]],[6,756,[930]],[6,756,[931]],[2,761,[760]],[2,763,[762]],[2,763,[790]],[2,763,[791]],[2,763,[814]],[2,763,[815]],[9,764,[766]],[8,765,[767]],[8,765,[821]],[8,765,[823]],[2,772,[773]],[2,776,[762]],[2,776,[790]],[2,776,[804]],[2,776,[815]],[2,776,[829]],[2,777,[762]],[2,777,[791]],[2,777,[804]],[2,777,[815]],[2,777,[828]],[6,778,[845]],[6,778,[899]],[6,778,[927]],[6,779,[751]],[6,779,[753]],[6,779,[781]],[6,779,[863]],[6,779,[865]],[6,779,[891]],[6,779,[893]],[6,780,[845]],[6,780,[899]],[6,780,[927]],[4,783,[782]],[4,783,[796]],[4,783,[797]],[6,784,[785]],[6,784,[868]],[6,784,[869]],[6,784,[922]],[6,784,[923]],[9,792,[794]],[9,793,[795]],[4,799,[798]],[4,799,[854]],[4,799,[855]],[2,803,[786]],[2,803,[787]],[2,803,[802]],[2,805,[790]],[2,805,[791]],[2,805,[804]],[2,805,[814]],[2,805,[815]],[2,805,[828]],[2,805,[829]],[6,806,[808]],[6,806,[902]],[6,806,[903]],[6,806,[930]],[6,806,[931]],[6,807,[809]],[6,807,[863]],[6,807,[865]],[6,807,[891]],[6,807,[893]],[5,810,[811]],[5,810,[866]],[5,810,[867]],[5,810,[894]],[5,810,[895]],[6,812,[750]],[6,812,[752]],[6,812,[813]],[6,812,[868]],[6,812,[869]],[6,812,[922]],[6,812,[923]],[2,817,[786]],[2,817,[787]],[2,817,[816]],[2,819,[800]],[2,819,[801]],[2,819,[818]],[8,820,[822]],[5,824,[825]],[5,824,[880]],[5,824,[881]],[5,824,[894]],[5,824,[895]],[2,830,[788]],[2,830,[789]],[2,830,[831]],[2,832,[786]],[2,832,[787]],[2,832,[833]],[9,834,[836]],[6,835,[751]],[6,835,[753]],[6,835,[837]],[6,835,[863]],[6,835,[865]],[4,838,[796]],[4,838,[797]],[4,838,[839]],[6,840,[750]],[6,840,[752]],[6,840,[841]],[6,840,[868]],[6,840,[869]],[3,843,[842]],[6,844,[845]],[6,844,[926]],[6,844,[927]],[8,851,[821]],[8,851,[823]],[8,851,[849]],[4,853,[796]],[4,853,[797]],[4,853,[852]],[3,856,[857]],[3,861,[768]],[3,861,[769]],[3,861,[860]],[5,870,[871]],[5,870,[896]],[5,870,[897]],[3,873,[770]],[3,873,[771]],[3,873,[846]],[3,873,[847]],[3,873,[872]],[6,874,[875]],[6,874,[930]],[6,874,[931]],[9,877,[879]],[3,886,[770]],[3,886,[771]],[3,886,[846]],[3,886,[847]],[3,886,[887]],[3,888,[768]],[3,888,[769]],[3,888,[889]],[6,898,[899]],[6,898,[926]],[6,898,[927]],[8,905,[821]],[8,905,[823]],[8,905,[907]],[4,909,[854]],[4,909,[855]],[4,909,[908]],[5,910,[896]],[5,910,[897]],[5,910,[911]],[8,914,[915]],[8,919,[921]],[9,925,[924]],[8,929,[928]],[463,933,[938]],[463,934,[938]],[463,937,[938]],[458,939,[946]],[458,940,[945]],[461,944,[943]],[461,951,[943]],[461,953,[943]],[469,958,[957]],[468,959,[960]],[469,964,[957]],[469,965,[957]],[468,966,[960]],[468,967,[960]],[466,972,[976]],[466,973,[976]],[465,974,[975]],[466,977,[976]],[465,978,[975]],[465,979,[975]],[2,240,[0]],[2,241,[0]],[2,242,[0]],[2,243,[0]],[2,244,[0]],[2,245,[0]],[3,246,[1]],[3,247,[1]],[3,248,[1]],[3,249,[1]],[3,250,[1]],[3,251,[1]],[4,252,[2]],[4,253,[2]],[4,254,[2]],[4,255,[2]],[4,256,[2]],[4,257,[2]],[5,258,[3]],[5,259,[3]],[5,260,[3]],[5,261,[3]],[5,262,[3]],[5,263,[3]],[6,264,[4]],[6,265,[4]],[6,266,[4]],[6,267,[4]],[6,268,[4]],[6,269,[4]],[7,270,[5]],[7,271,[5]],[7,272,[5]],[7,273,[5]],[7,274,[5]],[7,275,[5]],[8,276,[6]],[8,277,[6]],[8,278,[6]],[8,279,[6]],[8,280,[6]],[8,281,[6]],[9,282,[7]],[9,283,[7]],[9,284,[7]],[9,285,[7]],[9,286,[7]],[9,287,[7]],[10,288,[8]],[10,289,[8]],[11,290,[9]],[11,291,[9]],[12,292,[10]],[12,293,[10]],[13,294,[11]],[13,295,[11]],[14,296,[12]],[14,297,[12]],[15,298,[13]],[15,299,[13]],[16,300,[14]],[16,301,[14]],[17,302,[15]],[17,303,[15]],[18,304,[16]],[18,305,[16]],[19,306,[17]],[19,307,[17]],[20,308,[18]],[20,309,[18]],[21,310,[19]],[21,311,[19]],[22,312,[20]],[22,313,[20]],[23,314,[21]],[23,315,[21]],[24,316,[22]],[24,317,[22]],[25,318,[23]],[25,319,[23]],[26,320,[24]],[26,321,[24]],[27,322,[25]],[27,323,[25]]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new file mode 100644
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diff --git a/research/e8-joint-frame-retiming/stages/kernel-v2-word.json b/research/e8-joint-frame-retiming/stages/kernel-v2-word.json
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+        45,
+        46,
+        49,
+        50,
+        53,
+        54,
+        57,
+        58,
+        60,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        75,
+        76,
+        79,
+        80,
+        83,
+        84,
+        87,
+        89,
+        90,
+        93,
+        94,
+        96,
+        99,
+        100,
+        103,
+        105,
+        106,
+        109,
+        110,
+        113,
+        114,
+        117,
+        118
+      ]
+    ]
+  ],
+  "primitive_input_sha256": "cb2afa377baeb8578e867ecda0f81caa68b2dac9cca805f41247754cfe91deb5",
+  "preparation": "Expand every D/A/B/C [frame,destination,sources] into [frame,destination,[source]] in original source order before applying gate-index changes."
+}
diff --git a/research/e8-joint-frame-retiming/vendor/clifford_exact.py b/research/e8-joint-frame-retiming/vendor/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/clifford_exact.py
@@ -0,0 +1,149 @@
+"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals.
+Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d.
+The tableau is supplemented by a literal circuit, so global phases are kept.
+"""
+from dataclasses import dataclass
+
+def parity(x):return x.bit_count()&1
+def rank(rows):
+ p={}
+ for x in rows:
+  while x:
+   b=x.bit_length()-1
+   if b not in p:p[b]=x;break
+   x^=p[b]
+ return len(p)
+def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<<j for j in range(n)) for i in range(n))
+def mv(rows,x):return sum(parity(r&x)<<i for i,r in enumerate(rows))
+def inv(rows,n):
+ a=[r|(1<<(n+i)) for i,r in enumerate(rows)]
+ for j in range(n):
+  k=next(i for i in range(j,n) if a[i]>>j&1);a[j],a[k]=a[k],a[j]
+  for i in range(n):
+   if i!=j and a[i]>>j&1:a[i]^=a[j]
+ assert [r&((1<<n)-1) for r in a]==[1<<i for i in range(n)]
+ return tuple(r>>n for r in a)
+def basis_extend(cols,n):
+ out=[]
+ for x in list(cols)+[1<<i for i in range(n)]:
+  if rank(out+[x])>len(out):out.append(x)
+ assert len(out)==n
+ return tuple(out)
+def nullspace(rows,n):
+ a=list(rows);p=[];k=0
+ for j in range(n):
+  t=next((i for i in range(k,len(a)) if a[i]>>j&1),None)
+  if t is None:continue
+  a[t],a[k]=a[k],a[t]
+  for i in range(len(a)):
+   if i!=k and a[i]>>j&1:a[i]^=a[k]
+  p.append(j);k+=1
+ return tuple((1<<j)|sum(((a[i]>>j)&1)<<v for i,v in enumerate(p)) for j in range(n) if j not in p)
+def pmul(a,b):
+ x,z,p=a;y,w,q=b
+ return x^y,z^w,(p+q+2*parity(z&y))%4
+def identity(n):return tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,0) for i in range(n)])
+def apply(T,p):
+ n=len(T)//2;x,z,ph=p;out=(0,0,ph)
+ for i in range(n):
+  if x>>i&1:out=pmul(out,T[i])
+ for i in range(n):
+  if z>>i&1:out=pmul(out,T[n+i])
+ return out
+def compose(A,B):return tuple(apply(A,p) for p in B)
+def inverse(T):
+ n=len(T)//2;cols=[x|(z<<n) for x,z,p in T];rows=transpose(cols,2*n);cols_inv=transpose(inv(rows,2*n),2*n);out=[]
+ for j,w in enumerate(cols_inv):
+  x=w&((1<<n)-1);z=w>>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4))
+ return tuple(out)
+def qvalue(Q,alpha,x,n):
+ return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4
+def mul_i(a,p):
+ x,y=a;p%=4
+ return [(x,y),(-y,x),(-x,-y),(y,-x)][p]
+@dataclass
+class Op:
+ n:int
+ tab:tuple
+ circuit:list
+ def then(self,b):
+  assert self.n==b.n
+  return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit)
+ def adjoint(self):
+  circ=[]
+  for e in reversed(self.circuit):
+   if e[0]=='P':circ.append(('P',inv(e[1],self.n)))
+   elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2])))
+   elif e[0]=='C':circ.append(('C',e[1],-e[2]))
+   elif e[0]=='phase':circ.append(('phase',(-e[1])%4))
+   else:circ.append(e)
+  return Op(self.n,inverse(self.tab),circ)
+ def zero_state(self,basis=0):
+  N=1<<self.n;vec=[(0,0)]*N;vec[basis]=(1,0);den=0
+  for e in self.circuit:
+   if e[0]=='P':
+    v=[(0,0)]*N
+    for x,a in enumerate(vec):v[mv(e[1],x)]=a
+    vec=v
+   elif e[0]=='X':vec=[vec[x^e[1]] for x in range(N)]
+   elif e[0]=='D':vec=[mul_i(a,qvalue(e[1],e[2],x,self.n)) for x,a in enumerate(vec)]
+   elif e[0]=='phase':vec=[mul_i(a,e[1]) for a in vec]
+   elif e[0]=='C':
+    q,sgn=e[1:];v=[]
+    for x,(a,b) in enumerate(vec):
+     c,d=vec[x^q]
+     # C=(1+i)I/2+(1-i)X/2; inverse conjugates both coefficients.
+     v.append((a-sgn*b+c+sgn*d,b+sgn*a+d-sgn*c))
+    vec=v;den+=1
+   else:raise AssertionError(e)
+   while den and all((a&1)==(b&1)==0 for a,b in vec):vec=[(a//2,b//2) for a,b in vec];den-=1
+  return vec,den
+def ident(n):return Op(n,identity(n),[])
+def perm(n,G):
+ cols=transpose(G,n);gi=inv(G,n)
+ return Op(n,tuple([(a,0,0) for a in cols]+[(0,a,0) for a in gi]),[('P',tuple(G))])
+def diag(n,Q,alpha=None):
+ Q=tuple(Q);assert transpose(Q,n)==Q
+ alpha=tuple(alpha) if alpha is not None else tuple((Q[i]>>i)&1 for i in range(n))
+ assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n))
+ return Op(n,tuple([(1<<i,Q[i],alpha[i]) for i in range(n)]+[(0,1<<i,0) for i in range(n)]),[('D',Q,alpha)])
+def cgate(n,q,sgn=1):
+ return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(q if q>>i&1 else 0,1<<i,(3*sgn)%4 if q>>i&1 else 0) for i in range(n)]),[('C',q,sgn)])
+def xgate(n,b):return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,2*((b>>i)&1)) for i in range(n)]),[('X',b)])
+def fourier(n,axes=None):
+ out=ident(n)
+ for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<<i))
+ return out
+def hadamard(n,axes):
+ axes=list(axes);Q=tuple(1<<i if i in axes else 0 for i in range(n));S=diag(n,Q)
+ return S.then(fourier(n,axes)).then(S)
+def canonical_frame(n,U):
+ r=len(U)
+ if r==0:return ident(n)
+ if r==n:return fourier(n)
+ G=transpose(basis_extend(U,n),n);gi=inv(G,n);Q=tuple((1<<i)^sum(parity(gi_i&gi_j)<<j for j,gi_j in enumerate(transpose(gi,n))) for i,gi_i in enumerate(transpose(gi,n)))
+ K=perm(n,G).then(diag(n,Q))
+ return K.adjoint().then(fourier(n,range(r))).then(K)
+def monomial(op):
+ n=op.n;T=op.tab;assert all(x==0 and p%2==0 for x,z,p in T[n:]);G=transpose([x for x,z,p in T[:n]],n);b=mv(G,sum((p//2)<<i for i,(x,z,p) in enumerate(T[n:])))
+ gt=transpose(G,n);cols=[mv(gt,z) for x,z,p in T[:n]];Q=transpose(cols,n);alpha=[(p-2*parity(b&z))%4 for x,z,p in T[:n]]
+ out=diag(n,Q,alpha).then(perm(n,G)).then(xgate(n,b));assert out.tab==T
+ vec,den=op.zero_state();assert den==0 and all(a==(0,0) for i,a in enumerate(vec) if i!=b);phase=[(1,0),(0,1),(-1,0),(0,-1)].index(vec[b]);out=out.then(Op(n,identity(n),[('phase',phase)]));assert out.zero_state()==op.zero_state()
+ return out,dict(matrix_rows=G,offset=b,quadratic_rows=Q,linear_Z4=alpha,phase=phase)
+def lower_child(op):
+ n=op.n;Bcols=[x for x,z,p in op.tab[n:]];r=rank(Bcols)
+ if not r:
+  mon,rec=monomial(op);return dict(rank=0,left=rec,right=None),mon
+ G=transpose(basis_extend(Bcols,n),n);A=inv(G,n);PA=perm(n,A);part=op.then(PA);Bcols=[x for x,z,p in part.tab[n:]];Dcols=[z for x,z,p in part.tab[n:]]
+ picks=[];selected=[]
+ for j,x in enumerate(Bcols):
+  if rank(selected+[x])>len(selected):picks.append(j);selected.append(x)
+ assert len(picks)==r and all(x>>r==0 for x in Bcols)
+ Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<<r)-1) for j in picks],r)
+ Qsmall=tuple(sum(parity(row&col)<<j for j,col in enumerate(transpose(Bi,r))) for row in Dr);Q=Qsmall+(0,)*(n-r);DQ=diag(n,Q)
+ V=part.then(DQ).then(hadamard(n,range(r)));assert all(x==0 for x,z,p in V.tab[n:]);Vmon,Vrec=monomial(V)
+ S=diag(n,tuple(1<<i if i<r else 0 for i in range(n)))
+ left=S.adjoint().then(DQ.adjoint()).then(PA.adjoint());right=Vmon.then(S.adjoint()).then(xgate(n,(1<<r)-1))
+ lmon,lrec=monomial(left);rmon,rrec=monomial(right);compiled=rmon.then(fourier(n,range(r))).then(lmon)
+ assert compiled.tab==op.tab and compiled.zero_state()==op.zero_state()
+ return dict(rank=r,left=lrec,right=rrec),compiled
diff --git a/research/e8-joint-frame-retiming/vendor/engines/base_two_moment.py b/research/e8-joint-frame-retiming/vendor/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/e8-joint-frame-retiming/vendor/engines/moment.py b/research/e8-joint-frame-retiming/vendor/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/e8-joint-frame-retiming/vendor/engines/outer.py b/research/e8-joint-frame-retiming/vendor/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/e8-joint-frame-retiming/vendor/export_records.py b/research/e8-joint-frame-retiming/vendor/export_records.py
new file mode 100644
index 0000000000..3632d37048
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/export_records.py
@@ -0,0 +1,72 @@
+"""Export a bitE8/1 word to the PR249 record format read by PR #266's official cohort checkers and PR #315's engines.
+usage: python3 export_records.py word.json[.gz] OUTDIR   ->  OUTDIR/{249-records.bin,249-states.json,frames.json}
+Records are int32 six-tuples: MOVE(0,role,old,new,rank,0), ADD(1,dst,src,1,frame,phase), COPY(2,centre,temp,frame,ZERO,rank),
+ERASE(3,centre,temp,frame,ZERO,0).  A multi-source gate becomes one ADD per source, preceded by the MOVEs of every
+register of the gate to the gate frame.  Frames: integer basis rows B (label vectors of the frame's root lines in the
+word's coordinates, a rational basis) and integer annihilator rows A (standard dot product), as PR #266 expects.
+Dylan Crow, with Anthropic Claude assistance; Apache-2.0."""
+import sys, json, gzip, struct, os
+from fractions import Fraction as Fr
+from math import gcd
+def load(p):
+    with (gzip.open(p,'rt') if p.endswith('.gz') else open(p)) as f: return json.load(f)
+c=load(sys.argv[1]); out=sys.argv[2]; os.makedirs(out,exist_ok=True)
+v,R,h=c['v'],c['R'],c['h']; n=2*v+R; lines=c['lines']
+def basis(idx):
+    rows=[]; piv=[]; B=[]
+    for i in idx:
+        x=[Fr(a) for a in lines[i]]
+        for p,r in zip(piv,rows):
+            if x[p]: f=x[p]/r[p]; x=[a-f*b for a,b in zip(x,r)]
+        nz=[k for k in range(h) if x[k]]
+        if nz: rows.append(x); piv.append(nz[0]); B.append(list(lines[i]))
+    return B,rows,piv
+def annihilator(rows,piv):
+    # rows in echelon (pivot columns piv); free columns give the null space of the row space under the dot product
+    # reduce to RREF
+    R_=[r[:] for r in rows]
+    for i,(p,r) in enumerate(zip(piv,R_)):
+        R_[i]=[a/r[p] for a in r]
+    for i,p in enumerate(piv):
+        for j in range(len(R_)):
+            if j!=i and R_[j][p]: f=R_[j][p]; R_[j]=[a-f*b for a,b in zip(R_[j],R_[i])]
+    free=[k for k in range(h) if k not in piv]; A=[]
+    for f in free:
+        a=[Fr(0)]*h; a[f]=Fr(1)
+        for i,p in enumerate(piv): a[p]=-R_[i][f]
+        L=1
+        for x in a: L=L*x.denominator//gcd(L,x.denominator)
+        ai=[int(x*L) for x in a]; g=0
+        for x in ai: g=gcd(g,abs(x))
+        A.append([x//g for x in ai])
+    return A
+frames={}
+for k,idx in enumerate(c['frames']):
+    B,rows,piv=basis(idx); A=annihilator(rows,piv) if B else [[int(i==j) for j in range(h)] for i in range(h)]
+    assert all(sum(a*b for a,b in zip(x,y))==0 for x in A for y in B) and len(A)+len(B)==h
+    frames[str(k)]=dict(dim=len(B),B=B,A=A)
+dim=[frames[str(k)]['dim'] for k in range(len(c['frames']))]
+ZERO=[k for k in range(len(dim)) if dim[k]==0]; assert len(ZERO)==1; ZERO=ZERO[0]
+cur=list(c['start']); rec=[]
+def move(r,f):
+    if cur[r]!=f: rec.append((0,r,cur[r],f,dim[f]-dim[cur[r]],0)); cur[r]=f
+def run(gates,ph):
+    for f,d,srcs in gates:
+        for r in [d]+srcs: move(r,f)
+        for s in srcs: rec.append((1,d,s,1,f,ph))
+run(c['D'],1); run(c['A'],2)
+temp=n
+for k,q in enumerate(c['ret']):
+    fq=cur[q]; rec.append((2,q,temp,fq,ZERO,dim[fq]))
+    for t,row in enumerate(c['scatter']):
+        if k in row: rec.append((1,v+t,temp,1,ZERO,3))
+    rec.append((3,q,temp,fq,ZERO,0))
+run(c['B'],4); run(c['C'],5)
+for r in range(n): move(r,c['final'][r])
+with open(out+'/249-records.bin','wb') as f:
+    for e in rec: f.write(struct.pack('<6i',*e))
+st=dict(n=n,v=v,h=h,R=R,ZERO=ZERO,initial={str(r):c['start'][r] for r in range(n)},final={str(r):c['final'][r] for r in range(n)},
+        retained_totals=c['ret'],source_owned_roles=[],regs=[])
+json.dump(st,open(out+'/249-states.json','w'),sort_keys=True,separators=(',',':'))
+json.dump(dict(frames=frames),open(out+'/frames.json','w'),sort_keys=True,separators=(',',':'))
+print('exported',len(rec),'records,',len(frames),'frames, n',n,'ZERO',ZERO)
diff --git a/research/e8-joint-frame-retiming/vendor/hamming_packets.py b/research/e8-joint-frame-retiming/vendor/hamming_packets.py
new file mode 100644
index 0000000000..c129996656
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/hamming_packets.py
@@ -0,0 +1,253 @@
+"""A structural prototype: mutable source bases and simultaneous signed packets.
+
+Input geometry is the pinned PR370 Hamming E8 root table. The binary realization,
+packet construction, two-shear synthesis and arbitrary-dirt replay below are new
+local experiments. This does NOT produce a complete improved E8 supplier.
+"""
+import gzip
+import hashlib
+import itertools as it
+import json
+import random
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('work/complex-network/hamming');OUT.mkdir(parents=True,exist_ok=True)
+SRC=Path('work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz')
+word=json.load(gzip.open(SRC));roots=word['lines'];v=len(roots)
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in roots] for a in roots]
+C=[sum((1^(G[i][j]&1))<<j for j in range(v)) for i in range(v)]
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+
+def inside(a,b):return basis(a+b)==b
+
+indices=[]
+for i,row in enumerate(C):
+    if len(basis([C[j] for j in indices]+[row]))>len(indices):indices.append(i)
+assert len(indices)==9
+gram=[sum(((C[i]>>j)&1)<<k for k,j in enumerate(indices)) for i in indices]
+def ip(a,b):
+    return sum(((a>>i)&1)*((gram[i]&b).bit_count()&1) for i in range(9))&1
+orth=[]
+for step in range(9):
+    choices=[x for x in range(1,512) if ip(x,x) and all(not ip(x,y) for y in orth)]
+    chosen=next(x for x in choices if step==8 or any(y!=x and not ip(x,y) for y in choices))
+    orth.append(chosen)
+assert all(ip(x,y)==int(i==j) for i,x in enumerate(orth) for j,y in enumerate(orth))
+ports=[]
+for i in range(v):
+    row=sum(((C[i]>>j)&1)<<k for k,j in enumerate(indices))
+    ports.append(sum(((row&e).bit_count()&1)<<k for k,e in enumerate(orth)))
+assert len(set(ports))==v and all(p.bit_count()&1 for p in ports)
+assert all(((ports[i]&ports[j]).bit_count()&1)==((C[i]>>j)&1) for i in range(v) for j in range(v))
+
+blocks=defaultdict(list);frame_lines={}
+for i,r in enumerate(roots):
+    support=tuple(k for k,x in enumerate(r) if x)
+    if len(support)==4:blocks[support].append(i)
+    else:assert len(support)==1;frame_lines[support[0]]=i
+assert len(blocks)==14 and all(len(xs)==8 for xs in blocks.values())
+
+def sparse_add(rows,t,s,q):
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+
+def simulate(n,events):
+    rows=[{r:Q(1)} for r in range(n)]
+    for t,s,q in events:sparse_add(rows,t,s,q)
+    return rows
+
+def serialize(events):return [[t,s,q.numerator,q.denominator] for t,s,q in events]
+
+packet_table={};module_receipts=[];all_programs=[]
+for block,ids in sorted(blocks.items()):
+    ids=sorted(ids);pos={s:i for i,s in enumerate(ids)}
+    tetrads=[sorted(s for s in ids if sum(roots[s][k]<0 for k in block)%2==p) for p in (0,1)]
+    assert all(len(t)==4 for t in tetrads)
+    faces=[]
+    for i,j in it.combinations(block,2):
+        for epsilon in (-1,1):
+            support=[s for s in ids if roots[s][i]*roots[s][j]==epsilon]
+            content={s:Q(roots[s][i]) for s in support}
+            frame=basis([ports[s] for s in support]);assert len(frame)==3
+            key=(block,(i,j),epsilon);packet_table[key]=(content,frame)
+            faces.append((key,content,frame))
+    pair_uses=defaultdict(list)
+    for f,(_,content,frame) in enumerate(faces):
+        for tet in tetrads:
+            pair=tuple(s for s in tet if s in content)
+            assert len(pair)==2
+            pair_uses[pair].append(f)
+    assert len(pair_uses)==12 and all(len(fs)==2 for fs in pair_uses.values())
+    bysource=defaultdict(list)
+    for pair in sorted(pair_uses):
+        for s in pair:bysource[s].append(pair)
+    # One of the three pair branches is carried by x itself, two by helpers.
+    regs={};nextreg=8;events=[];event_frames=[];cur=[basis([ports[s]]) for s in ids]
+    start=list(cur);dead=[]
+    def add(t,s,q,F):
+        assert t!=s and inside(cur[t],F) and inside(cur[s],F)
+        cur[t]=cur[s]=F;events.append((t,s,Q(q)));event_frames.append(F)
+    for s in ids:
+        for j,pair in enumerate(sorted(bysource[s])):
+            if j==0:reg=pos[s]
+            else:
+                reg=nextreg;nextreg+=1;cur.append(());start.append(())
+                add(reg,pos[s],1,basis([ports[s]]))
+            regs[pair,s]=reg
+    assert nextreg==24
+    partial={}
+    for pair,fs in sorted(pair_uses.items()):
+        s,t=pair;a,b=regs[pair,s],regs[pair,t];f,g=fs
+        alpha,beta=faces[f][1][s],faces[f][1][t]
+        gamma,delta=faces[g][1][s],faces[g][1][t]
+        assert alpha*delta-beta*gamma in (-2,2)
+        F=basis([ports[s],ports[t]]);assert len(F)==2
+        add(a,b,beta/alpha,F)
+        k=gamma/(delta-gamma*beta/alpha)
+        add(b,a,k,F)
+        partial[f,pair]=(a,alpha)
+        partial[g,pair]=(b,delta-gamma*beta/alpha)
+    pre_packets=simulate(24,events)
+    def clean_rank(registers):
+        piv={}
+        for reg in registers:
+            row=[pre_packets[reg].get(i,Q(0)) for i in range(8)]
+            for j in sorted(piv):
+                q=row[j]
+                if q:row=[a-q*b for a,b in zip(row,piv[j])]
+            j=next((i for i,q in enumerate(row) if q),None)
+            if j is not None:
+                q=row[j];piv[j]=[a/q for a in row]
+        return len(piv)
+    choices=[[value for (ff,pair),value in partial.items() if ff==f] for f in range(12)]
+    rng=random.Random(38639);orientation=None
+    for trial in range(4096):
+        bits=rng.randrange(1<<12)
+        if clean_rank([pieces[1-((bits>>f)&1)][0] for f,pieces in enumerate(choices)])==8:
+            orientation=bits;break
+    assert orientation is not None
+    outputs=[]
+    for f,(key,content,F) in enumerate(faces):
+        pieces=[value for (ff,pair),value in partial.items() if ff==f]
+        assert len(pieces)==2
+        if orientation>>f&1:pieces.reverse()
+        (a,alpha),(b,beta)=pieces
+        add(a,b,beta/alpha,F)
+        outputs.append((a,alpha));dead.append(b)
+    assert len(set(r for r,a in outputs))==12 and len(set(dead))==12
+    assert not set(dead)&{r for r,a in outputs}
+    core=simulate(24,events)
+    for f,(reg,scale) in enumerate(outputs):
+        clean={ids[j]:scale*x for j,x in core[reg].items() if j<8 and x}
+        assert clean==faces[f][1]
+
+    # Probe complete borrowing: output each packet, cancel its old dirt at label
+    # zero, then undo every source/helper operation at the full frame.
+    # Actual supplier consumers and their remaining chronology are NOT inferred.
+    n=36;main=events.copy();dirt=[];chosen_targets=[]
+    for f,(reg,scale) in enumerate(outputs):
+        main.append((24+f,reg,scale))
+        for j,q in core[reg].items():
+            if j>=8:dirt.append((24+f,j,-scale*q))
+        valid=[t for t in range(v) if all((ports[t]&x).bit_count()%2==0 for x in faces[f][2])]
+        assert valid;chosen_targets.append(valid[0])
+    cleanup=[(t,s,-q) for t,s,q in reversed(events)]
+    actual=simulate(n,dirt+main+cleanup)
+    for r in range(24):assert actual[r]=={r:Q(1)}
+    for f in range(12):
+        expected={24+f:Q(1)}
+        expected.update({pos[s]:q for s,q in faces[f][1].items()})
+        assert actual[24+f]==expected
+    # A mutation of the compensator must corrupt at least one arbitrary dirt column.
+    wrong=simulate(n,main+cleanup)
+    assert any(wrong[r]!=actual[r] for r in range(24,36))
+    # Inverse-transpose: transpose and negate each elementary shear in the SAME
+    # event order. Reversing as well would generally compute the wrong map.
+    dual=simulate(n,[(s,t,-q) for t,s,q in dirt+main+cleanup])
+    for r in range(n):
+        expected={r:Q(1)}
+        if r<8:
+            expected.update({24+f:-content[ids[r]] for f,(_,content,F) in enumerate(faces) if ids[r] in content})
+        assert dual[r]==expected
+    receipt={'block':block,'source_lines':ids,'packets':12,'pair_butterflies':12,
+             'packet_additions':len(events),'live_source_registers_borrowed':8,
+             'helper_registers':16,'total_source_and_helper_registers':24,
+             'retired_register_clean_rank':8,
+             'independent_pair_branch_comparison_helpers':48,
+             'comparison_scope':'48 is a specified independent two-input-form implementation, not the helper count of the current r783 supplier.',
+             'frame_rank_counts':dict(Counter(map(len,event_frames))),
+             'all_dirty_columns_forward_and_inverse_transpose':n,
+             'compensator_omission_rejected':True,
+             'scope':'A 12-output packet factory and probe sinks. Not a complete 120-port supplier or global frame schedule.'}
+    module_receipts.append(receipt)
+    all_programs.append({'receipt':receipt,'start_frames':start,'events':serialize(events),
+                         'event_frames':event_frames,'outputs':[[r,str(q)] for r,q in outputs],
+                         'dead_registers':dead,
+                         'dirt':serialize(dirt),'cleanup':serialize(cleanup),
+                         'probe_target_ports':[ports[t] for t in chosen_targets]})
+
+# Reconstruct the entire signed E8 neighbour correction from the packet family.
+# This proves all 120 rational source columns of the abstract decomposition.
+decomposition=[]
+for target,r in enumerate(roots):
+    row=defaultdict(Q);terms=[];support=[i for i,x in enumerate(r) if x]
+    if len(support)==4:
+        c=tuple(support)
+        for d in blocks:
+            inter=tuple(sorted(set(c)&set(d)))
+            if len(inter)!=2:continue
+            i,j=inter;epsilon=r[i]*r[j];content,F=packet_table[d,inter,epsilon]
+            coefficient=-Q(r[i],2)
+            assert all((ports[target]&p).bit_count()%2==0 for p in F)
+            for s,a in content.items():row[s]+=coefficient*a
+            terms.append({'source_block':d,'pair':inter,'epsilon':epsilon,'coefficient':str(coefficient)})
+        for s in blocks[c]+list(frame_lines.values()):
+            if s!=target and G[target][s]:row[s]-=Q(G[target][s],2)
+    else:
+        i=support[0]
+        for d in blocks:
+            if i in d:
+                for s in blocks[d]:row[s]-=Q(roots[s][i],2)
+    expected={s:-Q(G[target][s],2) for s in range(v) if s!=target and G[target][s]}
+    assert {s:a for s,a in row.items() if a}==expected
+    # Eight coordinate centers recover the diagonal after side corrections.
+    for s in range(v):
+        center=sum(Q(r[i]*roots[s][i],4) for i in range(8))
+        assert center+row.get(s,Q(0))==int(s==target)
+    decomposition.append({'target':target,'cross_block_packets':terms,'side_support':len(expected)})
+
+program_path=OUT/'PACKET-PROGRAMS.json.gz'
+program_path.write_bytes(gzip.compress(json.dumps(all_programs,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+report={'status':'PASS_STRUCTURAL_PACKET_PROTOTYPE_NOT_A_NEW_SUPPLIER',
+        'source_sha256':hashlib.sha256(SRC.read_bytes()).hexdigest(),
+        'binary_address_dimension':9,'binary_gram_rank':len(indices),
+        'binary_ports':ports,'root_lines':roots,
+        'binary_gram_identity':'p_s dot p_t = 1 + (root_s dot root_t / 2) mod 2',
+        'modules':module_receipts,'signed_packets':len(packet_table),
+        'full_target_decomposition_columns':120,'full_target_decomposition_entries':120*120,
+        'program_sha256':hashlib.sha256(program_path.read_bytes()).hexdigest(),
+        'decomposition':decomposition,
+        'remaining':['Joint scheduling and charging of all packet fan-outs and target accumulations',
+                     'Forming all eight centers from the available mixed source basis without an uncharged restore',
+                     'Full 120-port arbitrary-dirt forward/backward program and restored work stocks',
+                     'Exact complex adapters and global phases; finite invoice; two independent prices and outer assembly'],
+        'no_new_coarse_b_or_kappa_claim':True}
+(OUT/'PROTOTYPE.json').write_text(json.dumps(report,indent=2)+'\n')
+print('PASS: 14 factories, 168 signed packets; each factory uses 8 source + 16 helper registers')
+print('PASS: exact dirty forward and inverse-transpose columns, omission controls, all 14400 decoder entries')
+print('NOT A SUPPLIER: global scheduling, mixed-basis centers, phase and full price remain open')
diff --git a/research/e8-joint-frame-retiming/vendor/kernel417/LICENSE b/research/e8-joint-frame-retiming/vendor/kernel417/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/kernel417/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
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+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
+      exercising permissions granted by this License.
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+      "Source" form shall mean the preferred form for making modifications,
+      including but not limited to software source code, documentation
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+
+      "Object" form shall mean any form resulting from mechanical
+      transformation or translation of a Source form, including but
+      not limited to compiled object code, generated documentation,
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+
+      "Work" shall mean the work of authorship, whether in Source or
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+
+      "Derivative Works" shall mean any work, whether in Source or Object
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+      "Contribution" shall mean any work of authorship, including
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diff --git a/research/e8-joint-frame-retiming/vendor/kernel417/e8core.py b/research/e8-joint-frame-retiming/vendor/kernel417/e8core.py
new file mode 100644
index 0000000000..f2874bae8e
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/kernel417/e8core.py
@@ -0,0 +1,203 @@
+"""Our own engine for bitE8/1 words (E8 root-line labels, h = 8): frame algebra over Q via root-line masks,
+legality/F2 replay, five-stage histogram, exact bit coarse saving and PR #315 outer assembly (our engine copies).
+Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0."""
+import gzip, json, os, importlib.util
+from fractions import Fraction as Q
+from collections import Counter
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+def _load(n):
+    s = importlib.util.spec_from_file_location('e8_' + n, os.path.join(HERE, "engines", n + ".py"))
+    m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+moment = _load('moment'); other = _load('base_two_moment'); outer = _load('outer')
+
+B2 = Q(876248285600677, 10**18)   # Sussman E8 five-stage (PR #352)
+B3 = Q(932783231884153, 10**18)   # DaysSky seven-stage B_3 (PR #363; no Lean proof)
+
+
+def load_word(p):
+    with (gzip.open(p, 'rt') if p.endswith('.gz') else open(p)) as f:
+        return json.load(f)
+
+
+def save_word(c, p):
+    with gzip.open(p, 'wt') as f:
+        json.dump(c, f, separators=(',', ':'))
+
+
+def rank(vecs):
+    rows = [[Q(x) for x in r] for r in vecs]; rk = 0
+    n = len(rows[0]) if rows else 0
+    for col in range(n):
+        p = next((i for i in range(rk, len(rows)) if rows[i][col] != 0), None)
+        if p is None: continue
+        rows[rk], rows[p] = rows[p], rows[rk]
+        for i in range(len(rows)):
+            if i != rk and rows[i][col] != 0:
+                f = rows[i][col] / rows[rk][col]; rows[i] = [a - f * b for a, b in zip(rows[i], rows[rk])]
+        rk += 1
+    return rk
+
+
+class Lat:
+    """Root-spanned subspaces of Q^8 represented by the mask of root lines they contain."""
+    def __init__(self, lines):
+        self.lines = [tuple(x) for x in lines]; self.v = len(lines)
+        self._dim = {0: 0}; self._close = {}
+        # Gram (form <x,y>/2) for orthogonality
+        self.ip = [[sum(a * b for a, b in zip(x, y)) // 2 for y in self.lines] for x in self.lines]
+
+    def close(self, mask):
+        """mask of all root lines in span(roots of mask)"""
+        if mask in self._close: return self._close[mask]
+        idx = [i for i in range(self.v) if mask >> i & 1]
+        basis = []
+        for i in idx:
+            if rank([self.lines[j] for j in basis] + [self.lines[i]]) > len(basis): basis.append(i)
+        d = len(basis); out = 0
+        if d == 8: out = (1 << self.v) - 1
+        elif d:
+            B = [self.lines[j] for j in basis]
+            for i in range(self.v):
+                if rank(B + [self.lines[i]]) == d: out |= 1 << i
+        self._close[mask] = out; self._close[out] = out; self._dim[out] = d
+        return out
+
+    def dim(self, mask):
+        if mask not in self._dim: self.close(mask)
+        return self._dim[mask]
+
+    def basis(self, mask):
+        b = []
+        for i in range(self.v):
+            if mask >> i & 1 and rank([self.lines[j] for j in b] + [self.lines[i]]) > len(b): b.append(i)
+        return b
+
+    def perp(self, t):
+        return self.close(sum(1 << j for j in range(self.v) if self.ip[t][j] == 0))
+
+
+def to_masks(c, L):
+    return [L.close(sum(1 << i for i in fr)) for fr in c['frames']]
+
+
+PHASES = ('D', 'A', 'B', 'C')
+
+
+def replay(c, L=None, masks=None, check_f2=True, span=True, span_mode='z'):
+    """Exact legality + F2 replay + histogram of a bitE8/1 word. Returns dict(H_local, steps, ...).
+    Legality: each register's frames nested (mask inclusion = exact Q-subspace inclusion for root-spanned frames) and
+    strictly increasing at each move; every gate at one common frame; D compensation at frame 0; y at frame 0 at the
+    scatter; COPY of retained totals; final frames (x, helpers FULL; y_t at its cap t-perp).
+    Source-span: every non-target operand's x-support lies in the gate frame."""
+    L = L or Lat(c['lines']); masks = masks or to_masks(c, L)
+    v, R, h = c['v'], c['R'], c['h']; n = 2 * v + R; FULL = (1 << v) - 1
+    cur = [masks[f] for f in c['start']]
+    for r in range(v): assert cur[r] == L.close(1 << r), 'x start'
+    for r in range(v, 2 * v): assert cur[r] == 0, 'y start at 0'
+    sig = [L.dim(cur[r]) for r in range(n)]
+    H = Counter(); steps = 0; viol = []
+    val = [1 << i for i in range(n)]
+    zsupp = [{i: 1} if i < v else {} for i in range(n)]  # integer support of each register over the x columns (all ADDs are +1)
+    def climb(r, m):
+        nonlocal steps
+        if cur[r] == m: return
+        assert cur[r] & ~m == 0 and cur[r] != m, ('not nested', r)
+        H[L.dim(m) - L.dim(cur[r])] += 1; steps += 1; cur[r] = m
+    def run(gates, ph):
+        for k, (f, d, srcs) in enumerate(gates):
+            m = masks[f]
+            assert d not in srcs and len(set(srcs)) == len(srcs), (ph, k)   # rohanarun: source destinations allowed (#433 source-basis gates); spans checked below
+            for x in [d] + srcs: climb(x, m)
+            for s in srcs:
+                val[d] ^= val[s]
+                if span:
+                    if s < v or s >= 2 * v:
+                        ms = sum(1 << i for i in zsupp[s])
+                        if ms & ~m: viol.append((ph, k, s))
+                    zd = zsupp[d]
+                    for i, a in zsupp[s].items():
+                        w = zd.get(i, 0) + a
+                        if w: zd[i] = w
+                        else: zd.pop(i, None)
+                    if span_mode == 'f2':
+                        zsupp[d] = {i: 1 for i in range(v) if val[d] >> i & 1}
+            if span and (d >= 2 * v or d < v):
+                md = sum(1 << i for i in zsupp[d])
+                if md & ~m: viol.append((ph, k, d))
+    run(c['D'], 'D')
+    for r in range(v, n): assert cur[r] == masks[c['start'][r]], 'D compensation at frame 0 (helpers untouched otherwise)'
+    run(c['A'], 'A')
+    for t in range(v): assert cur[v + t] == 0, 'y at frame 0 at the scatter'
+    copies = [val[q] for q in c['ret']]
+    for q in c['ret']:
+        assert q >= 2 * v or q < v; H[L.dim(cur[q])] += 1   # rohanarun: #433 retains totals in source rows
+    for t, row in enumerate(c['scatter']):
+        for k in row: val[v + t] ^= copies[k]
+    run(c['B'], 'B'); run(c['C'], 'C')
+    for r in range(n): climb(r, masks[c['final'][r]])
+    for r in range(v): assert cur[r] == FULL
+    for r in range(2 * v, n): assert cur[r] == FULL
+    for t in range(v): assert cur[v + t] == L.perp(t), 'y final at cap'
+    if check_f2:
+        for s in range(v): assert val[s] == 1 << s
+        for t in range(v): assert val[v + t] == (1 << (v + t)) | (1 << t), ('target', t)
+        for r in range(2 * v, n): assert val[r] == 1 << r, ('helper', r)
+    return dict(sig=sig, viol=viol, H=H, steps=steps, n=n, v=v, R=R, h=h, L=L, masks=masks, ncopy=len(c['ret']))
+
+
+def profile(H_local, v, h=8):
+    prof = Counter({j: 5 * c for j, c in H_local.items()})
+    for j in (2 * h - 2, h - 1, 2 * h + 2, 4): prof[j] += 2 * v
+    return prof
+
+
+def coarse(H, m, W):
+    grid = Q(1, 10**18)
+    root = moment.certify(dict(H), m, W, True); c = Q(int(Q(root['lower']) * 10**18), 10**18)
+    assert moment.moment(H, m, W, c, True)[1] < 1 < moment.moment(H, m, W, c + grid, True)[0]
+    fb = 32 * m * m * sum(H.values())
+    _, up = other.moment(m, W, list(H.items()), c); _, bad = other.moment(m, W, [(1, fb)], c)
+    lo, _ = other.moment(m, W, list(H.items()), c + grid); blo, _ = other.moment(m, W, [(1, fb)], c + grid)
+    assert up + Q(1, 10**16) * bad < 1 < lo + Q(1, 10**16) * blo
+    return c
+
+
+def kappa(c, b):
+    grid = Q(1, 10**18); eta = Q(1, 10**12); beta = Q(1, 10**9); cap = (1 - beta) * b
+    sv = min(c, Q(((cap - grid) * 10**18).__floor__(), 10**18)); binding = 'bit' if sv == c else 'complex'
+    chain = [Q(384599, 10**10)]
+    for _ in range(3):
+        a = (1 - sv) * sv + sv * chain[-1]; assert chain[-1] < a < sv < 1 - a; chain.append(a)
+    bit = chain[-1]
+    bridge = dict(proof='PROOF.md', representation='Exact powers with source-bound finite overcharges',
+                  semantic=dict(G=dict(base=2, exponent=30000), E=dict(base=2, exponent=100000), B_upper=dict(base=2, exponent=100001),
+                                C0=dict(base=2, exponent=210000), C1=1, strict_literal_gap=1, induction_gap_lower=1),
+                  rows=dict(coefficient=20161, degree=10**6, suffix_slope=4 * 10**6, degree_gap=Q(10**6) - Q(51 * 20161, 25)))
+    q = bit * (1 - 2 * eta); mn = (1 - eta) * q / (1 + q); t = mn * 10**18; k = Q((t.numerator - 1) // t.denominator, 10**18)
+    asm = outer.assembly(bit, b, bridge, k, eta=eta, beta=beta)
+    assert len(asm['strict_constraints']) == 47 and min(asm['strict_constraints'].values()) > 0
+    try:
+        outer.assembly(bit, b, bridge, k + grid, eta=eta, beta=beta); raise SystemExit('ADJACENT ADMITTED')
+    except AssertionError: pass
+    return k, binding
+
+
+def price_word(c, **kw):
+    r = replay(c, **kw)
+    v, h, R = r['v'], r['h'], r['R']; m = 5 * h
+    resid = sum(h - r['sig'][x] for x in range(2 * v, 2 * v + R))
+    T = 1 if resid % h == 0 else h
+    W = (4 * v * h + resid) * T // h; assert (4 * v * h + resid) * T % h == 0
+    prof = Counter({j: T * k for j, k in profile(r['H'], v, h).items()}); mass = sum(a * b for a, b in prof.items())
+    L_copy = h * r['ncopy']
+    assert m * W - mass == T * (4 * v - 5 * L_copy), ('deficit', m * W - mass)
+    assert 2 * max(prof) < m
+    cc = coarse(prof, m, W)
+    return dict(c=cc, H=r['H'], prof=prof, W=W, T=T, resid=resid, m=m, deficit=m * W - mass, replay=r)
+
+
+def phi_fn(m, W, a):
+    """linearized moment term per child of rank r (float), for search scoring"""
+    import math
+    return lambda r: r / (m * W) * math.exp(a * math.log(m / r))
diff --git a/research/e8-joint-frame-retiming/vendor/kernel417/engines/base_two_moment.py b/research/e8-joint-frame-retiming/vendor/kernel417/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/kernel417/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/e8-joint-frame-retiming/vendor/kernel417/engines/moment.py b/research/e8-joint-frame-retiming/vendor/kernel417/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/kernel417/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/e8-joint-frame-retiming/vendor/kernel417/engines/outer.py b/research/e8-joint-frame-retiming/vendor/kernel417/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/kernel417/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/e8-joint-frame-retiming/vendor/kernel417/stages.py b/research/e8-joint-frame-retiming/vendor/kernel417/stages.py
new file mode 100644
index 0000000000..9ef95d52f4
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/kernel417/stages.py
@@ -0,0 +1,143 @@
+"""Transcript stages on the E8 bit word (bitE8/1), applied from frozen selections, each bound to the exact input word.
+
+retime  (our #329 descent2 / #287 concave retiming, ported to E8 frames): every selected gate g gets a new frame F with
+        close(LB_g + prev frames of its participants) <= F <= rootspan(AND of their next frames), where LB_g is the
+        x-support of the non-target operands (source-span rule); pinned: D gates (frame 0), y at frame 0 at the scatter,
+        retained totals at FULL at COPY, start and final frames. Checked on the joint retimed configuration.
+kernel  (our #320/#329 shared-donor response kernel; #272/#299/#319 lineage): entry = pivot p, entrance E, donors D with
+        resp(p) = XOR resp(D) over F2, where resp(h) = the targets whose frame-0 completion (D) gates read h; E inside the
+        first frame of p and of every donor. p starts at E and leaves the D gates; each donor climbs to E at the start of
+        A and pays d += (its pivots) at E; after C it pays d += (its pivots) again at FULL (F2: d -= p).
+        Exclusivity: pivots are never donors, a donor serves one entrance. Total entrance rank = 0 mod 8 (integral
+        B_4 width W; the residuals then tile width-72 banks with 9 replicas, checked separately).
+
+usage: stages.py retime|kernel IN.json.gz OUT.json.gz SELECTION.json
+After applying, the full exact replay of e8core (legality, F2 on all columns, source spans) must pass and the output
+must equal the frozen output content hash. (This package uses the kernel stage only: on PR #376's word our retiming
+descent finds no move, before or after the kernel.)
+Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0."""
+import sys, os, json, hashlib
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+from e8core import *
+
+
+def content_sha(c):
+    return hashlib.sha256(json.dumps(c, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+
+
+class Framer:
+    def __init__(self, c):
+        self.fl = c['frames']; self.key = {}; self.v = c['v']
+        for k, fr in enumerate(self.fl): self.key.setdefault(sum(1 << i for i in fr), k)
+    def fid(self, m):
+        if m not in self.key: self.key[m] = len(self.fl); self.fl.append([i for i in range(self.v) if m >> i & 1])
+        return self.key[m]
+
+
+def mask_of(lines): return sum(1 << i for i in lines)
+
+
+def occurrences(c, masks):
+    """per register: list of (kind, ref) with pins ('p', mask) and gates ('g', (phase, k)) in time order"""
+    v = c['v']; n = 2 * v + c['R']; FULL = (1 << v) - 1
+    occ = [[('p', masks[c['start'][r]])] for r in range(n)]
+    for ph in ('D', 'A'):
+        for k, (f, d, s) in enumerate(c[ph]):
+            for x in [d] + s: occ[x].append(('g', (ph, k)))
+    for t in range(v): occ[v + t].append(('p', 0))
+    for q in c['ret']: occ[q].append(('p', FULL))
+    for ph in ('B', 'C'):
+        for k, (f, d, s) in enumerate(c[ph]):
+            for x in [d] + s: occ[x].append(('g', (ph, k)))
+    for r in range(n): occ[r].append(('p', masks[c['final'][r]]))
+    return occ
+
+
+def lower_bounds(c, L):
+    v = c['v']; n = 2 * v + c['R']; sup = [1 << i if i < v else 0 for i in range(n)]; lb = {}
+    for ph in ('D', 'A', 'B', 'C'):
+        for k, (f, d, srcs) in enumerate(c[ph]):
+            need = 0
+            for s in srcs:
+                sup[d] |= sup[s]
+                if s < v or s >= 2 * v: need |= sup[s]
+            if d >= 2 * v: need |= sup[d]
+            lb[(ph, k)] = L.close(need) if need else 0
+    return lb
+
+
+def retime(c, sel):
+    L = Lat(c['lines']); masks = to_masks(c, L); occ = occurrences(c, masks); lb = lower_bounds(c, L)
+    gm = {(ph, k): masks[g[0]] for ph in ('D', 'A', 'B', 'C') for k, g in enumerate(c[ph])}
+    pos = {}
+    for r, o in enumerate(occ):
+        for i, (kind, x) in enumerate(o):
+            if kind == 'g': pos.setdefault(x, []).append((r, i))
+    def fr(r, i):
+        kind, x = occ[r][i]; return x if kind == 'p' else gm[x]
+    seen = set()
+    for ph, k, old_lines, new_lines in sel:
+        g = (ph, k); assert ph != 'D' and g not in seen; seen.add(g)
+        assert gm[g] == L.close(mask_of(old_lines)), ('selection not bound to this word', g)
+        F = L.close(mask_of(new_lines)); assert F == mask_of(new_lines), 'frame given as all its root lines'
+        gm[g] = F
+    for g in seen:  # the joint retimed configuration: every moved gate inside its feasible interval
+        F = gm[g]; lo = lb[g]; hi = (1 << c['v']) - 1
+        for r, i in pos[g]: lo |= fr(r, i - 1); hi &= fr(r, i + 1)
+        assert lo & ~F == 0 and F & ~hi == 0, ('outside the feasible interval', g)
+    out = json.loads(json.dumps(c)); fm = Framer(out)
+    for ph in ('D', 'A', 'B', 'C'):
+        out[ph] = [[fm.fid(gm[(ph, k)]), d, list(s)] for k, (f, d, s) in enumerate(c[ph])]
+    return out
+
+
+def kernel(c, sel):
+    L = Lat(c['lines']); masks = to_masks(c, L); v = c['v']; n = 2 * v + c['R']; FULL = (1 << v) - 1
+    occ = occurrences(c, masks)
+    gm = {(ph, k): masks[g[0]] for ph in ('D', 'A', 'B', 'C') for k, g in enumerate(c[ph])}
+    first = {}
+    for h in range(2 * v, n):
+        assert masks[c['start'][h]] == 0
+        first[h] = next(x if kind == 'p' else gm[x] for kind, x in occ[h][1:] if (x if kind == 'p' else gm[x]) != 0)
+    resp = {}
+    for f, t, srcs in c['D']:
+        assert masks[f] == 0
+        for s in srcs: resp[s] = resp.get(s, 0) ^ (1 << (t - v))
+    ret = set(c['ret']); pivots = {}; donor_at = {}; tot = 0
+    for E_lines, p, D in sel:
+        E = L.close(mask_of(E_lines)); assert E == mask_of(E_lines) and E != 0
+        assert p not in ret and p not in pivots and p not in donor_at and 2 * v <= p < n
+        x = resp.get(p, 0)
+        for d in D:
+            assert d not in ret and d not in pivots and 2 * v <= d < n
+            assert donor_at.setdefault(d, E) == E, 'donor serves one entrance'
+            x ^= resp.get(d, 0)
+        assert x == 0, ('response relation fails', p)
+        for h in [p] + D: assert E & ~first[h] == 0, ('entrance not inside first frame', h)
+        pivots[p] = E; tot += L.dim(E)
+    assert not set(pivots) & set(donor_at)
+    assert tot % 8 == 0, 'total entrance rank 0 mod 8'
+    out = json.loads(json.dumps(c)); fm = Framer(out)
+    for p, E in pivots.items(): out['start'][p] = fm.fid(E)
+    out['D'] = [[f, t, [s for s in srcs if s not in pivots]] for f, t, srcs in c['D']]
+    byd = {}
+    for E_lines, p, D in sel:
+        for d in D: byd.setdefault((d, mask_of(E_lines)), []).append(p)
+    out['A'] = [[fm.fid(E), d, sorted(ps)] for (d, E), ps in sorted(byd.items())] + out['A']
+    out['C'] = out['C'] + [[fm.fid(FULL), d, sorted(ps)] for (d, E), ps in sorted(byd.items())]
+    return out, len(sel), tot, len(byd)
+
+
+if __name__ == '__main__':
+    st, inp, outp, selp = sys.argv[1:5]
+    c = load_word(inp); sel = json.load(open(selp))
+    assert sel['input_sha256'] == content_sha(c), 'selection bound to a different input word'
+    if st == 'retime':
+        w = retime(c, sel['gates']); info = '%d gates retimed' % len(sel['gates'])
+    else:
+        w, ne, tot, nd = kernel(c, sel['entries']); info = '%d entries, total entrance rank %d, %d donor slots' % (ne, tot, nd)
+    r = replay(w, span_mode='z'); assert not r['viol'], r['viol'][:5]
+    assert content_sha(w) == sel['output_sha256'], 'output differs from the frozen stage output'
+    save_word(w, outp)
+    print('   stage %s: %s | exact replay PASS (legality, F2 on %d columns, source spans) | local histogram %s | output sha %s'
+          % (st, info, r['n'], dict(sorted(r['H'].items())), sel['output_sha256'][:16]))
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/LICENSE b/research/e8-joint-frame-retiming/vendor/pr436/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
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+
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diff --git a/research/e8-joint-frame-retiming/vendor/pr436/NOTICE.md b/research/e8-joint-frame-retiming/vendor/pr436/NOTICE.md
new file mode 100644
index 0000000000..2c01026b8b
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/NOTICE.md
@@ -0,0 +1,51 @@
+# Notice
+
+Apache-2.0 (`LICENSE`). Prepared by eumemic with substantial Anthropic Claude assistance.
+
+## New in this package
+
+- `code/reuse/`: the elimination-reuse stage (`reuse.py`), the frame retiming (`retime.py`), their integer cost tables (`ecost.py`), the regeneration driver (`regen.py`) and the elimination-reuse negative controls (`controls.py`).
+- `data/params/params-r740.json`: our parameters for PR #370's producer. `discovery/` holds the search that nominated them.
+- `data/bit/bitE8-r740.json.gz` (the word) and `data/bit/reuse-ledger.json` (its inserted elimination gates).
+- `code/nine/global_word_g.py`, `audit_g.py`, `certify_g.py`: generalisations of PR #386's `global_word.py`, `audit.py` and `certify.py` to any bitE8/1 word whose helpers start at frame 0 and end at the full frame. `regress386.py` checks them against PR #386's own receipts. `cited.py` binds the cited complex savings to the PRs' receipts. `compose433.py` ports PR #433's bit pricing, finite invoice and tail.
+- `code/b4/kappa_b4.py`, `code/provenance.py`, `verify.sh`, `EXPECTED.json`, `data/complex-b-*.json`, `.github/workflows/e8-bit-elimination-reuse.yml`.
+
+## Vendored, byte-identical (git blob ids in `SOURCE-pr*.json`, checked by `code/provenance.py`)
+
+- **PR #370 (Dylan Crow / utcorvusvolat-dotcom, with Anthropic Claude assistance), commit b7fe9cd:**
+  - the producer `code/bit/producer/`;
+  - the independent checker and its controls `code/bit/independent/`;
+  - the record exporter and the record-level controls;
+  - PR #266's official cohort checkers as generalised there (`legality_h.cpp`, `columns_h.cpp`, NCOPY);
+  - `gram_frames.py`, `stage_cohort.py`;
+  - PR #315's engines (`code/pricing/`, DreamingOfClouds);
+  - nlohmann/json (`json.hpp`, MIT licence in its header);
+  - the E8 bit word `data/bit/bitE8-r865.json.gz`;
+  - `LICENSE`.
+- **PR #381 (DaysSky, assisted with Claude), commit 00765b2:** the B_K checkers `columns_k.cpp`, `geometry_k.py`, `tile_k.py`, `certify_bit_k.py`, `finite_k.py`, `cost.py`, `receipts_k.py`, and PR #363's `bridged.py` (DaysSky).
+- **PR #386 (Zhihao Chen / jacklightChen, with OpenAI Codex assistance), commit dd11cf8:**
+  - `geometry.py` (compressed nine-stage bit geometry, unchanged);
+  - the portable `bits/stdc++.h`;
+  - the validation receipts `GLOBAL.json`, `AUDIT.json` and `COMBINED.json`, used only as regression references.
+- **PR #417 (Chafik Boukhalfa / chafreaky, with Anthropic Claude assistance), commit 3f681fb:**
+  - `bootstrap.py` (their reimplementation of rohanarun's PR #392 refined pricing tail), `e8core.py` and its copies of PR #315's engines;
+  - `apply376.py`;
+  - the final kernel word, used as a B_4 control.
+- **PR #376 (applecrusher, with OpenAI Codex assistance), commit 92328da:** `frame-selection.json`, `reuse-selection.json` and `LICENSE-pr376`, as vendored in PR #417.
+- **PR #426 (ai-nanachi, with OpenAI Codex assistance), commit 88d5525:** the R767 bit word, used only as a priced comparison and B_3 control, and `LICENSE-pr426`.
+- **PR #425 (Zhihao Chen / jacklightChen, with OpenAI Codex assistance), commit e11ccea:** the validation receipt `FINAL.json`, which states the cited b and κ.
+- **PR #431 (Rohan Arun / rohanarun, with OpenAI Codex assistance; draft), commit db4f465:** the validation receipt `VALIDATION-LOCAL.json`, which states the cited b and κ.
+- **PR #433 (icekylinx, with OpenAI Codex assistance), commit 6d92445:** `CERTIFICATE.json`, which states the cited complex b, the R758 bit c and κ. `code/nine/compose433.py` is our port of #433's `code/bit_price.py` and `code/combined.py` arithmetic. No #433 code is vendored or run.
+
+## Cited, not rebuilt
+
+Complex coarse savings in `data/complex-b-nine.json` and `data/complex-b-b4.json`, each with its PR, commit and receipt (git blob):
+
+- compressed nine-stage layout:
+  - PR #433 (icekylinx; `data/complex-b-433.json`, bound to its certificate by `compose433.py`);
+  - PR #386 (#377's component), PR #425 (jacklightChen) and PR #431 (rohanarun, draft), bound to their receipts by `code/nine/cited.py`.
+- B_4: PR #424, #407 (chafreaky), #410 (eumemic) and #409 (rohanarun).
+
+No complex construction is rebuilt here.
+
+The E8 label family follows Jacob Sussman's introduction of E8 for the complex supplier.
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/README.md b/research/e8-joint-frame-retiming/vendor/pr436/README.md
new file mode 100644
index 0000000000..5ddb576f02
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/README.md
@@ -0,0 +1,182 @@
+κ = 1128983115440183/10¹⁸ (conditional; bit-bound) with PR #433's complex supplier
+
+# An E8 bit word with 740 helpers: dead helper slots reused through F₂ relations
+
+This package is a bit-side supplier: an E8 bit word in PR #370's format (h = 8, v = 120, 9 retained totals) with **R = 740 helpers**. For comparison, #370 has 865, #376 has 822, #426 has 767 and #433 has 758. In the compressed nine-stage layout of PR #386 (m = 64), which #425, #431 and #433 use, its coarse saving is
+
+**c = 282564789736676592463/(2.5·10²³) ≈ 1.130259158946706·10⁻³**
+
+on PR #433's 10⁻²⁴ grid. On #386's 10⁻¹⁸ grid it is 565129579473353/(5·10¹⁷).
+
+PR #433 (icekylinx) pairs its split-centre complex supplier, b = 1183986549206329/10¹⁸ ≈ 1.183987·10⁻³, with a 758-helper bit word, c = 1.122122700265139·10⁻³. #433's bit side binds, at κ = 1.120864952258278·10⁻³. With this word in place of R758, through #433's own bit engine, finite invoice and six-level tail:
+
+**κ = 1128983115440183/10¹⁸ ≈ 1.128983115440183·10⁻³**, bit-bound, **+0.7243 % over #433**.
+
+The bit c is +0.7251 % over #433's R758. As controls, the same code reproduces #433's bit c from #433's stated R758 profile, and #433's κ from #433's (c, b), exactly. The complex side still has 4.75 % of headroom over this c.
+
+## Bit coarse savings
+
+| bit word | R | compressed nine-stage (#386 layout, m = 64) | B₄ unsplit (#381 layout, m = 72) | B₃ unsplit (m = 56) |
+| --- | ---: | ---: | ---: | ---: |
+| PR #370 (`bitE8-r865`) | 865 | **1057833103534317/10¹⁸** (= #386, #425, #431) | **249162322049641/(2.5·10¹⁷)** (= #381) | 9.912261·10⁻⁴ |
+| PR #376 (R822) | 822 | 1084538480613107/10¹⁸ | **255384852701747/(2.5·10¹⁷)** (= #390 … #424) | **8128527708459/(8·10¹⁵)** (= #376, #389 baseline) |
+| PR #417 (R822 + shared-donor kernel) | 822 | — (entrance residuals do not fill #386's rank-8 slots) | **1044063934627389/10¹⁸** (= #417) | 1.037508·10⁻³ |
+| PR #426 (R767, clean-reset reuse) | 767 | 1116714040089377/10¹⁸ | 1.051689·10⁻³ | **104575879789097/10¹⁷** (= #426) |
+| PR #433 (R758: #426 + source-basis totals) | 758 | **561061350132569610283/(5·10²³)** (= #433, 10⁻²⁴ grid) | — | — |
+| **this word** | **740** | **282564789736676592463/(2.5·10²³) ≈ 1.130259·10⁻³** | **1064525457834209/10¹⁸ ≈ 1.064525·10⁻³** | **1058066102700151/10¹⁸ ≈ 1.058066·10⁻³** |
+
+Compressed nine-stage values are on #386's 10⁻¹⁸ grid, except #433's and this word's, which are on #433's 10⁻²⁴ grid. On the 10⁻¹⁸ grid this word is 565129579473353/(5·10¹⁷).
+
+Bold entries in the control rows are the values the cited PRs publish. `verify.sh` reproduces each exactly with the same code that prices this word. Most come from the PR's own word. #433's R758 value comes from the R758 profile stated in #433, because the package does not ship that word. The other entries are computed here and are not published by those PRs.
+
+This word compared with the best published bit c in each layout:
+
+| layout | best published bit c | this word |
+| --- | --- | ---: |
+| compressed nine-stage | #433's R758 | +0.725 % |
+| B₄ | #417 | +1.960 % |
+| B₃ | #426 | +1.177 % |
+
+Against #426's R767 word priced in the same layouts, this word is +1.213 % (compressed nine-stage) and +1.221 % (B₄). The five-stage saving (PR #370's independent checker) is 9.63227·10⁻⁴.
+
+## κ with cited complex suppliers
+
+| complex supplier (cited, not rebuilt) | layout and tail | b | κ with this word | κ as published |
+| --- | --- | ---: | ---: | ---: |
+| **PR #433 (icekylinx)** | compressed nine-stage; #433's tail | 1183986549206329/10¹⁸ | **1128983115440183/10¹⁸** (bit-bound) | 560432476129139/(5·10¹⁷) (bit-bound, R758) |
+| PR #431 (rohanarun, draft) | compressed nine-stage; #386's tail | 529046848168159/(5·10¹⁷) | 1056975315151441/10¹⁸ (complex-bound) | 1056715272872389/10¹⁸ at db4f465 (bit-bound, #370 word); 1056975315151441/10¹⁸ at 71c5988 (with #376's retimed bit word) |
+| PR #425 (jacklightChen) | compressed nine-stage; #386's tail | 52455248902029/(5·10¹⁶) | 524002754014103/(5·10¹⁷) | same |
+| PR #386 (#377's component) | compressed nine-stage; #386's tail | 999240641319551/10¹⁸ | 998243154231047/10¹⁸ | same |
+| PR #424 (chafreaky) | B₄; #392's refined tail | 254887067002137341481/(2.5·10²³) | 1018509848057013/10¹⁸ | same |
+| PR #410, #409, #407 | B₄; #392's refined tail | as cited by #417 | as published | same |
+
+All κ values are on the 10⁻¹⁸ grid and satisfy PR #315's 47 strict outer inequalities. The next grid point is rejected. The three tails:
+
+- **#433's tail** (`compose433.py`, ported from #433's `bit_price.py` and `combined.py`):
+  - c is the 10⁻²⁴-grid lower endpoint of PR #315's `certify`, with the 10⁻¹⁶ bad-branch allowance, and is checked by the second engine;
+  - η = β = 10⁻¹⁸, seed min(c, (1 − β)b) − 10⁻²⁴, six bootstrap levels;
+  - zero η, zero β and unit β are rejected as well;
+  - the finite invoice charges the prefix at the next multiple of 64 bits: here 123 bits, charged 128.
+- **#386's tail** (#386, #425, #431): three bootstrap steps, η = 10⁻¹², β = 10⁻⁹. The seed is strictly below (1 − β) times both suppliers (#431's policy).
+- **B₄:** #392's refined tail, as reimplemented in PR #417's `bootstrap.refine`.
+
+With #431's complex supplier the complex side binds. Every bit word above #431's b gives that κ, including #376's and #426's words in this layout. #431's later head uses #376's retimed word. The PR #370 word reproduces #431's κ at db4f465, and #425's and #386's κ, exactly.
+
+## The word
+
+1. **PR #370's producer, unchanged, with new parameters.** `data/params/params-r740.json` differs from #370's `params-r865.json` in 67 of 520 entries. It was found by a local search with the reuse pass in the objective (`discovery/`). The producer gives a word with R = 863.
+2. **Elimination reuse** (`code/reuse/reuse.py`).
+   - A helper is dead after its last gate in phases A and B. It still holds a leftover x-content: an F₂ sum of source lines, at its last frame.
+   - Before a later helper is born at frame F, the pass looks for an F₂ relation content(r₀) = Σ_{q∈S} content(q) among dead slots whose frames lie inside F. It emits r₀ += S at the join G of their frames (G ⊆ F). r₀ then holds no x-content and hosts the new helper.
+   - The relation is found by Gaussian elimination over F₂. The cheapest relation with |S| ≤ 3 replaces it when one exists, scored by the extra climbing of r₀ and of the eliminators.
+   - The 9 retained totals take dead slots too. The slot's leftover x-lines are read from the sources at the full frame.
+   - The dirt compensation D and the cleanup C are rebuilt as in #370's `fullword.py`.
+   - **114 helper slots and 9 totals are reused: R 863 → 740.**
+   - **Prior and concurrent work.**
+     - #376 reused helper lifetimes by aliasing: 43 reuses.
+     - #426 (ai-nanachi, posted first) uses the same mechanism as this pass. It zeroes a retired helper's x-content with exact two- or three-parent "clean resets" before reusing the slot, rebuilds D and C, and keeps the totals protected. It makes 55 resets on #376's R822 word (R767).
+     - This pass was developed independently. It differs in four ways: it searches every dead slot inside the birth frame by elimination, uses cost-scored relations with up to three eliminators, puts the totals on dead slots as well, and starts from a re-parameterised #370 producer word (R863).
+   - **#433's source-basis trick does not apply here.** The trick computes the nine retained sums in source rows, which removes #426's nine dedicated total helpers (R767 → 758). In this word the totals already sit on slots of earlier helpers, and no helper is born after them, so the trick would remove no register.
+3. **Retiming** (`code/reuse/retime.py`, the idea of #389). Each gate moves to its lowest or highest legal frame when that lowers Σ r ln(64/r) over its registers' adjacent steps: 37 gate moves.
+
+All search choices use integer costs computed with Python's correctly rounded `decimal` logarithm, so the word is the same on every platform. One invocation's local histogram is {1: 2355, 2: 884, 3: 489, 4: 425, 5: 62, 8: 9}: 4,224 blocks, of which 9 are copies. Gates D/A/B/C: 120/1873/472/1873; 944 frames.
+
+## Verify
+
+    BOOST_INCLUDE=/usr/include bash research/e8-bit-elimination-reuse/verify.sh /fresh/output/dir
+    bash research/e8-bit-elimination-reuse/verify.sh --quick /fresh/output/dir
+
+Requirements: Python 3.11+ with numpy, mpmath and sympy (`requirements.txt`); a C++17 compiler (`CXX`); Boost headers (`BOOST_INCLUDE`). `--quick` skips the regressions on #370's word, the comparison words in the compressed nine-stage layout, and the B₃ rows. The workflow `.github/workflows/e8-bit-elimination-reuse.yml` runs both modes on Python 3.12 and 3.14.
+
+0. **Manifest and provenance.** `MANIFEST.sha256`. The git blob id of all 52 vendored files is checked against `SOURCE-pr*.json`: #370, #376, #381, #386, #417, #425, #426, #431 and #433.
+1. **The word from pinned inputs.**
+   - Control: #370's producer regenerates #370's word from its own parameters.
+   - `regen.py` rebuilds this word from our parameters (producer → reuse → retiming). It must equal the shipped word, and the reuse ledger must match.
+   - #376's R822 word is rebuilt from #370's word and #376's two witnesses with #417's `apply376.py`, as a control word.
+2. **One invocation, exact.**
+   - #370's independent checker: the 120 E8 root lines; nested frames; common gate frames; F₂ on all 980 columns, dirty helpers included; Gram determinants on 935 used frames (prime 2 only); the five-stage root.
+   - #370's 6 word-level controls, rejected.
+   - 6 elimination-reuse controls, rejected by the same checker: drop an elimination gate, drop one eliminator, drop one x-line read of a total's undo, lower an elimination below an eliminator's frame, remove all 123 elimination gates, move a total's undo gate to frame 0.
+3. **Official checkers.**
+   - PR #266's cohort legality, as generalised in #370 (NCOPY = 9): 19,527 records, 15,294 common-frame ADDs.
+   - Five-stage formal columns: 1,220 columns, prefix payload 64 bits < 104.
+   - #381's B₄ formal columns: all 1,700 physical columns over F₂ through 9 invocations, 18 twin bridges and the terminal exchange. All 18 omitted-bridge controls are rejected.
+   - #370's 6 record-level controls are rejected, including the unmodified copy count NCOPY = 8.
+4. **Nondegeneracy.** `gram_frames.py`: all 944 frames positive definite under the E8 form. Prime witnesses are valid; the only prime is 2.
+5. **Retained totals.** 9 COPY/ERASE episodes at the full frame (rank 8).
+6. **Compressed nine-stage layout (#386).**
+   - #386's `geometry.py`, unchanged: 120 port routes, 1,080 route checks, at most 77 route factors with denominators {1, 2, 4}, and the bank slots. It is bound to this word by the equality of the 120 label vectors.
+   - `global_word_g.py`, our generalisation of #386's `global_word.py`:
+     - both reflected local streams replay all 980 columns;
+     - the scalar replay over 9 stages covers 7,620 independent columns;
+     - 72 local invocations, 1,405,944 emitted events and 53,280 bank assignments (6,660 banks of 8 whole rank-8 slots, no padding);
+     - live stock 64v + 9R = 14,340;
+     - deficit 2,496 = 8(8v − 9·72);
+     - max child 42 of 64, so two-level halving;
+     - prefix bound 2¹⁸·776⁵·17,724⁴ of 123 bits, under #386's 192-bit allowance.
+   - `audit_g.py`: 944 exact rational projectors and 3,263 nested pairs. #386's 8 template mutations are rejected.
+   - `cited.py`: each cited complex b, and that PR's own κ, must equal the fields of the PR's receipt. The receipts are #386's `COMBINED.json`, #425's `FINAL.json` and #431's `VALIDATION-LOCAL.json`, vendored and pinned by blob id.
+   - `certify_g.py`: both PR #315 engines with the 10⁻¹⁶ fallback admit c and reject c + 10⁻¹⁸. The finite coefficient has 123 bits; the two-level coefficient has 282 bits, below 2⁵¹²; the row coefficient is 18,355 < 20,161. κ is then computed with each cited complex b.
+   - `compose433.py`: PR #433's bit engine, finite invoice and six-level tail, ported from #433's `bit_price.py` and `combined.py`.
+     - Controls: #433's stated R758 profile prices to #433's bit c, and #433's (c, b) gives #433's κ. Both are bound to #433's `CERTIFICATE.json`, which is vendored and pinned.
+     - Then this word's c, invoice and κ with #433's complex b: next grid point, zero η, zero β and unit β are rejected.
+   - **Regression:** on #370's word the same three scripts reproduce #386's `GLOBAL.json`, `AUDIT.json` and the bit, finite and κ fields of `COMBINED.json`, field for field. They also reproduce #425's and #431's κ.
+   - **Comparison:** the same chain prices #376's word (rebuilt in step 1) and #426's word in this layout. Each gives the same κ with #431, since each has c > b.
+7. **B₄ (#381's layout, unsplit).**
+   - #381's `geometry_k.py` on this word: PR234 routes on 9 blocks, idle gap ranks equal to `bridged.py`, the 9-window entrance completion, max child 50 (halving degree 2).
+   - `tile_k.py`: 740 banks of 9 rank-8 residuals with T = 9 replicas.
+   - `certify_bit_k.py` prices this word and the #370, #376 and #417 controls.
+   - `receipts_k.py` and `finite_k.py`: the finite bill at m = 72. The coefficient has 48 bits, below 2⁸⁰; the payload prefix is 64 bits; the internal row coefficient is 10,370.
+   - `kappa_b4.py` computes κ with the cited B₄ suppliers.
+   - **Regression:** `columns_k` at K = 2 gives the five-stage `columns_h` receipt.
+8. **B₃ (informational).** Formal columns at K = 3 (1,460 columns), banks with T = 7, and prices with the #376 and #426 controls.
+9. **Summary** against `EXPECTED.json`.
+
+Locally, the C++ checkers were built against a 128-bit, overflow-checked stand-in for `boost::multiprecision::cpp_int`, because the preparing machine has no Boost. CI compiles them against libboost-dev.
+
+## Retained assumptions and open obligations
+
+- **Everything PR #370 admits:**
+  - 9 retained totals at h = 8;
+  - PR234's banks for a non-paired-cube family;
+  - the inherited all-size weighted bit compiler, prime/tape/precision and analytic interfaces.
+- **The compressed nine-stage layout is PR #386's:**
+  - its window, bank and route arguments (PROOF.txt there);
+  - two-level halving (max child 42 of 64);
+  - its finite charges.
+  Our scripts check this word against those arguments' finite conditions; they add no new argument.
+- **B₄ is PR #381's:** halving degree two on the bit side (#375, #381); no Lean proof of B_K.
+- **The complex suppliers are cited by pinned reference and not rebuilt:**
+  - the headline κ depends on #433's split-centre complex supplier (its PROOF.md), which builds on #425's written scalar-interface extension;
+  - #433's complex b, its six-level tail (#392's refined form, η = β = 10⁻¹⁸) and all its obligations remain #433's.
+  - #431 (a draft) and the other cited suppliers are listed only for comparison.
+- **#433's bit finite charge is adopted for the headline:** the prefix is charged at the next multiple of 64 bits (here 123 bits, charged 128, inside #386's 192-bit allowance), and the two-level coefficient is below 2⁵¹² (here 282 bits).
+- This is a conditional finite construction, not a formal verification of the multiplication theorem. No Lean proof is claimed.
+- **Not measured:** stacking #417's shared-donor kernel on this word. It applies to B_K banks. It does not apply to #386's whole-block banks, whose slots need rank-8 residuals.
+
+## Credits
+
+- **Dylan Crow (utcorvusvolat-dotcom), PR #370:** the E8 bit word format, the producer whose output we reuse, the independent checker and the generalised official checkers.
+- **applecrusher, PR #376:** helper-lifetime reuse, which the elimination reuse generalises.
+- **ai-nanachi:**
+  - PR #389: the frame-retiming idea;
+  - PR #426: clean-reset reuse, the same slot-reuse mechanism, published first (developed independently here), and its R767 word as a comparison.
+- **icekylinx, PR #433:**
+  - the split-centre complex supplier that the headline κ uses;
+  - its bit engine, finite invoice and six-level tail, ported here;
+  - the R758 comparison.
+- **DaysSky:**
+  - PR #381: the B₄ layout and checkers;
+  - PR #375: halving degree two;
+  - PR #363: B_K and `bridged.py`.
+- **Zhihao Chen (jacklightChen):**
+  - PR #386: the compressed nine-stage bit layout and its checkers, generalised here;
+  - PR #425: the mutable-basis complex word.
+- **Chafik Boukhalfa (chafreaky), PR #417:** the B₄ pricing tail port, the #376 rebuild and the kernel-word control.
+- **Rohan Arun (rohanarun):**
+  - PR #431: a cited complex supplier and the two-supplier seed policy;
+  - PR #392: the refined pricing tail.
+- **Jacob Sussman:** the E8 family and the bridged word.
+- **PR #266 and PR #315 (DreamingOfClouds) lineage:** the official checkers, the moment engines and the outer assembly.
+
+Prepared by eumemic with substantial Anthropic Claude assistance. Apache-2.0 (`LICENSE`); see `NOTICE.md`.
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/compile.py b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/compile.py
new file mode 100644
index 0000000000..86b12507ef
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/compile.py
@@ -0,0 +1,201 @@
+"""Dylan Crow, with Anthropic Claude assistance; Apache-2.0. Compile a Re-Pair hierarchy into an explicit bit word (frames = root masks) and price it.
+Registers: x 0..119, y 120..239, helpers 240.. .  Gate: (phase, frame, dst, [srcs])  dst += sum(srcs) over F2."""
+import e8lib as E, frames as Fm, price as P
+from collections import defaultdict, Counter
+V=E.V
+class Word:
+    def __init__(self):
+        self.nh=0; self.A=[]; self.B=[]; self.ret=[]
+    def helper(self):
+        r=2*V+self.nh; self.nh+=1; return r
+def X(s): return s
+def Y(t): return V+t
+def compile_h(h, low=True, drop=frozenset(), centres=None):
+    need=h.need
+    needed=set(); todo=[u for t in range(V) for u in need[t]]
+    while todo:
+        u=todo.pop()
+        if u in needed: continue
+        needed.add(u)
+        if h.kids[u]: todo.extend(h.kids[u])
+    rules=sorted((u for u in needed if h.kids[u]), key=lambda u:(h.dim[u],u))
+    # low reads: longest nested chain of needed symbols per target
+    lowset=set()
+    if low:
+        for t in range(V):
+            it=sorted(need[t], key=lambda u:(h.dim[u],u)); best={}
+            for j,u in enumerate(it):
+                b=[u]
+                for i in range(j):
+                    v=it[i]
+                    if (h.dim[v]<h.dim[u] and Fm.inside(h.frame[v],h.frame[u])) and len(best[v])+1>len(b): b=best[v]+[u]
+                best[u]=b
+            ch=max(best.values(),key=len) if best else []
+            for u in ch:
+                if h.dim[u]<7 and (t,u) not in drop: lowset.add((t,u))
+    uses=defaultdict(list)
+    for w in rules:
+        for c in h.kids[w]: uses[c].append((0,h.dim[w],h.frame[w],w))
+    for t in range(V):
+        for u in need[t]:
+            if (t,u) in lowset: uses[u].append((1,h.dim[u],h.frame[u],t))
+            else: uses[u].append((1,7,Fm.HYP[t],t))
+    chains={}; chain_of={}
+    for u in needed:
+        ev=sorted(uses[u]); cl=[]
+        for e in ev:
+            best=None
+            for i,ch in enumerate(cl):
+                last=ch[-1]
+                if last[0]==1 and last[1]==7 and last[2]!=e[2]: continue
+                if last[2]==e[2] or (last[1]<e[1] and Fm.inside(last[2],e[2])):
+                    if best is None or cl[best][-1][1]<last[1]: best=i
+            if best is None: cl.append([e]); best=len(cl)-1
+            else: cl[best].append(e)
+            chain_of[(u,e[0],e[3])]=best
+        chains[u]=cl
+    W=Word(); reg={}
+    # phase A: sources
+    for s in range(V):
+        if s not in needed: continue
+        cl=chains[s]
+        xi=None
+        for i,ch in enumerate(cl):
+            if all(e[0]==0 for e in ch): xi=i; break
+        car=[]
+        for i,ch in enumerate(cl):
+            if i==xi: reg[(s,i)]=X(s)
+            else:
+                q=W.helper(); car.append(q); reg[(s,i)]=q
+        if car: W.A.append((Fm.LINE[s],X(s),None,car))   # fan-out copy: each carrier += x_s at line
+    inplace=0
+    for w in rules:
+        F=h.frame[w]; ks=h.kids[w]
+        info=[]
+        for c in ks:
+            i=chain_of[(c,0,w)]; ch=chains[c][i]
+            info.append((c,i,ch[-1][0]==0 and ch[-1][3]==w))
+        host=None
+        for c,i,end in info:
+            if end and reg[(c,i)]>=2*V: host=(c,i); break
+        if host:
+            q=reg.pop(host); srcs=[reg[(c,i)] for c,i,_ in info if (c,i)!=host]
+            W.A.append((F,q,srcs,None)); inplace+=1
+        else:
+            q=W.helper(); W.A.append((F,q,[reg[(c,i)] for c,i,_ in info],None))
+        reg[(w,0)]=q
+        n=len(chains[w])
+        if n>1:
+            qs=[W.helper() for _ in range(n-1)]
+            W.A.append((F,q,None,qs))
+            for i,qq in enumerate(qs): reg[(w,i+1)]=qq
+    # totals
+    cent=centres or default_centres()
+    for sup in cent:
+        q=W.helper(); W.A.append((Fm.FULL,q,[X(s) for s in range(V) if sup>>s&1],None)); W.ret.append(q)
+    # phase B: deliveries sorted by frame dim
+    ev=[]
+    for t in range(V):
+        hyp=[]
+        for u in need[t]:
+            r=reg[(u,chain_of[(u,1,t)])]
+            if (t,u) in lowset: ev.append((h.dim[u],h.frame[u],Y(t),[r]))
+            else: hyp.append(r)
+        if hyp: ev.append((7,Fm.HYP[t],Y(t),hyp))
+    ev.sort(key=lambda e:(e[0],e[2]))
+    for d,F,yt,srcs in ev: W.B.append((F,yt,srcs,None))
+    W.stats=dict(R=W.nh,rules=len(rules),inplace=inplace,low=len(lowset),chains=sum(len(c) for c in chains.values()))
+    return W
+_DC=None
+def default_centres():
+    """T0 = all lines; T_i = {S : B(a_i,S)=1} for a basis a_i of E8/2E8 given by 8 lines spanning it mod 2."""
+    global _DC
+    if _DC: return _DC
+    # pick 8 lines whose images are independent mod 2 : use B-matrix rank
+    B=[[E.G[a][b]&1 for b in range(V)] for a in range(V)]
+    rows=[]; basis=[]; piv={}
+    for a in range(V):
+        m=sum(B[a][b]<<b for b in range(V)); m0=m
+        while m:
+            p=m.bit_length()-1
+            if p in piv: m^=piv[p]
+            else: piv[p]=m; basis.append(a); break
+        if len(basis)==8: break
+    _DC=[(1<<V)-1]+[sum(B[a][b]<<b for b in range(V)) for a in basis]
+    return _DC
+def decoder(cent):
+    """for each target t, the set of centres it reads so that sum = 1 + B(t,.) (as masks); verify."""
+    import itertools
+    full=(1<<V)-1
+    B=[sum((E.G[a][b]&1)<<b for b in range(V)) for a in range(V)]
+    reads=[]
+    for t in range(V):
+        want=full^B[t]
+        found=None
+        for k in range(len(cent)+1):
+            for C in itertools.combinations(range(len(cent)),k):
+                m=0
+                for c in C: m^=cent[c]
+                if m==want: found=C; break
+            if found is not None: break
+        assert found is not None
+        reads.append(found)
+    return reads
+def chains_of_word(W, cent_reads=None):
+    """legality replay: returns per-register list of frame dims, asserts nesting and common frame."""
+    nreg=2*V+W.nh
+    cur=[Fm.LINE[s] for s in range(V)]+[0]*V+[0]*W.nh
+    dims=[[1] for _ in range(V)]+[[0] for _ in range(V+W.nh)]
+    def climb(r,F):
+        if cur[r]==F: return
+        assert Fm.inside(cur[r],F) and cur[r]!=F, ('not nested',r)
+        cur[r]=F; dims[r].append(Fm.dim(F))
+    for ph in ('A','B'):
+        if ph=='B':
+            for q in W.ret: assert cur[q]==Fm.FULL
+            assert all(cur[Y(t)]==0 for t in range(V))
+        for F,dst,srcs,outs in getattr(W,ph):
+            regs=[dst]+(srcs or [])+(outs or [])
+            assert len(set(regs))==len(regs)
+            for r in regs: climb(r,F)
+    for s in range(V): climb(X(s),Fm.FULL)
+    for t in range(V): climb(Y(t),Fm.HYP[t])
+    for q in range(2*V,nreg): climb(q,Fm.FULL)
+    return dims
+def f2_check(W, need_low=None):
+    """forward F2 replay on source columns only (no dirt): y_t must end with exactly x_t (after centre reads)."""
+    val=[1<<s for s in range(V)]+[0]*V+[0]*W.nh
+    for F,dst,srcs,outs in W.A:
+        if srcs is not None:
+            for s in srcs: val[dst]^=val[s]
+        if outs is not None:
+            for o in outs: val[o]^=val[dst]
+    cent=[val[q] for q in W.ret]
+    reads=decoder(cent)
+    for t in range(V):
+        for c in reads[t]: val[Y(t)]^=cent[c]
+    for F,dst,srcs,outs in W.B:
+        if srcs is not None:
+            for s in srcs: val[dst]^=val[s]
+        if outs is not None:
+            for o in outs: val[o]^=val[dst]
+    bad=[t for t in range(V) if val[Y(t)]!=1<<t]
+    xbad=[s for s in range(V) if val[s]!=1<<s]
+    return bad,xbad
+def evaluate(W):
+    dims=chains_of_word(W)
+    steps=Counter()
+    for d in dims:
+        for a,b in zip(d,d[1:]): steps[b-a]+=1
+    s,deficit,D=P.price(steps,W.nh)
+    return s,deficit,D,steps
+if __name__=='__main__':
+    import pickle,sys
+    from repair import Hier
+    import __main__; __main__.Hier=Hier
+    h=pickle.load(open(sys.argv[1],'rb'))
+    W=compile_h(h)
+    print(W.stats)
+    print('f2 check bad targets/x:',[len(z) for z in f2_check(W)])
+    s,deficit,D,steps=evaluate(W)
+    print('R',W.nh,'saving %.6e'%s,'deficit',deficit,'D %.0f'%D,sorted(steps.items()))
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/compile2.py b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/compile2.py
new file mode 100644
index 0000000000..a7bdfdfbe4
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/compile2.py
@@ -0,0 +1,142 @@
+"""Dylan Crow, with Anthropic Claude assistance; Apache-2.0. Compile v2: A-rules (built from sources) before the scatter, B-rules (helpers only) and deliveries after,
+interleaved by frame dimension.  Low reads at the symbol's own frame along one nested chain per target."""
+import e8lib as E, frames as Fm, price as P, compile as C
+from collections import defaultdict, Counter
+V=E.V
+def needed_symbols(h):
+    needed=set(); todo=[u for t in range(V) for u in h.need[t]]
+    while todo:
+        u=todo.pop()
+        if u in needed: continue
+        needed.add(u)
+        if h.kids[u]: todo.extend(h.kids[u])
+    return needed
+PHASEMODE=['allA']
+def phases(h,needed):
+    ph={}
+    def get(u):
+        if u<V: return 'S'
+        if u in ph: return ph[u]
+        ks=[get(c) for c in h.kids[u]]
+        if PHASEMODE[0]=='allA':
+            ph[u]='A' if all(k in ('S','A') for k in ks) else 'B'
+        else:
+            ph[u]='A' if ('S' in ks and all(k in ('S','A') for k in ks)) else 'B'
+        return ph[u]
+    for u in needed:
+        if u>=V: get(u)
+    return ph
+def choose_low(h, needed, ph, drop=frozenset(), mode='longest'):
+    lowset=set()
+    for t in range(V):
+        it=sorted(h.need[t], key=lambda u:(h.dim[u],u)); best={}
+        for j,u in enumerate(it):
+            b=[u]
+            for i in range(j):
+                v=it[i]
+                if h.dim[v]<h.dim[u] and Fm.inside(h.frame[v],h.frame[u]) and len(best[v])+1>len(b): b=best[v]+[u]
+            best[u]=b
+        ch=max(best.values(),key=len) if best else []
+        for u in ch:
+            if h.dim[u]<7 and (t,u) not in drop: lowset.add((t,u))
+    return lowset
+def compile2(h, lowset=None, drop=frozenset(), centres=None):
+    needed=needed_symbols(h); ph=phases(h,needed)
+    if lowset is None: lowset=choose_low(h,needed,ph,drop)
+    # uses: (phaseorder, dim, kind, frame, who)   phaseorder 0=A 1=B ; kind 0 rule-child 1 delivery
+    uses=defaultdict(list)
+    for w in needed:
+        if w<V: continue
+        po=0 if ph[w]=='A' else 1
+        for c in h.kids[w]: uses[c].append((po,h.dim[w],0,h.frame[w],w))
+    for t in range(V):
+        for u in h.need[t]:
+            if (t,u) in lowset: uses[u].append((1,h.dim[u],1,h.frame[u],t))
+            else: uses[u].append((1,7,1,Fm.HYP[t],t))
+    chains={}; chain_of={}
+    for u in needed:
+        ev=sorted(uses[u],key=lambda e:(e[0],e[1],e[2],e[4]))
+        cl=[]
+        for e in ev:
+            best=None
+            for i,ch in enumerate(cl):
+                last=ch[-1]
+                if last[2]==1 and last[1]==7 and last[3]!=e[3]: continue
+                if last[3]==e[3] or (last[1]<e[1] and Fm.inside(last[3],e[3])):
+                    if best is None or cl[best][-1][1]<last[1]: best=i
+            if best is None: cl.append([e]); best=len(cl)-1
+            else: cl[best].append(e)
+            chain_of[(u,e[2],e[4])]=best
+        chains[u]=cl
+    W=C.Word(); reg={}
+    # sources: x takes a chain made only of A-uses (prefer the longest); others carriers
+    for s in range(V):
+        if s not in needed: continue
+        cl=chains[s]; xi=None
+        cand=[i for i,ch in enumerate(cl) if all(e[0]==0 for e in ch)]
+        if cand: xi=max(cand,key=lambda i:len(cl[i]))
+        car=[]
+        for i in range(len(cl)):
+            if i==xi: reg[(s,i)]=C.X(s)
+            else: q=W.helper(); car.append(q); reg[(s,i)]=q
+        if car: W.A.append((Fm.LINE[s],C.X(s),None,car))
+    W.ncarrier=sum(1 for k,r in reg.items() if r>=2*V)
+    inplace=[0]; ncopy=[0]
+    def form(w,lst):
+        F=h.frame[w]; info=[]
+        for c in h.kids[w]:
+            i=chain_of[(c,0,w)]; ch=chains[c][i]
+            info.append((c,i,ch[-1][2]==0 and ch[-1][4]==w))
+        host=None
+        for c,i,end in info:
+            if end and reg[(c,i)]>=2*V: host=(c,i); break
+        if host:
+            q=reg.pop(host); lst.append((F,q,[reg[(c,i)] for c,i,_ in info if (c,i)!=host],None)); inplace[0]+=1
+        else:
+            q=W.helper(); lst.append((F,q,[reg[(c,i)] for c,i,_ in info],None))
+        reg[(w,0)]=q; n=len(chains[w])
+        if n>1:
+            qs=[W.helper() for _ in range(n-1)]; ncopy[0]+=n-1
+            lst.append((F,q,None,qs))
+            for i,qq in enumerate(qs): reg[(w,i+1)]=qq
+    Arules=sorted((w for w in needed if w>=V and ph[w]=='A'),key=lambda w:(h.dim[w],w))
+    for w in Arules: form(w,W.A)
+    cent=centres or C.default_centres()
+    for sup in cent:
+        q=W.helper(); W.A.append((Fm.FULL,q,[C.X(s) for s in range(V) if sup>>s&1],None)); W.ret.append(q)
+    # phase B events
+    ev=[]
+    for w in needed:
+        if w>=V and ph[w]=='B': ev.append((h.dim[w],0,w))
+    lowby=defaultdict(list)
+    for (t,u) in lowset: lowby[u].append(t)
+    for u in lowby: ev.append((h.dim[u],1,u))
+    for t in range(V): ev.append((7,2,t))
+    ev.sort()
+    for d,k,a in ev:
+        if k==0: form(a,W.B)
+        elif k==1:
+            u=a
+            for t in sorted(lowby[u]):
+                W.B.append((h.frame[u],C.Y(t),[reg[(u,chain_of[(u,1,t)])]],None))
+        else:
+            t=a; srcs=[reg[(u,chain_of[(u,1,t)])] for u in h.need[t] if (t,u) not in lowset]
+            if srcs: W.B.append((Fm.HYP[t],C.Y(t),srcs,None))
+    W.stats=dict(R=W.nh,carriers=W.ncarrier,Arules=len(Arules),Brules=sum(1 for w in needed if w>=V and ph[w]=='B'),
+                 inplace=inplace[0],copies=ncopy[0],low=len(lowset),chains=sum(len(c) for c in chains.values()))
+    return W
+if __name__=='__main__':
+    import pickle,sys
+    from repair import Hier
+    import __main__; __main__.Hier=Hier
+    try:
+        import ham1; __main__.SH=ham1.SH
+    except Exception: pass
+    h=pickle.load(open(sys.argv[1],'rb'))
+    if len(sys.argv)>2: PHASEMODE[0]=sys.argv[2]
+    W=compile2(h)
+    print(W.stats)
+    print('f2 check bad targets/x:',[len(z) for z in C.f2_check(W)])
+    s,deficit,D,steps=C.evaluate(W)
+    print('R',W.nh,'saving %.6e'%s,'deficit',deficit,'D %.0f'%D,sorted(steps.items()))
+    import diag; diag.diag(W)
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/e8lib.py b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/e8lib.py
new file mode 100644
index 0000000000..8464b956f6
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/e8lib.py
@@ -0,0 +1,79 @@
+"""Dylan Crow, with Anthropic Claude assistance; Apache-2.0. E8 root lines in Q^8 (standard coordinates, doubled to integers), F2 images, basic linear algebra."""
+import itertools
+from fractions import Fraction as Fr
+
+def roots2():
+    """E8 roots times 2 (integer vectors): 2(±e_i±e_j) and (±1)^8 with even number of minus signs."""
+    R=[]
+    for i,j in itertools.combinations(range(8),2):
+        for a in (2,-2):
+            for b in (2,-2):
+                v=[0]*8; v[i]=a; v[j]=b; R.append(tuple(v))
+    for signs in itertools.product((1,-1),repeat=8):
+        if signs.count(-1)%2==0: R.append(tuple(signs))
+    return R
+
+def ip(u,v):  # true inner product of roots given doubled coordinates
+    return sum(a*b for a,b in zip(u,v))//4
+
+import os
+def roots_hamming():
+    """E8 via Construction A from the [8,4,4] extended Hamming code: x in Z^8, x mod 2 in H8, |x|^2=4.
+    Inner product of roots = <x,y>/2. Returned scaled so that ip() (which divides by 4) works: multiply by sqrt2? no:
+    we return 2*x/sqrt... -> use integer vectors y=x and a separate scale."""
+    H=[]
+    for a in itertools.product((0,1),repeat=4):
+        g=[(1,1,1,1,0,0,0,0),(1,1,0,0,1,1,0,0),(1,0,1,0,1,0,1,0),(0,1,1,0,1,0,0,1)]
+        w=[sum(a[k]*g[k][i] for k in range(4))%2 for i in range(8)]
+        H.append(tuple(w))
+    R=[]
+    for i in range(8):
+        for sg in (2,-2):
+            v=[0]*8; v[i]=sg; R.append(tuple(v))
+    for w in H:
+        if sum(w)==4:
+            idx=[i for i in range(8) if w[i]]
+            for sg in itertools.product((1,-1),repeat=4):
+                v=[0]*8
+                for i,s_ in zip(idx,sg): v[i]=s_
+                R.append(tuple(v))
+    return R
+COORD=os.environ.get('E8COORD','std')
+if COORD=='ham':
+    ALL=[tuple(a for a in r) for r in roots_hamming()]
+    def ip(u,v): return sum(a*b for a,b in zip(u,v))//2
+else:
+    ALL=roots2()
+assert len(ALL)==240
+LINES=[]
+seen=set()
+for r in ALL:
+    if r in seen: continue
+    neg=tuple(-a for a in r); seen.add(r); seen.add(neg)
+    # canonical: first nonzero coordinate positive
+    LINES.append(r if [a for a in r if a][0]>0 else neg)
+V=len(LINES); assert V==120
+G=[[ip(LINES[a],LINES[b]) for b in range(V)] for a in range(V)]
+ORTH=[[b for b in range(V) if G[a][b]==0] for a in range(V)]
+NEIGH=[[b for b in range(V) if abs(G[a][b])==1] for a in range(V)]
+assert all(len(o)==63 and len(n)==56 for o,n in zip(ORTH,NEIGH))
+
+def rank_q(vecs):
+    """rank over Q of integer vectors"""
+    rows=[list(map(Fr,v)) for v in vecs]
+    r=0; n=len(rows[0]) if rows else 0
+    for c in range(n):
+        p=None
+        for i in range(r,len(rows)):
+            if rows[i][c]!=0: p=i;break
+        if p is None: continue
+        rows[r],rows[p]=rows[p],rows[r]
+        for i in range(len(rows)):
+            if i!=r and rows[i][c]!=0:
+                f=rows[i][c]/rows[r][c]
+                rows[i]=[x-f*y for x,y in zip(rows[i],rows[r])]
+        r+=1
+    return r
+
+def span_dim(idx):
+    return rank_q([LINES[i] for i in idx]) if idx else 0
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/frames.py b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/frames.py
new file mode 100644
index 0000000000..b28c3b2413
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/frames.py
@@ -0,0 +1,45 @@
+"""Dylan Crow, with Anthropic Claude assistance; Apache-2.0. Root-spanned rational subspaces of Q^8, represented by the bitmask of E8 root lines they contain."""
+import e8lib as E
+from fractions import Fraction as Fr
+V=E.V
+L=E.LINES
+_cache={}
+def _basis(idx):
+    rows=[]
+    piv=[]
+    for i in idx:
+        v=[Fr(a) for a in L[i]]
+        for (p,b) in zip(piv,rows):
+            if v[p]!=0:
+                f=v[p]/b[p]; v=[x-f*y for x,y in zip(v,b)]
+        nz=[k for k in range(8) if v[k]!=0]
+        if nz:
+            rows.append(v); piv.append(nz[0])
+    return rows,piv
+def _inspan(v,rows,piv):
+    v=[Fr(a) for a in v]
+    for (p,b) in zip(piv,rows):
+        if v[p]!=0:
+            f=v[p]/b[p]; v=[x-f*y for x,y in zip(v,b)]
+    return all(x==0 for x in v)
+def closure(mask):
+    """mask of all root lines in the rational span of the lines in mask; returns (closed_mask, dim)"""
+    r=_cache.get(mask)
+    if r is not None: return r
+    idx=[i for i in range(V) if mask>>i&1]
+    rows,piv=_basis(idx)
+    cm=0
+    for i in range(V):
+        if mask>>i&1 or _inspan(L[i],rows,piv): cm|=1<<i
+    r=(cm,len(rows))
+    _cache[mask]=r; _cache[cm]=r
+    return r
+def dim(mask): return closure(mask)[1]
+FULL=(1<<V)-1
+ZERO=0
+HYP=[sum(1<<s for s in E.ORTH[t]) for t in range(V)]
+LINE=[1<<s for s in range(V)]
+def join(a,b): return closure(a|b)[0]
+def inside(a,b): return a&~b==0   # for closed masks
+for t in range(V): assert closure(HYP[t])==(HYP[t],7)
+assert closure(FULL)==(FULL,8)
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/fullword.py b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/fullword.py
new file mode 100644
index 0000000000..104f01b780
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/fullword.py
@@ -0,0 +1,75 @@
+"""Producer of the bitE8 word (Dylan Crow, with Anthropic Claude assistance; Apache-2.0).
+usage: E8COORD=ham python3 fullword.py params-r865.json out.json[.gz]
+Turn a compiled Word into a complete reversible bit word (JSON 'bitE8/1'):
+   D: dirt compensation at frame 0 (y_t += helper r for every helper whose initial value reaches y_t)
+   A: phase A (word), S: scatter (y_t += copies of retained totals at frame 0), B: phase B,
+   C: cleanup at the full frame (reverse of every helper-destination gate of A and B).
+Gate = [frame_id, dst, [srcs]] meaning dst += sum(srcs) over F2."""
+import json, gzip, sys
+import e8lib as E, frames as Fm, compile as C
+V=E.V
+def build(W):
+    nreg=2*V+W.nh
+    frames={}
+    def fid(mask):
+        if mask not in frames: frames[mask]=len(frames)
+        return frames[mask]
+    fid(0); fid(Fm.FULL)
+    def flat(lst):
+        out=[]
+        for F,dst,srcs,outs in lst:
+            f=fid(F)
+            if srcs is not None: out.append([f,dst,list(srcs)])
+            if outs is not None:
+                for o in outs: out.append([f,o,[dst]])
+        return out
+    A=flat(W.A); B=flat(W.B)
+    # decoder reads
+    vals=[0]*nreg
+    cent_sup=None
+    # compute retained totals' x-content after A to derive scatter table
+    val=[1<<s for s in range(V)]+[0]*V+[0]*W.nh
+    for f,d,srcs in A:
+        for s in srcs: val[d]^=val[s]
+    cent=[val[q] for q in W.ret]
+    reads=C.decoder(cent)
+    scat=[list(r) for r in reads]
+    # dirt reaching y: symbolic over dirt columns only
+    dv=[0]*nreg
+    for r in range(2*V,nreg): dv[r]=1<<(r-2*V)
+    for f,d,srcs in A:
+        for s in srcs: dv[d]^=dv[s]
+    cdirt=[dv[q] for q in W.ret]
+    for t in range(V):
+        for c in reads[t]: dv[V+t]^=cdirt[c]
+    for f,d,srcs in B:
+        for s in srcs: dv[d]^=dv[s]
+    D=[]
+    for t in range(V):
+        m=dv[V+t]; srcs=[]
+        while m:
+            b=m&-m; r=b.bit_length()-1; m^=b; srcs.append(2*V+r)
+        if srcs: D.append([fid(0),V+t,srcs])
+    Cl=[]
+    for f,d,srcs in reversed(A+B):
+        if d>=2*V: Cl.append([fid(Fm.FULL),d,srcs])
+    fr=[None]*len(frames)
+    for mk,i in frames.items(): fr[i]=[s for s in range(V) if mk>>s&1]
+    start=[fid(Fm.LINE[s]) for s in range(V)]+[fid(0)]*V+[fid(0)]*W.nh
+    final=[fid(Fm.FULL)]*V+[fid(Fm.HYP[t]) for t in range(V)]+[fid(Fm.FULL)]*W.nh
+    return dict(format='bitE8/1',coords=E.COORD,h=8,v=V,R=W.nh,lines=[list(r) for r in E.LINES],
+                form='<x,y>/2' if E.COORD=='ham' else '<x,y>/4',frames=fr,start=start,final=final,
+                ret=list(W.ret),scatter=scat,D=D,A=A,B=B,C=Cl)
+def save(cert,path):
+    data=json.dumps(cert,separators=(',',':'),sort_keys=True).encode()
+    if path.endswith('.gz'):
+        with open(path,'wb') as fh:
+            with gzip.GzipFile(filename='',mode='wb',fileobj=fh,mtime=0) as gz: gz.write(data)
+    else: open(path,'wb').write(data)
+if __name__=='__main__':
+    import ast, ham2, compile2 as C2
+    Pd={ast.literal_eval(k):v for k,v in json.load(open(sys.argv[1]))} if sys.argv[1]!='-' else {}
+    ham2.P.clear(); ham2.P.update(Pd)
+    h=ham2.build(0,True); W=C2.compile2(h)
+    cert=build(W); save(cert,sys.argv[2])
+    print('R',W.nh,'gates D/A/B/C',len(cert['D']),len(cert['A']),len(cert['B']),len(cert['C']),'frames',len(cert['frames']))
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/ham1.py b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/ham1.py
new file mode 100644
index 0000000000..8086649a5f
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/ham1.py
@@ -0,0 +1,81 @@
+"""Dylan Crow, with Anthropic Claude assistance; Apache-2.0. Hand-structured bit-E8 hierarchy in Hamming coordinates (E8COORD=ham)."""
+import os, sys, itertools, pickle
+assert os.environ.get('E8COORD')=='ham'
+import e8lib as E, frames as Fm
+from collections import defaultdict
+V=E.V
+L=E.LINES
+idx={}
+for i,r in enumerate(L): idx[r]=i; idx[tuple(-a for a in r)]=i
+frame_line=[idx[tuple(2 if k==i else 0 for k in range(8))] for i in range(8)]
+blocks=sorted(set(tuple(k for k in range(8) if r[k]) for r in L if sum(1 for a in r if a)==4))
+assert len(blocks)==14
+def cw_lines(c): return [i for i,r in enumerate(L) if tuple(k for k in range(8) if r[k])==c]
+class SH:
+    """hierarchy with XOR semantics"""
+    def __init__(self):
+        self.content=[1<<s for s in range(V)]; self.frame=[Fm.LINE[s] for s in range(V)]; self.dim=[1]*V
+        self.kids=[None]*V; self.key={c:i for i,c in enumerate(self.content)}; self.need=[set() for _ in range(V)]
+    def sym(self,parts):
+        """symbol = XOR of parts (symbols), built left to right as a binary chain"""
+        cur=parts[0]
+        for p in parts[1:]:
+            c=self.content[cur]^self.content[p]
+            w=self.key.get(c)
+            if w is None:
+                w=len(self.content); self.content.append(c); f,d=Fm.closure(self.frame[cur]|self.frame[p])
+                self.frame.append(f); self.dim.append(d); self.kids.append((cur,p)); self.key[c]=w
+            cur=w
+        return cur
+def build(variant=0):
+    h=SH()
+    # relative sign of line r on pair (i,j)
+    def rel(r,i,j): return 1 if r[i]*r[j]>0 else -1
+    Lsym={}; Psym={}
+    for c in blocks:
+        ls=cw_lines(c)
+        for (i,j) in itertools.combinations(c,2):
+            for rho in (1,-1):
+                mem=[s for s in ls if rel(L[s],i,j)==rho]
+                assert len(mem)==4
+                # split into two pairs: pair lines that agree on the remaining pair (k,l) relative sign
+                k,l=[q for q in c if q not in (i,j)]
+                a=[s for s in mem if rel(L[s],k,l)==1]; b=[s for s in mem if rel(L[s],k,l)==-1]
+                pa=h.sym(sorted(a)); pb=h.sym(sorted(b))
+                Lsym[(c,i,j,rho)]=h.sym([pa,pb])
+    Dsym={}
+    for c in blocks:
+        i,j=c[0],c[1]
+        Dsym[c]=h.sym([Lsym[(c,i,j,1)],Lsym[(c,i,j,-1)]]+[frame_line[q] for q in c])
+    Msym={}
+    for c in blocks:
+        for (i,j) in itertools.combinations(c,2):
+            others=[c2 for c2 in blocks if c2!=c and i in c2 and j in c2]
+            assert len(others)==2
+            for rho in (1,-1):
+                Msym[(c,i,j,rho)]=h.sym([Lsym[(others[0],i,j,rho)],Lsym[(others[1],i,j,rho)]])
+    comp={c:[c2 for c2 in blocks if not set(c)&set(c2)][0] for c in blocks}
+    for c in blocks:
+        cb=comp[c]
+        for t in cw_lines(c):
+            r=L[t]
+            def rho(i,j): return -rel(r,i,j)
+            i,j,k,l=c   # level-5 pair (i,j), level-6 triangle (i,j,k)
+            need=[Dsym[cb], Msym[(c,i,j,rho(i,j))], h.sym([Msym[(c,i,k,rho(i,k))],Msym[(c,j,k,rho(j,k))]]),
+                  Msym[(c,i,l,rho(i,l))],Msym[(c,j,l,rho(j,l))],Msym[(c,k,l,rho(k,l))]]
+            need+=[s for s in cw_lines(c) if E.G[t][s]==0]
+            h.need[t]=set(need)
+    for m in range(8):
+        t=frame_line[m]
+        need=[Dsym[c] for c in blocks if m not in c]+[frame_line[q] for q in range(8) if q!=m]
+        h.need[t]=set(need)
+    # verify XOR
+    for t in range(V):
+        x=0
+        for u in h.need[t]: x^=h.content[u]
+        assert x==Fm.HYP[t],(t,bin(x^Fm.HYP[t]).count('1'))
+    return h
+if __name__=='__main__':
+    h=build()
+    pickle.dump(h,open('hier_ham1.pkl','wb'))
+    print('symbols',len(h.content)-V,'reads',sum(len(n) for n in h.need))
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/ham2.py b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/ham2.py
new file mode 100644
index 0000000000..842f76b245
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/ham2.py
@@ -0,0 +1,131 @@
+"""Dylan Crow, with Anthropic Claude assistance; Apache-2.0. Hamming-coordinate bit-E8 design with pi-coset pairing (E8COORD=ham)."""
+import os, sys, itertools, pickle
+assert os.environ.get('E8COORD')=='ham'
+import e8lib as E, frames as Fm
+from ham1 import SH, blocks, cw_lines, frame_line, idx
+V=E.V; L=E.LINES
+def proj_dir(S,c):
+    """projection of line S onto C_c as a normalized tuple (sign-canonical) or None if zero"""
+    v=[L[S][k] if k in c else 0 for k in range(8)]
+    if not any(v): return None
+    f=[a for a in v if a][0]
+    return tuple(a if f>0 else -a for a in v)
+FRAMEOPT=[True,0,0]
+P={}
+LSKEYS=set()
+def par(k,n):
+    return P.get(k,0)%n
+def build(pairing=0, fold=True):
+    h=SH()
+    comp={c:[c2 for c2 in blocks if not set(c)&set(c2)][0] for c in blocks}
+    # L sets: lines of block c2 with projection onto C_c (c != c2, |c&c2|=2) along b-line p
+    Lsets={}
+    for c2 in blocks:
+        for c in blocks:
+            if len(set(c)&set(c2))!=2: continue
+            for S in cw_lines(c2):
+                p=proj_dir(S,c)
+                Lsets.setdefault((c2,p),set()).add(S)
+    Lsets={k:sorted(v) for k,v in Lsets.items()}
+    for k,v in Lsets.items(): assert len(v)==4,(k,v)
+    Lsym={}
+    for (c2,p),mem in Lsets.items():
+        # split into two pairs by the relative sign on the other two coordinates of c2
+        oth=[q for q in c2 if p[q]==0]
+        sp=par(('ls',c2,p),3); LSKEYS.add(('ls',c2,p))
+        if sp==0:
+            a=[s for s in mem if L[s][oth[0]]*L[s][oth[1]]>0]; b=[s for s in mem if L[s][oth[0]]*L[s][oth[1]]<0]
+        else:
+            q0=[q for q in c2 if p[q]!=0][0]
+            a=[s for s in mem if L[s][q0]*L[s][oth[sp-1]]>0]; b=[s for s in mem if L[s][q0]*L[s][oth[sp-1]]<0]
+        Lsym[(c2,p)]=h.sym([h.sym(sorted(a)),h.sym(sorted(b))])
+    Msym={}
+    for c in blocks:
+        for (c2,p),s in Lsets.items():
+            pass
+    for (c2,p) in Lsets:
+        # p is a b-line of the block c for which p's support pair lies: find blocks c containing supp(p) other than c2
+        supp=tuple(q for q in range(8) if p[q])
+        for c in blocks:
+            if c!=c2 and set(supp)<=set(c):
+                Msym.setdefault((c,p),[]).append(Lsym[(c2,p)])
+    for k in list(Msym):
+        assert len(Msym[k])==2
+        Msym[k]=h.sym(sorted(Msym[k]))
+    Dsym={}; Bcw={}
+    for c in blocks:
+        ls=cw_lines(c)
+        # E(D4(c)) = all 8 codeword lines of c + 4 frame lines
+        p=None
+        for (c2,pp),s in Lsym.items():
+            pass
+        # use two complementary L-like halves: split by relative sign on (c0,c1)
+        i,j=c[0],c[1]
+        A=[s for s in ls if L[s][i]*L[s][j]>0]; B=[s for s in ls if L[s][i]*L[s][j]<0]
+        Bcw[c]=h.sym([h.sym(sorted(A[:2])+sorted(A[2:])), h.sym(sorted(B)) ])
+        Dsym[c]=h.sym([Bcw[c]]+[frame_line[q] for q in c])
+    def bdir(u,w):
+        """the two b-line directions in the plane span(L[u],L[w]) (vectors a+-b normalized)"""
+        out=[]
+        for sg in (1,-1):
+            v=tuple(x+sg*y for x,y in zip(L[u],L[w]))
+            f=[a for a in v if a][0]
+            v=tuple(a//2 if f>0 else -a//2 for a in v)
+            out.append(v)
+        return out
+    for c in blocks:
+        cb=comp[c]
+        ls=cw_lines(c)
+        # pi-cosets: 4 mutually orthogonal lines
+        cos=[]
+        rem=set(ls)
+        while rem:
+            t=min(rem); Q=[t]+[s for s in rem if s!=t and E.G[t][s]==0]
+            assert len(Q)==4 and all(E.G[a][b]==0 for a in Q for b in Q if a!=b)
+            cos.append(Q); rem-=set(Q)
+        for Q in cos:
+            pr_=(pairing+par(('pair',c,min(Q)),3))%3
+            pairs=[(Q[0],Q[1+pr_]),tuple(q for q in Q[1:] if q!=Q[1+pr_])]
+            partner={}
+            for x,y in pairs: partner[x]=y; partner[y]=x
+            for t in Q:
+                d=partner[t]; a,b=[q for q in Q if q not in (t,d)]
+                p5,p6=sorted(bdir(a,b))
+                if par(('l5',min(t,d)),2): p5,p6=p6,p5
+                M=lambda p: Msym[(c,p)]
+                need=[Dsym[cb], M(p5), h.sym([M(p6),a,b])]
+                q1,q2=sorted(bdir(a,d)); r1,r2=sorted(bdir(b,d))
+                fo=par(('fold',t),2) if fold else 2
+                if fo==0:
+                    need+=[h.sym([M(q1),M(q2),d]), h.sym([M(r1),M(r2)])]
+                elif fo==1:
+                    need+=[h.sym([M(q1),M(q2)]), h.sym([M(r1),M(r2),d])]
+                else:
+                    need+=[h.sym([M(q1),M(q2)]), h.sym([M(r1),M(r2)]), d]
+                h.need[t]=set(need)
+    for m in range(8):
+        t=frame_line[m]
+        if not FRAMEOPT[0]:
+            h.need[t]=set([Dsym[c] for c in blocks if m not in c]+[frame_line[q] for q in range(8) if q!=m]); continue
+        avoid=[c for c in blocks if m not in c]
+        c0=avoid[(FRAMEOPT[1]+par(('fc0',m),7))%len(avoid)]
+        ns=[q for q in range(8) if q!=m and q not in c0]
+        n=ns[(FRAMEOPT[2]+par(('fn',m),3))%len(ns)]
+        A6=[q for q in range(8) if q not in (m,n)]
+        in6=[c for c in avoid if set(c)<=set(A6) and c!=c0]; assert len(in6)==2
+        top=[c for c in avoid if n in c]; assert len(top)==4
+        # pair top blocks so each pair spans a 6-dim coordinate space (always true)
+        need=[Dsym[c0], h.sym([Bcw[in6[0]],Bcw[in6[1]]]+[frame_line[q] for q in A6 if q not in c0]),
+              h.sym([Bcw[top[0]],Bcw[top[1]],frame_line[n]]), h.sym([Bcw[top[2]],Bcw[top[3]]])]
+        h.need[t]=set(need)
+    for t in range(V):
+        x=0
+        for u in h.need[t]: x^=h.content[u]
+        assert x==Fm.HYP[t],(t,bin(x^Fm.HYP[t]).count('1'))
+    return h
+if __name__=='__main__':
+    pr=int(sys.argv[1]) if len(sys.argv)>1 else 0
+    fold=(sys.argv[2]!='nofold') if len(sys.argv)>2 else True
+    h=build(pr,fold)
+    pickle.dump(h,open('hier_ham2_%d_%s.pkl'%(pr,fold),'wb'))
+    print('symbols',len(h.content)-V,'reads',sum(len(n) for n in h.need))
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/params-r865.json b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/params-r865.json
new file mode 100644
index 0000000000..110b4d94d8
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/params-r865.json
@@ -0,0 +1,2082 @@
+[
+[
+"('fc0', 0)",
+3
+],
+[
+"('fc0', 1)",
+3
+],
+[
+"('fc0', 2)",
+0
+],
+[
+"('fc0', 3)",
+0
+],
+[
+"('fc0', 4)",
+3
+],
+[
+"('fc0', 5)",
+0
+],
+[
+"('fc0', 6)",
+2
+],
+[
+"('fc0', 7)",
+0
+],
+[
+"('fn', 0)",
+1
+],
+[
+"('fn', 1)",
+1
+],
+[
+"('fn', 2)",
+0
+],
+[
+"('fn', 3)",
+0
+],
+[
+"('fn', 4)",
+0
+],
+[
+"('fn', 5)",
+0
+],
+[
+"('fn', 6)",
+0
+],
+[
+"('fn', 7)",
+2
+],
+[
+"('fold', 10)",
+1
+],
+[
+"('fold', 100)",
+1
+],
+[
+"('fold', 101)",
+0
+],
+[
+"('fold', 102)",
+1
+],
+[
+"('fold', 103)",
+0
+],
+[
+"('fold', 104)",
+1
+],
+[
+"('fold', 105)",
+0
+],
+[
+"('fold', 106)",
+1
+],
+[
+"('fold', 107)",
+0
+],
+[
+"('fold', 108)",
+1
+],
+[
+"('fold', 109)",
+0
+],
+[
+"('fold', 11)",
+1
+],
+[
+"('fold', 110)",
+1
+],
+[
+"('fold', 111)",
+0
+],
+[
+"('fold', 112)",
+1
+],
+[
+"('fold', 113)",
+1
+],
+[
+"('fold', 114)",
+0
+],
+[
+"('fold', 115)",
+0
+],
+[
+"('fold', 116)",
+0
+],
+[
+"('fold', 117)",
+0
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\ No newline at end of file
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/price.py b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/price.py
new file mode 100644
index 0000000000..9014d97d51
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/bit/producer/price.py
@@ -0,0 +1,23 @@
+# Dylan Crow, with Anthropic Claude assistance; Apache-2.0.
+import math
+from collections import Counter
+def price(steps, R, v=120, h=8, L=72, ncent=9, exact=True):
+    """steps: Counter of step ranks over x, y, helpers for ONE invocation (centres added here).
+    Five-stage: H5 = 5*(steps + centres) + 2v*(2h-2,h-1,2h+2,4); W = 4v+R; m=5h."""
+    m=5*h
+    H=Counter()
+    for r,n in steps.items(): H[r]+=5*n
+    H[h]+=5*ncent  # centres at full frame (rank = frame dim = h)
+    for r in (2*h-2,h-1,2*h+2,4): H[r]+=2*v
+    W=4*v+R
+    mass=sum(r*n for r,n in H.items())
+    g=lambda r:r*math.log(m/r)
+    D=sum(n*g(r) for r,n in H.items())
+    s1=(W*m-mass)/D
+    if not exact: return s1,W*m-mass,D
+    lo,hi=0.0,0.01
+    for _ in range(80):
+        s=(lo+hi)/2
+        if sum(n*(r/m)**(1-s) for r,n in H.items())>W: hi=s
+        else: lo=s
+    return lo,W*m-mass,D
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/controls.py b/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/controls.py
new file mode 100644
index 0000000000..ceb15852b7
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/controls.py
@@ -0,0 +1,71 @@
+"""Negative controls for the elimination reuse: every mutant of the final word must be rejected by PR #370's
+independent all-column checker (code/bit/independent/checkword.py, run unchanged in a subprocess, as PR #370's
+mutate.py does). The mutated gates are the inserted elimination gates listed in the reuse ledger written by regen.py.
+usage: controls.py WORD.json.gz LEDGER.json PRICING_DIR
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import copy
+import gzip
+import json
+import os
+import subprocess
+import sys
+import tempfile
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+CHECK = os.path.join(HERE, "..", "bit", "independent", "checkword.py")
+word, ledger, pricing = sys.argv[1:4]
+w = json.load(gzip.open(word, "rt"))
+led = json.load(open(ledger))
+v = w["v"]
+elim = [(ph, i) for ph, i, kind in led["eliminations"] if kind == "helper"]
+undo = [(ph, i) for ph, i, kind in led["eliminations"] if kind == "total"]
+assert len(elim) == led["helpers"] and len(undo) == led["totals"]
+for ph, i in elim + undo:     # each ledger entry is an elimination into a helper slot
+    assert w[ph][i][1] >= 2 * v and w[ph][i][2]
+lines = [frozenset(f) for f in w["frames"]]   # frames are closed: frame a lies inside frame b iff lines[a] <= lines[b]
+
+
+def prev_frame(c, ph, i, r):
+    """frame id of register r just before gate (ph, i) (its last earlier gate in D, A, ... or its start frame)"""
+    f = c["start"][r]
+    for p in ("D", "A", "B", "C"):
+        for k, g in enumerate(c[p]):
+            if (p, k) == (ph, i):
+                return f
+            if r == g[1] or r in g[2]:
+                f = g[0]
+    raise AssertionError("gate not found")
+
+
+muts = []
+c = copy.deepcopy(w); ph, i = elim[0]; del c[ph][i]
+muts.append(("omit the first helper elimination gate (the reused slot keeps a leftover x-content)", c))
+c = copy.deepcopy(w); ph, i = next((p, k) for p, k in elim if len(w[p][k][2]) >= 2); c[ph][i][2].pop()
+muts.append(("omit one eliminator of a helper elimination with two or more eliminators", c))
+c = copy.deepcopy(w); ph, i = undo[0]; c[ph][i][2].pop()
+muts.append(("omit one x-line read of a retained-total undo gate", c))
+c = copy.deepcopy(w)
+for ph, i in elim:
+    f, d, srcs = c[ph][i]
+    low = prev_frame(c, ph, i, d)
+    if lines[low] < lines[f] and any(not lines[prev_frame(c, ph, i, s)] <= lines[low] for s in srcs):
+        c[ph][i][0] = low
+        break
+else:
+    raise AssertionError("no elimination gate above its slot's own frame")
+muts.append(("an elimination gate lowered to the reused slot's own frame (below an eliminator's frame)", c))
+c = copy.deepcopy(w)
+for ph, i in sorted(elim + undo, key=lambda z: (z[0], -z[1])):
+    del c[ph][i]
+muts.append(("reuse without elimination: all %d elimination and undo gates removed" % (len(elim) + len(undo)), c))
+c = copy.deepcopy(w); ph, i = undo[0]; c[ph][i][0] = w["start"][v]
+muts.append(("a retained-total undo gate moved from the full frame to frame 0", c))
+tmpd = tempfile.mkdtemp()
+for k, (name, c) in enumerate(muts):
+    p = os.path.join(tmpd, "mut%d.json.gz" % k)
+    with gzip.open(p, "wt") as fh:
+        json.dump(c, fh)
+    r = subprocess.run([sys.executable, "-I", "-B", CHECK, p, pricing], capture_output=True, text=True)
+    assert r.returncode != 0, "mutant accepted: " + name
+    print("   REJECTED %s :: %s" % (name, (r.stderr.strip().splitlines() or ["?"])[-1][:90]))
+print("PASS all %d elimination-reuse negative controls rejected by PR #370's independent checker" % len(muts))
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/ecost.py b/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/ecost.py
new file mode 100644
index 0000000000..4ec2a959b1
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/ecost.py
@@ -0,0 +1,20 @@
+"""Integer step-cost tables for the search heuristics of reuse.py and retime.py.
+
+cost(r) = r ln(m / r) (the per-child term of the linearised moment equation), scaled by 10^12 and rounded half-even
+with Python's decimal module (correctly rounded natural logarithm), so every comparison made by the two stages is an
+integer comparison and gives the same word on every platform.  The tables only steer the deterministic choices of the
+stages; the word they produce is checked and priced exactly elsewhere.
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+from decimal import Decimal, localcontext, ROUND_HALF_EVEN
+
+SCALE = 10 ** 12
+
+
+def table(m, rmax):
+    out = [0] * (rmax + 1)
+    with localcontext() as ctx:
+        ctx.prec = 60
+        for r in range(1, rmax + 1):
+            x = Decimal(r) * (Decimal(m) / Decimal(r)).ln() * SCALE
+            out[r] = int(x.to_integral_value(rounding=ROUND_HALF_EVEN))
+    return out
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/regen.py b/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/regen.py
new file mode 100644
index 0000000000..529de1b8b3
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/regen.py
@@ -0,0 +1,49 @@
+"""Regenerate the word from pinned inputs.
+
+  1. PR #370's producer, unchanged (ham2.build -> compile2 -> fullword.build), with our producer parameters
+     (data/params/params-r740.json, found by discovery/search_params.py)            -> raw word (R = 863)
+  2. reuse.reuse: helper-slot reuse by elimination of dead registers               -> reused word
+  3. retime.retime: single-gate frame retiming (6 sweeps, M = 64)                  -> final word
+Each word is written as PR #370's fullword.save does (sorted keys, compact JSON, gzip mtime 0).
+usage: regen.py PARAMS.json OUT_RAW.json.gz OUT_REUSED.json.gz OUT_FINAL.json.gz OUT_LEDGER.json
+OUT_LEDGER lists the inserted elimination gates (phase, index, kind) of the final word, for the negative controls.
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import ast
+import json
+import os
+import sys
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+os.environ["E8COORD"] = "ham"
+sys.path.insert(0, os.path.join(HERE, "..", "bit", "producer"))
+sys.path.insert(0, HERE)
+import compile2 as C2  # noqa: E402  (PR #370 producer)
+import fullword  # noqa: E402  (PR #370 producer)
+import ham2  # noqa: E402  (PR #370 producer)
+import reuse as RU  # noqa: E402
+import retime as RT  # noqa: E402
+
+params, out_raw, out_reused, out_final, out_ledger = sys.argv[1:6]
+Pd = {ast.literal_eval(k): v for k, v in json.load(open(params))}
+ham2.P.clear()
+ham2.P.update(Pd)
+h = ham2.build(0, True)
+W = C2.compile2(h)
+raw = fullword.build(W)
+fullword.save(raw, out_raw)
+print("   1. PR #370 producer with our parameters: R %d, gates D/A/B/C %d/%d/%d/%d, frames %d"
+      % (raw["R"], len(raw["D"]), len(raw["A"]), len(raw["B"]), len(raw["C"]), len(raw["frames"])), flush=True)
+reused, nre = RU.reuse(raw)
+fullword.save(reused, out_reused)
+print("   2. elimination reuse: %d dead slots reused by later helpers, %d by the retained totals: R %d -> %d"
+      % (nre["helpers"], nre["totals"], raw["R"], reused["R"]), flush=True)
+final, moved = RT.retime(reused, sweeps=6, M=64)
+fullword.save(final, out_final)
+for ph, i, kind in nre["eliminations"]:      # retiming moves frames only: the ledger positions are unchanged
+    assert final[ph][i][1:] == reused[ph][i][1:]
+with open(out_ledger, "w") as fh:
+    json.dump(dict(helpers=nre["helpers"], totals=nre["totals"], eliminations=nre["eliminations"]), fh)
+    fh.write("\n")
+print("   3. retiming: %d gate moves; final R %d, gates D/A/B/C %d/%d/%d/%d, frames %d"
+      % (moved, final["R"], len(final["D"]), len(final["A"]), len(final["B"]), len(final["C"]), len(final["frames"])),
+      flush=True)
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/retime.py b/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/retime.py
new file mode 100644
index 0000000000..9c3e94b800
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/retime.py
@@ -0,0 +1,112 @@
+"""Single-gate frame retiming of a bitE8/1 word (our implementation of the idea of PR #389, ai-nanachi).
+
+Every A, B and C gate may move to the join of its registers' previous frames (the lowest legal frame) or to the
+root-spanned meet of their next frames (the highest legal frame), whichever lowers the integer step cost
+sum over its registers of cost(rank in) + cost(rank out), cost(r) = r ln(M/r) (ecost.py; M = 64 by default, the
+width of the compressed nine-stage layout). Sweeps alternate direction until no gate moves. D gates (frame 0), the
+targets at frame 0 at the scatter, the retained totals at the full frame, start and final frames are pinned.
+Requires the PR #370 producer modules on sys.path with E8COORD=ham (see regen.py).
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import os
+from collections import defaultdict
+
+assert os.environ.get("E8COORD") == "ham", "set E8COORD=ham before importing (see regen.py)"
+import frames as Fm  # noqa: E402  (PR #370 producer: exact root-spanned closure over Q)
+from ecost import table  # noqa: E402
+
+
+def _bits(mask):
+    out = []
+    while mask:
+        b = mask & -mask
+        out.append(b.bit_length() - 1)
+        mask ^= b
+    return out
+
+
+def retime(w, sweeps=6, M=64):
+    v = w["v"]
+    rc = table(M, M)
+    frames = [sum(1 << s for s in f) for f in w["frames"]]
+    FULL = (1 << v) - 1
+    dcache = {}
+
+    def dim(mask):
+        if mask not in dcache:
+            dcache[mask] = Fm.closure(mask)[1] if mask else 0
+        return dcache[mask]
+
+    nodes = []   # dict(mask, regs, fixed, phase, gate)
+    for ph in ("D", "A"):
+        for g in w[ph]:
+            nodes.append(dict(mask=frames[g[0]], regs=[g[1]] + g[2], fixed=(ph == "D"), phase=ph, gate=g))
+    for q in w["ret"]:
+        nodes.append(dict(mask=FULL, regs=[q], fixed=True, phase="pin", gate=None))
+    for t in range(v):
+        nodes.append(dict(mask=0, regs=[v + t], fixed=True, phase="pin", gate=None))
+    for ph in ("B", "C"):
+        for g in w[ph]:
+            nodes.append(dict(mask=frames[g[0]], regs=[g[1]] + g[2], fixed=False, phase=ph, gate=g))
+    byreg = defaultdict(list)
+    for i, n in enumerate(nodes):
+        for r in n["regs"]:
+            byreg[r].append(i)
+    prev, nxt = {}, {}
+    for r, ids in byreg.items():
+        for p, i in enumerate(ids):
+            prev[i, r] = ids[p - 1] if p else ("start", r)
+            nxt[i, r] = ids[p + 1] if p + 1 < len(ids) else ("final", r)
+
+    def frame_of(key):
+        if isinstance(key, int):
+            return nodes[key]["mask"]
+        kind, r = key
+        return frames[w[kind][r]]
+
+    def node_cost(i, mask):
+        c = 0
+        dm = dim(mask)
+        for r in nodes[i]["regs"]:
+            c += rc[dm - dim(frame_of(prev[i, r]))] + rc[dim(frame_of(nxt[i, r])) - dm]
+        return c
+
+    moved_total = 0
+    for sweep in range(sweeps):
+        moved = 0
+        order = [i for i, n in enumerate(nodes) if not n["fixed"]]
+        if sweep % 2:
+            order.reverse()
+        for i in order:
+            lo, hi = 0, FULL
+            for r in nodes[i]["regs"]:
+                lo |= frame_of(prev[i, r])
+                hi &= frame_of(nxt[i, r])
+            lo = Fm.closure(lo)[0] if lo else 0
+            hi = Fm.closure(hi)[0] if hi else 0
+            if lo & ~hi:
+                continue
+            old = nodes[i]["mask"]
+            best = min([old, lo, hi], key=lambda m_: node_cost(i, m_))   # ties keep the old frame
+            if node_cost(i, best) < node_cost(i, old):
+                nodes[i]["mask"] = best
+                moved += 1
+        moved_total += moved
+        if not moved:
+            break
+    fid = {m: i for i, m in enumerate(frames)}
+
+    def frame_id(mask):
+        if mask not in fid:
+            fid[mask] = len(frames)
+            frames.append(mask)
+        return fid[mask]
+
+    out = {ph: [] for ph in "DABC"}
+    for n in nodes:
+        if n["phase"] == "pin":
+            continue
+        g = n["gate"]
+        out[n["phase"]].append([frame_id(n["mask"]), g[1], list(g[2])])
+    cert = dict(w)
+    cert.update(frames=[_bits(m) for m in frames], D=out["D"], A=out["A"], B=out["B"], C=out["C"])
+    return cert, moved_total
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/reuse.py b/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/reuse.py
new file mode 100644
index 0000000000..df455a0b37
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/code/reuse/reuse.py
@@ -0,0 +1,258 @@
+"""Helper-slot reuse by elimination of dead registers (bitE8/1 words).
+
+A helper is dead after its last phase-A/B gate. It still holds a leftover x-content (an F2 combination of source
+lines) at its death frame. Before the birth gate of a later helper whose first frame is fb, look among the dead slots
+whose current frame lies inside fb for a linear relation of their x-contents over F2:
+    content(r0) = XOR_{q in S} content(q).
+Emit the gate  r0 += S  at G = the join of the current frames of r0 and S (G lies inside fb). Afterwards r0 holds no
+x-content (only helper dirt, which the rebuilt compensation D and cleanup C account for), so r0 hosts the new helper.
+The eliminators S move to G and stay dead there. The relation is chosen by Gaussian elimination over F2 on the
+candidates sorted by frame dimension, then replaced by the cheapest relation with |S| <= 3 under the integer step costs
+of ecost.py (extra climbing of r0 and of the eliminators), when one exists.
+The 9 retained totals (born at the full frame) also take dead slots: the leftover x-lines of the chosen slot are read
+from the sources at the full frame, which zeroes its x-content.
+D (dirt compensation at frame 0) and C (cleanup at the full frame) are rebuilt exactly as PR #370's fullword.py does.
+Same idea as PR #376's helper-lifetime reuse (applecrusher), generalised from aliasing to linear relations.
+Requires the PR #370 producer modules on sys.path with E8COORD=ham (see regen.py).
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import os
+
+assert os.environ.get("E8COORD") == "ham", "set E8COORD=ham before importing (see regen.py)"
+import e8lib as E  # noqa: E402  (PR #370 producer, unchanged)
+import frames as Fm  # noqa: E402  (PR #370 producer: exact root-spanned closure over Q)
+from ecost import table  # noqa: E402
+
+RC = table(40, 8)          # step cost r ln(40/r) of the five-stage ledger, as integers
+MAXS_PAIRS = 60            # pair/triple relations are searched when at most this many dead slots fit
+
+
+def _step(a, b):
+    return RC[b - a] if b > a else 0
+
+
+def _dim(mask):
+    return Fm.closure(mask)[1] if mask else 0
+
+
+def _bits(mask):
+    out = []
+    while mask:
+        b = mask & -mask
+        out.append(b.bit_length() - 1)
+        mask ^= b
+    return out
+
+
+def sparse_relation(cands, dead, fb):
+    """cheapest (r0, S) with content(r0) = XOR content(S), |S| <= 3, scored by the extra climbing of the
+    eliminators (death frame -> G -> full instead of death frame -> full) and of r0 (death frame -> G -> birth
+    frame instead of 0 -> birth frame and death frame -> full); None if no such relation fits inside fb"""
+    best = None
+    single = {}
+    for q in cands:
+        single.setdefault(dead[q][0], []).append(q)
+    pairs = {}
+    if len(cands) <= MAXS_PAIRS:
+        for i, a in enumerate(cands):
+            for b in cands[i + 1:]:
+                pairs.setdefault(dead[a][0] ^ dead[b][0], []).append((a, b))
+    dfb = _dim(fb)
+
+    def score(r0, S):
+        G = dead[r0][1]
+        for q in S:
+            G |= dead[q][1]
+        G, dg = Fm.closure(G) if G else (0, 0)
+        if G & ~fb:
+            return None
+        d0 = _dim(dead[r0][1])
+        c = _step(d0, dg) + _step(dg, dfb) - _step(d0, 8) - _step(0, dfb)
+        for q in S:
+            if dead[q][1] != G:
+                dq = _dim(dead[q][1])
+                c += _step(dq, dg) + _step(dg, 8) - _step(dq, 8)
+        return c
+
+    for r0 in cands:
+        x = dead[r0][0]
+        opts = []
+        if x == 0:
+            opts.append([])
+        for q in single.get(x, []):
+            if q != r0:
+                opts.append([q])
+        for a, b in pairs.get(x, []):
+            if r0 not in (a, b):
+                opts.append([a, b])
+        if len(cands) <= MAXS_PAIRS:
+            for a in cands:
+                if a == r0:
+                    continue
+                for b, c_ in pairs.get(x ^ dead[a][0], []):
+                    if r0 not in (b, c_) and a not in (b, c_):
+                        opts.append([a, b, c_])
+                        break
+        for S in opts:
+            sc = score(r0, S)
+            if sc is not None and (best is None or sc < best[0]):
+                best = (sc, r0, S)
+    return None if best is None else (best[1], best[2])
+
+
+def reuse(w, maxr=10 ** 9):
+    """returns (new word, dict(helpers=..., totals=...) reuse counts); w is a bitE8/1 word from PR #370's fullword.build (helpers start at
+    frame 0 and end at the full frame)"""
+    v, R = w["v"], w["R"]
+    assert w["format"] == "bitE8/1" and w["coords"] == "ham" and w["lines"] == [list(r) for r in E.LINES]
+    assert all(not w["frames"][w["start"][r]] for r in range(2 * v, 2 * v + R))
+    frames = [sum(1 << s for s in f) for f in w["frames"]]
+    fid = {m: i for i, m in enumerate(frames)}
+    XM = (1 << v) - 1
+
+    def frame_id(mask):
+        if mask not in fid:
+            fid[mask] = len(frames)
+            frames.append(mask)
+        return fid[mask]
+
+    nA = len(w["A"])
+    gates = [list(g) for g in w["A"]] + [list(g) for g in w["B"]]
+    first, last = {}, {}
+    for k, (f, d, srcs) in enumerate(gates):
+        for r in [d] + srcs:
+            if r >= 2 * v:
+                first.setdefault(r, k)
+                last[r] = k
+    ret = set(w["ret"])
+    val = [1 << s for s in range(v)] + [0] * (v + R)    # x-content only (helpers never read targets)
+    cont_at = {}
+    for k, (f, d, srcs) in enumerate(gates):
+        for s in srcs:
+            val[d] ^= val[s]
+        for r in [d] + srcs:
+            if r >= 2 * v and last.get(r) == k:
+                cont_at[r] = (val[r] & XM, frames[f])
+    births = sorted((first[r], r) for r in range(2 * v, 2 * v + R) if r in first and r not in ret)
+    deaths = sorted((last[r], r) for r in cont_at if r not in ret)
+    dead = {}          # physical slot -> [x-content, current frame mask, death gate index]
+    rename = {}        # logical register born later -> physical slot it reuses
+    insert_before = {}
+    di = 0
+    nre = 0
+
+    def bury(upto):
+        nonlocal di
+        while di < len(deaths) and deaths[di][0] < upto:
+            k, r = deaths[di]
+            di += 1
+            x, f = cont_at[r]
+            dead[rename.get(r, r)] = [x, f, k]
+
+    for kb, rb in births:
+        bury(kb)
+        if nre >= maxr:
+            continue
+        fb = frames[gates[kb][0]]
+        cands = sorted((_dim(fm), p) for p, (x, fm, k) in dead.items() if (fm & ~fb) == 0)
+        if not cands:
+            continue
+        basis = []     # (vector, set of slots) with distinct leading bits
+        found = None
+        for dm, p in cands:
+            y, comb = dead[p][0], {p}
+            for bv, bs in basis:
+                if y >> (bv.bit_length() - 1) & 1:
+                    y ^= bv
+                    comb ^= bs
+            if y == 0:
+                found = (p, sorted(q for q in comb if q != p))
+                break
+            basis.append((y, comb))
+            basis.sort(key=lambda z: -z[0])
+        if found is None:
+            continue
+        found = sparse_relation([p for _, p in cands], dead, fb) or found
+        r0, S = found
+        G = dead[r0][1]
+        for q in S:
+            G |= dead[q][1]
+        G = Fm.closure(G)[0] if G else 0
+        assert G & ~fb == 0
+        x = dead[r0][0]
+        for q in S:
+            x ^= dead[q][0]
+        assert x == 0, "not a relation"
+        if S:
+            insert_before.setdefault(kb, []).append([frame_id(G), r0, list(S), "helper"])
+        for q in S:
+            dead[q][1] = G
+        assert dead[r0][2] < kb
+        del dead[r0]
+        rename[rb] = r0
+        nre += 1
+    # retained totals (born at the full frame) reuse dead slots: undo by reading the slot's x-lines at the full frame
+    FULLM = (1 << v) - 1
+    ntot = 0
+    for q in w["ret"]:
+        kq = first[q]
+        bury(kq)
+        free = [p for p in dead if dead[p][2] < kq]      # only slots already dead at the total's birth
+        if not free:
+            continue
+        r0 = min(free, key=lambda p: (bin(dead[p][0]).count("1"), p))
+        xs = _bits(dead[r0][0])
+        if xs:
+            insert_before.setdefault(kq, []).append([frame_id(FULLM), r0, xs, "total"])
+        del dead[r0]
+        rename[q] = r0
+        ntot += 1
+    out, kinds = [], []
+    for k, g in enumerate(gates):
+        for f, d, srcs, kind in insert_before.get(k, []):
+            out.append([f, d, srcs])
+            kinds.append(kind)
+        f, d, srcs = g
+        out.append([f, rename.get(d, d), [rename.get(s, s) for s in srcs]])
+        kinds.append(None)
+    nA2 = nA + sum(len(insert_before.get(k, [])) for k in range(nA))
+    A2, B2 = out[:nA2], out[nA2:]
+    # ledger of the inserted elimination gates: (phase, index in that phase, kind); retime.py keeps gate positions
+    ledger = [["A", i, kd] if i < nA2 else ["B", i - nA2, kd] for i, kd in enumerate(kinds) if kd]
+    alive = sorted(set(range(2 * v, 2 * v + R)) - set(rename))
+    newid = {r: 2 * v + i for i, r in enumerate(alive)}
+    for i in range(2 * v):
+        newid[i] = i
+    R2 = len(alive)
+
+    def ren(gl):
+        return [[f, newid[d], [newid[s] for s in srcs]] for f, d, srcs in gl]
+
+    A2, B2 = ren(A2), ren(B2)
+    ret2 = [newid[rename.get(q, q)] for q in w["ret"]]
+    # dirt compensation and cleanup, rebuilt as in PR #370's fullword.build
+    nreg = 2 * v + R2
+    dv = [0] * nreg
+    for r in range(2 * v, nreg):
+        dv[r] = 1 << (r - 2 * v)
+    for f, d, srcs in A2:
+        for s in srcs:
+            dv[d] ^= dv[s]
+    cdirt = [dv[q] for q in ret2]
+    for t in range(v):
+        for k in w["scatter"][t]:
+            dv[v + t] ^= cdirt[k]
+    for f, d, srcs in B2:
+        for s in srcs:
+            dv[d] ^= dv[s]
+    zero, full = frame_id(0), frame_id(FULLM)
+    D = []
+    for t in range(v):
+        srcs = [2 * v + b for b in _bits(dv[v + t])]
+        if srcs:
+            D.append([zero, v + t, srcs])
+    Cl = [[full, d, srcs] for f, d, srcs in reversed(A2 + B2) if d >= 2 * v]
+    start = w["start"][:2 * v] + [w["start"][2 * v]] * R2
+    final = w["final"][:2 * v] + [w["final"][2 * v]] * R2
+    cert = dict(w)
+    cert.update(R=R2, frames=[_bits(m) for m in frames], start=start, final=final, ret=ret2, D=D, A=A2, B=B2, C=Cl)
+    return cert, dict(helpers=nre, totals=ntot, eliminations=ledger)
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/data/bit/bitE8-r740.json.gz b/research/e8-joint-frame-retiming/vendor/pr436/data/bit/bitE8-r740.json.gz
new file mode 100644
index 0000000000..8a8ce996b8
Binary files /dev/null and b/research/e8-joint-frame-retiming/vendor/pr436/data/bit/bitE8-r740.json.gz differ
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/data/bit/reuse-ledger.json b/research/e8-joint-frame-retiming/vendor/pr436/data/bit/reuse-ledger.json
new file mode 100644
index 0000000000..51eb63c7d8
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/data/bit/reuse-ledger.json
@@ -0,0 +1 @@
+{"helpers": 114, "totals": 9, "eliminations": [["A", 973, "helper"], ["A", 975, "helper"], ["A", 986, "helper"], ["A", 993, "helper"], ["A", 995, "helper"], ["A", 1002, "helper"], ["A", 1009, "helper"], ["A", 1011, "helper"], ["A", 1018, "helper"], ["A", 1025, "helper"], ["A", 1027, "helper"], ["A", 1034, "helper"], ["A", 1036, "helper"], ["A", 1043, "helper"], ["A", 1050, "helper"], ["A", 1052, "helper"], ["A", 1059, "helper"], ["A", 1061, "helper"], ["A", 1068, "helper"], ["A", 1075, "helper"], ["A", 1082, "helper"], ["A", 1085, "helper"], ["A", 1088, "helper"], ["A", 1091, "helper"], ["A", 1094, "helper"], ["A", 1097, "helper"], ["A", 1100, "helper"], ["A", 1103, "helper"], ["A", 1106, "helper"], ["A", 1109, "helper"], ["A", 1112, "helper"], ["A", 1115, "helper"], ["A", 1118, "helper"], ["A", 1121, "helper"], ["A", 1124, "helper"], ["A", 1127, "helper"], ["A", 1130, "helper"], ["A", 1133, "helper"], ["A", 1136, "helper"], ["A", 1139, "helper"], ["A", 1142, "helper"], ["A", 1145, "helper"], ["A", 1148, "helper"], ["A", 1151, "helper"], ["A", 1154, "helper"], ["A", 1157, "helper"], ["A", 1160, "helper"], ["A", 1163, "helper"], ["A", 1166, "helper"], ["A", 1169, "helper"], ["A", 1172, "helper"], ["A", 1175, "helper"], ["A", 1178, "helper"], ["A", 1181, "helper"], ["A", 1184, "helper"], ["A", 1187, "helper"], ["A", 1190, "helper"], ["A", 1193, "helper"], ["A", 1196, "helper"], ["A", 1199, "helper"], ["A", 1202, "helper"], ["A", 1205, "helper"], ["A", 1209, "helper"], ["A", 1213, "helper"], ["A", 1216, "helper"], ["A", 1219, "helper"], ["A", 1222, "helper"], ["A", 1225, "helper"], ["A", 1228, "helper"], ["A", 1231, "helper"], ["A", 1234, "helper"], ["A", 1237, "helper"], ["A", 1240, "helper"], ["A", 1243, "helper"], ["A", 1246, "helper"], ["A", 1249, "helper"], ["A", 1252, "helper"], ["A", 1255, "helper"], ["A", 1258, "helper"], ["A", 1261, "helper"], ["A", 1268, "helper"], ["A", 1271, "helper"], ["A", 1274, "helper"], ["A", 1277, "helper"], ["A", 1280, "helper"], ["A", 1283, "helper"], ["A", 1286, "helper"], ["A", 1289, "helper"], ["A", 1294, "helper"], ["A", 1299, "helper"], ["A", 1304, "helper"], ["A", 1308, "helper"], ["A", 1312, "helper"], ["A", 1315, "helper"], ["A", 1318, "helper"], ["A", 1321, "helper"], ["A", 1324, "helper"], ["A", 1329, "helper"], ["A", 1334, "helper"], ["A", 1339, "helper"], ["A", 1344, "helper"], ["A", 1348, "helper"], ["A", 1352, "helper"], ["A", 1355, "helper"], ["A", 1358, "helper"], ["A", 1367, "helper"], ["A", 1370, "helper"], ["A", 1379, "helper"], ["A", 1384, "helper"], ["A", 1409, "helper"], ["A", 1414, "helper"], ["A", 1427, "helper"], ["A", 1823, "helper"], ["A", 1840, "helper"], ["A", 1855, "total"], ["A", 1857, "total"], ["A", 1859, "total"], ["A", 1861, "total"], ["A", 1863, "total"], ["A", 1865, "total"], ["A", 1867, "total"], ["A", 1869, "total"], ["A", 1871, "total"]]}
diff --git a/research/e8-joint-frame-retiming/vendor/pr436/data/params/params-r740.json b/research/e8-joint-frame-retiming/vendor/pr436/data/params/params-r740.json
new file mode 100644
index 0000000000..d9bc74d95b
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr436/data/params/params-r740.json
@@ -0,0 +1 @@
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61)", 0], ["('pair', (4, 5, 6, 7), 62)", 0], ["('pair', (4, 5, 6, 7), 63)", 2]]
\ No newline at end of file
diff --git a/research/e8-joint-frame-retiming/vendor/pr438/complex_phases.py b/research/e8-joint-frame-retiming/vendor/pr438/complex_phases.py
new file mode 100644
index 0000000000..6f199bc139
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr438/complex_phases.py
@@ -0,0 +1,22 @@
+"""Bind unchanged exact phase evidence, or regenerate all selected phase pairs."""
+import gzip,hashlib,json,os,subprocess,sys
+from pathlib import Path
+P=Path(__file__).resolve().parent.parent;O=Path('split-centres')
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+c=json.load(gzip.open(O/'CANONICAL-WORD.json.gz'))
+r=json.loads((P/'inputs/complex-phase-receipt.json').read_text())
+raw=gzip.decompress((P/'inputs/complex-phase-recipes.json.gz').read_bytes());recipes=json.loads(raw)
+assert sha(O/'CANONICAL-WORD.json.gz')==r['canonical_word_sha256']
+assert hashlib.sha256(raw).hexdigest()==r['recipe_sha256']
+edges=set(map(tuple,c['edges']))|{(a,b) for f in c['center_frames'] for a,b in ((f,0),(0,f))}
+assert {(z['old'],z['new']) for z in recipes['children']}==edges
+assert len(recipes['children'])==len(edges) and len(recipes['endpoint_adapters'])==240
+for z in recipes['children']:assert z['rank']==abs(len(c['frames'][z['old']])-len(c['frames'][z['new']]))
+if os.environ.get('E8_REPLAY_PHASES')=='1':
+ subprocess.run([sys.executable,'-B',str(P/'code/complex_phases_full.py')],check=True)
+ assert (O/'CLIFFORD-RECIPES.json').read_bytes()==raw
+else:
+ (O/'CLIFFORD-RECIPES.json').write_bytes(raw)
+ r['validation_mode']='Reuse exact phase evidence bound to the unchanged canonical word and recipe hashes'
+ (O/'CLIFFORD-REVIEW.json').write_text(json.dumps(r,indent=2)+'\n')
+print('PASS source-bound phase recipes',len(edges))
diff --git a/research/e8-joint-frame-retiming/vendor/pr439/LICENSE b/research/e8-joint-frame-retiming/vendor/pr439/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr439/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
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+      incurred by, or claims asserted against, such Contributor by reason
+      of your accepting any such warranty or additional liability.
+
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+
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+   Licensed under the Apache License, Version 2.0 (the "License");
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+
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diff --git a/research/e8-joint-frame-retiming/vendor/pr439/NOTICE.md b/research/e8-joint-frame-retiming/vendor/pr439/NOTICE.md
new file mode 100644
index 0000000000..3dfad2ad57
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr439/NOTICE.md
@@ -0,0 +1,26 @@
+# Attribution and scope
+
+New kernel selection, explicit residual route witnesses, integration and audits:
+chafreaky, with substantial OpenAI Codex assistance. Apache-2.0.
+
+- eumemic, PR #436 (`da8ca2025472553ac9b36f4400138ed48a6a0e3b`): R740 bit word,
+  reconstruction, elimination/reuse, independent checkers and #433 composition.
+  The entire parent package is byte-identical, including its notices, licenses,
+  source pins and Anthropic Claude disclosure.
+- chafreaky, PR #417: shared-donor kernel, exact local replay and tiling code;
+  the earlier implementation had substantial Anthropic Claude assistance.
+- rohanarun, PR #435 (`2c9c833ac8709402c37fc88a6a23393fb0d397fb`): prior mixed-width
+  residual-bank composition on #433. The new implementation derives from the
+  pinned #436 global/audit code and adds explicit residual isometries and controls.
+- icekylinx, PR #433: split-centre complex supplier, bit finite invoice and tail,
+  with OpenAI Codex assistance; the complex result is cited, not rebuilt here.
+- jacklightChen, PRs #386 and #425: compressed nine-stage geometry and the
+  mutable-basis complex interface, with OpenAI Codex assistance.
+- utcorvusvolat-dotcom / Dylan Crow, PR #370: E8 bit format, producer and
+  independent checker lineage, with Anthropic Claude assistance.
+- applecrusher (#376), ai-nanachi (#389/#426), DaysSky (#363/#375/#381),
+  DreamingOfClouds (#315), Jacob Sussman, and all earlier credited contributors:
+  see the unchanged `parent436/NOTICE.md` and source-specific notices.
+
+Do not infer an unconditional theorem or a new Lean proof from the finite
+certificates. No inherited author or AI-assistance disclosure has been removed.
diff --git a/research/e8-joint-frame-retiming/vendor/pr439/bank_routes.py b/research/e8-joint-frame-retiming/vendor/pr439/bank_routes.py
new file mode 100644
index 0000000000..919fe32f7e
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr439/bank_routes.py
@@ -0,0 +1,64 @@
+"""Exact residual bank routes for the kernel word; chafreaky with OpenAI Codex.
+
+The stored integer rows divided by two are an orthonormal basis. Entrance
+rows span E; the remaining rows span E-perp. A coordinate permutation sends
+the latter to the assigned contiguous block in a width-64 bank. This gives
+an explicit rational isometry, with only powers of two in denominators.
+"""
+from collections import Counter, deque
+from tile_m import tile
+
+
+def placement(widths):
+    by_width = {}
+    for rep in range(8):
+        for helper, width in enumerate(widths):
+            assert 0 < width <= 8
+            by_width.setdefault(width, deque()).append((rep, helper))
+    patterns = tile({w: len(q) for w, q in by_width.items()}, 64)
+    result = {}
+    bank = 0
+    for widths_in_bank, count in patterns:
+        for _ in range(count):
+            offset = 0
+            for width in widths_in_bank:
+                key = by_width[width].popleft()
+                result[key] = (bank, offset, width)
+                offset += width
+            assert offset == 64
+            bank += 1
+    assert all(not q for q in by_width.values())
+    assert len(result) == 8 * len(widths)
+    return result, bank
+
+
+def validate_isometries(rows, frames, roots, dimensions):
+    seen = set()
+    dot = lambda a, b: sum(x*y for x, y in zip(a, b))
+    for record in rows:
+        f = record['frame']
+        assert f not in seen
+        seen.add(f)
+        e = record['entrance_rank']
+        assert e == dimensions[f] and record['denominator'] == 2
+        basis = record['entrance_basis'] + record['residual_basis']
+        matrix = record['orthogonal_rows_numerator']
+        assert len(basis) == len(matrix) == 8
+        assert matrix == [roots[i] for i in basis]
+        assert all(len(r) == 8 and all(type(x) is int for x in r) for r in matrix)
+        assert all(dot(a,b) == 4*(i==j) for i,a in enumerate(matrix) for j,b in enumerate(matrix))
+        # The first e rows span precisely the frame, not only its dimension.
+        for i in frames[f]:
+            assert sum(dot(roots[i], q)**2 for q in matrix[:e]) == 4*dot(roots[i], roots[i])
+        assert len(record['entrance_basis']) == e
+        # This selected family needs coordinate permutations only. Checking the
+        # elementary reduction also bounds the literal route cost and primes.
+        reduced = [[x // 2 for x in row] for row in matrix]
+        assert all(x % 2 == 0 for row in matrix for x in row)
+        operations = record['gaussian_reduction']
+        assert len(operations) <= 7
+        for kind, i, j, scalar in operations:
+            assert kind == 'swap' and scalar is None and 0 <= i < 8 and 0 <= j < 8
+            reduced[i], reduced[j] = reduced[j], reduced[i]
+        assert reduced == [[int(i == j) for j in range(8)] for i in range(8)]
+    return seen
diff --git a/research/e8-joint-frame-retiming/vendor/pr439/e8core.py b/research/e8-joint-frame-retiming/vendor/pr439/e8core.py
new file mode 100644
index 0000000000..78983b3687
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr439/e8core.py
@@ -0,0 +1,203 @@
+"""Our own engine for bitE8/1 words (E8 root-line labels, h = 8): frame algebra over Q via root-line masks,
+legality/F2 replay, five-stage histogram, exact bit coarse saving and PR #315 outer assembly (our engine copies).
+Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0."""
+import gzip, json, os, importlib.util
+from fractions import Fraction as Q
+from collections import Counter
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+def _load(n):
+    s = importlib.util.spec_from_file_location('e8_' + n, os.path.join(HERE, "engines", n + ".py"))
+    m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+moment = _load('moment'); other = _load('base_two_moment'); outer = _load('outer')
+
+B2 = Q(876248285600677, 10**18)   # Sussman E8 five-stage (PR #352)
+B3 = Q(932783231884153, 10**18)   # DaysSky seven-stage B_3 (PR #363; no Lean proof)
+
+
+def load_word(p):
+    with (gzip.open(p, 'rt') if p.endswith('.gz') else open(p)) as f:
+        return json.load(f)
+
+
+def save_word(c, p):
+    with gzip.open(p, 'wt') as f:
+        json.dump(c, f, separators=(',', ':'))
+
+
+def rank(vecs):
+    rows = [[Q(x) for x in r] for r in vecs]; rk = 0
+    n = len(rows[0]) if rows else 0
+    for col in range(n):
+        p = next((i for i in range(rk, len(rows)) if rows[i][col] != 0), None)
+        if p is None: continue
+        rows[rk], rows[p] = rows[p], rows[rk]
+        for i in range(len(rows)):
+            if i != rk and rows[i][col] != 0:
+                f = rows[i][col] / rows[rk][col]; rows[i] = [a - f * b for a, b in zip(rows[i], rows[rk])]
+        rk += 1
+    return rk
+
+
+class Lat:
+    """Root-spanned subspaces of Q^8 represented by the mask of root lines they contain."""
+    def __init__(self, lines):
+        self.lines = [tuple(x) for x in lines]; self.v = len(lines)
+        self._dim = {0: 0}; self._close = {}
+        # Gram (form <x,y>/2) for orthogonality
+        self.ip = [[sum(a * b for a, b in zip(x, y)) // 2 for y in self.lines] for x in self.lines]
+
+    def close(self, mask):
+        """mask of all root lines in span(roots of mask)"""
+        if mask in self._close: return self._close[mask]
+        idx = [i for i in range(self.v) if mask >> i & 1]
+        basis = []
+        for i in idx:
+            if rank([self.lines[j] for j in basis] + [self.lines[i]]) > len(basis): basis.append(i)
+        d = len(basis); out = 0
+        if d == 8: out = (1 << self.v) - 1
+        elif d:
+            B = [self.lines[j] for j in basis]
+            for i in range(self.v):
+                if rank(B + [self.lines[i]]) == d: out |= 1 << i
+        self._close[mask] = out; self._close[out] = out; self._dim[out] = d
+        return out
+
+    def dim(self, mask):
+        if mask not in self._dim: self.close(mask)
+        return self._dim[mask]
+
+    def basis(self, mask):
+        b = []
+        for i in range(self.v):
+            if mask >> i & 1 and rank([self.lines[j] for j in b] + [self.lines[i]]) > len(b): b.append(i)
+        return b
+
+    def perp(self, t):
+        return self.close(sum(1 << j for j in range(self.v) if self.ip[t][j] == 0))
+
+
+def to_masks(c, L):
+    return [L.close(sum(1 << i for i in fr)) for fr in c['frames']]
+
+
+PHASES = ('D', 'A', 'B', 'C')
+
+
+def replay(c, L=None, masks=None, check_f2=True, span=True, span_mode='z'):
+    """Exact legality + F2 replay + histogram of a bitE8/1 word. Returns dict(H_local, steps, ...).
+    Legality: each register's frames nested (mask inclusion = exact Q-subspace inclusion for root-spanned frames) and
+    strictly increasing at each move; every gate at one common frame; D compensation at frame 0; y at frame 0 at the
+    scatter; COPY of retained totals; final frames (x, helpers FULL; y_t at its cap t-perp).
+    Source-span: every non-target operand's x-support lies in the gate frame."""
+    L = L or Lat(c['lines']); masks = masks or to_masks(c, L)
+    v, R, h = c['v'], c['R'], c['h']; n = 2 * v + R; FULL = (1 << v) - 1
+    cur = [masks[f] for f in c['start']]
+    for r in range(v): assert cur[r] == L.close(1 << r), 'x start'
+    for r in range(v, 2 * v): assert cur[r] == 0, 'y start at 0'
+    sig = [L.dim(cur[r]) for r in range(n)]
+    H = Counter(); steps = 0; viol = []
+    val = [1 << i for i in range(n)]
+    zsupp = [{i: 1} if i < v else {} for i in range(n)]  # integer support of each register over the x columns (all ADDs are +1)
+    def climb(r, m):
+        nonlocal steps
+        if cur[r] == m: return
+        assert cur[r] & ~m == 0 and cur[r] != m, ('not nested', r)
+        H[L.dim(m) - L.dim(cur[r])] += 1; steps += 1; cur[r] = m
+    def run(gates, ph):
+        for k, (f, d, srcs) in enumerate(gates):
+            m = masks[f]
+            assert d >= v and d not in srcs and len(set(srcs)) == len(srcs), (ph, k)
+            for x in [d] + srcs: climb(x, m)
+            for s in srcs:
+                val[d] ^= val[s]
+                if span:
+                    if s < v or s >= 2 * v:
+                        ms = sum(1 << i for i in zsupp[s])
+                        if ms & ~m: viol.append((ph, k, s))
+                    zd = zsupp[d]
+                    for i, a in zsupp[s].items():
+                        w = zd.get(i, 0) + a
+                        if w: zd[i] = w
+                        else: zd.pop(i, None)
+                    if span_mode == 'f2':
+                        zsupp[d] = {i: 1 for i in range(v) if val[d] >> i & 1}
+            if span and d >= 2 * v:
+                md = sum(1 << i for i in zsupp[d])
+                if md & ~m: viol.append((ph, k, d))
+    run(c['D'], 'D')
+    for r in range(v, n): assert cur[r] == masks[c['start'][r]], 'D compensation at frame 0 (helpers untouched otherwise)'
+    run(c['A'], 'A')
+    for t in range(v): assert cur[v + t] == 0, 'y at frame 0 at the scatter'
+    copies = [val[q] for q in c['ret']]
+    for q in c['ret']:
+        assert q >= 2 * v; H[L.dim(cur[q])] += 1
+    for t, row in enumerate(c['scatter']):
+        for k in row: val[v + t] ^= copies[k]
+    run(c['B'], 'B'); run(c['C'], 'C')
+    for r in range(n): climb(r, masks[c['final'][r]])
+    for r in range(v): assert cur[r] == FULL
+    for r in range(2 * v, n): assert cur[r] == FULL
+    for t in range(v): assert cur[v + t] == L.perp(t), 'y final at cap'
+    if check_f2:
+        for s in range(v): assert val[s] == 1 << s
+        for t in range(v): assert val[v + t] == (1 << (v + t)) | (1 << t), ('target', t)
+        for r in range(2 * v, n): assert val[r] == 1 << r, ('helper', r)
+    return dict(sig=sig, viol=viol, H=H, steps=steps, n=n, v=v, R=R, h=h, L=L, masks=masks, ncopy=len(c['ret']))
+
+
+def profile(H_local, v, h=8):
+    prof = Counter({j: 5 * c for j, c in H_local.items()})
+    for j in (2 * h - 2, h - 1, 2 * h + 2, 4): prof[j] += 2 * v
+    return prof
+
+
+def coarse(H, m, W):
+    grid = Q(1, 10**18)
+    root = moment.certify(dict(H), m, W, True); c = Q(int(Q(root['lower']) * 10**18), 10**18)
+    assert moment.moment(H, m, W, c, True)[1] < 1 < moment.moment(H, m, W, c + grid, True)[0]
+    fb = 32 * m * m * sum(H.values())
+    _, up = other.moment(m, W, list(H.items()), c); _, bad = other.moment(m, W, [(1, fb)], c)
+    lo, _ = other.moment(m, W, list(H.items()), c + grid); blo, _ = other.moment(m, W, [(1, fb)], c + grid)
+    assert up + Q(1, 10**16) * bad < 1 < lo + Q(1, 10**16) * blo
+    return c
+
+
+def kappa(c, b):
+    grid = Q(1, 10**18); eta = Q(1, 10**12); beta = Q(1, 10**9); cap = (1 - beta) * b
+    sv = min(c, Q(((cap - grid) * 10**18).__floor__(), 10**18)); binding = 'bit' if sv == c else 'complex'
+    chain = [Q(384599, 10**10)]
+    for _ in range(3):
+        a = (1 - sv) * sv + sv * chain[-1]; assert chain[-1] < a < sv < 1 - a; chain.append(a)
+    bit = chain[-1]
+    bridge = dict(proof='PROOF.md', representation='Exact powers with source-bound finite overcharges',
+                  semantic=dict(G=dict(base=2, exponent=30000), E=dict(base=2, exponent=100000), B_upper=dict(base=2, exponent=100001),
+                                C0=dict(base=2, exponent=210000), C1=1, strict_literal_gap=1, induction_gap_lower=1),
+                  rows=dict(coefficient=20161, degree=10**6, suffix_slope=4 * 10**6, degree_gap=Q(10**6) - Q(51 * 20161, 25)))
+    q = bit * (1 - 2 * eta); mn = (1 - eta) * q / (1 + q); t = mn * 10**18; k = Q((t.numerator - 1) // t.denominator, 10**18)
+    asm = outer.assembly(bit, b, bridge, k, eta=eta, beta=beta)
+    assert len(asm['strict_constraints']) == 47 and min(asm['strict_constraints'].values()) > 0
+    try:
+        outer.assembly(bit, b, bridge, k + grid, eta=eta, beta=beta); raise SystemExit('ADJACENT ADMITTED')
+    except AssertionError: pass
+    return k, binding
+
+
+def price_word(c, **kw):
+    r = replay(c, **kw)
+    v, h, R = r['v'], r['h'], r['R']; m = 5 * h
+    resid = sum(h - r['sig'][x] for x in range(2 * v, 2 * v + R))
+    T = 1 if resid % h == 0 else h
+    W = (4 * v * h + resid) * T // h; assert (4 * v * h + resid) * T % h == 0
+    prof = Counter({j: T * k for j, k in profile(r['H'], v, h).items()}); mass = sum(a * b for a, b in prof.items())
+    L_copy = h * r['ncopy']
+    assert m * W - mass == T * (4 * v - 5 * L_copy), ('deficit', m * W - mass)
+    assert 2 * max(prof) < m
+    cc = coarse(prof, m, W)
+    return dict(c=cc, H=r['H'], prof=prof, W=W, T=T, resid=resid, m=m, deficit=m * W - mass, replay=r)
+
+
+def phi_fn(m, W, a):
+    """linearized moment term per child of rank r (float), for search scoring"""
+    import math
+    return lambda r: r / (m * W) * math.exp(a * math.log(m / r))
diff --git a/research/e8-joint-frame-retiming/vendor/pr439/engines/base_two_moment.py b/research/e8-joint-frame-retiming/vendor/pr439/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr439/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/e8-joint-frame-retiming/vendor/pr439/engines/moment.py b/research/e8-joint-frame-retiming/vendor/pr439/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr439/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/e8-joint-frame-retiming/vendor/pr439/engines/outer.py b/research/e8-joint-frame-retiming/vendor/pr439/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr439/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/e8-joint-frame-retiming/vendor/pr439/tile_m.py b/research/e8-joint-frame-retiming/vendor/pr439/tile_m.py
new file mode 100644
index 0000000000..cd5fd9b539
--- /dev/null
+++ b/research/e8-joint-frame-retiming/vendor/pr439/tile_m.py
@@ -0,0 +1,93 @@
+"""Residual census (8 - sigma per helper) and an exact zero-padding bank tiling of width m = (2K+1)h with T replicas:
+tile() and economy_tile() verbatim from our PR #329 bank_template.py (via code/tile.py of our dtst3 package).
+usage: tile_m.py WORD.json.gz M [replicas]  (replicas default: the least T with T x residual sum = 0 mod M that tiles)"""
+import sys,os,collections
+from collections import Counter
+sys.path.insert(0,os.path.dirname(os.path.abspath(__file__)))
+from e8core import *
+def economy_tile(blocks, m):
+    """Exact zero-padding tiling used when the filler search of tile() runs out of filler blocks (the kernel pivots
+    and early restorations of the stage stack add many residual widths that do not divide m; the PR #299 analogue at
+    p = 12 was the (r^4, 24, 4^(24-r)) re-tiling). The fillers are the two most numerous widths dividing m (here the
+    full helper width h and the rank-4 entrance residual). Each other width w, in decreasing order, gets the bank
+    w^a F^c f^b (w*a + F*c + f*b = m) that spends the fewest narrow fillers f per w block (then the largest a), plus
+    at most one bank w^r F^c' f^b' for the remainder r = n mod a. The leftover fillers fill pure banks F^(m/F),
+    f^(m/f) and y residue banks F^j f^k. Every bank sums to m and every block is used exactly once (no padding)."""
+    from fractions import Fraction
+    blocks = {w: n for w, n in blocks.items() if n}
+    div = sorted((w for w in blocks if m % w == 0), key=lambda w: (-blocks[w], w))
+    assert len(div) >= 2, ('economy tiling needs two filler widths', blocks)
+    F, f = sorted(div[:2], reverse=True)
+
+    def fill(rest):
+        """(c, b) with F*c + f*b = rest, c maximal (fewest narrow fillers); None if impossible."""
+        return next(((c, (rest - F*c)//f) for c in range(rest//F, -1, -1) if (rest - F*c) % f == 0), None)
+
+    left = {F: blocks[F], f: blocks[f]}; out = []
+    for w in sorted((x for x in blocks if x not in (F, f)), reverse=True):
+        n = blocks[w]
+        opts = [(Fraction(cb[1], a), -a, a, cb) for a in range(m//w, 0, -1) for cb in [fill(m - w*a)] if cb]
+        assert opts, ('no bank for width', w)
+        _, _, a, (c, b) = min(opts); q, r = divmod(n, a)
+        if q: out.append(((w,)*a + (F,)*c + (f,)*b, q)); left[F] -= q*c; left[f] -= q*b
+        if r:
+            cb = fill(m - w*r); assert cb, ('no remainder bank', w, r)
+            out.append(((w,)*r + (F,)*cb[0] + (f,)*cb[1], 1)); left[F] -= cb[0]; left[f] -= cb[1]
+    assert left[F] >= 0 and left[f] >= 0, ('fillers exhausted', left)
+    pF, pf = m//F, m//f
+    for y in range((pF*pf) + 1):
+        for j in range(1 if y else 0, pF if y else 1):
+            if (m - F*j) % f: continue
+            k = (m - F*j)//f; aF, af = left[F] - y*j, left[f] - y*k
+            if aF >= 0 and af >= 0 and aF % pF == 0 and af % pf == 0:
+                out += ([((F,)*j + (f,)*k, y)] if y else []) + ([((F,)*pF, aF//pF)] if aF else []) + ([((f,)*pf, af//pf)] if af else [])
+                return out
+    raise AssertionError(('no exact zero-padding tiling', blocks, m))
+
+
+def tile(blocks, m):
+    """Exact tiling of {width: number of blocks} into banks of total width m, as ((widths, banks), ...).
+
+    A width dividing m fills pure banks. A width w not dividing m is mixed with a filler width f dividing m:
+    banks w^a f^b with a maximal (w*a + f*b = m), then at most one bank w^r f^t for the remainder r. Fillers
+    are tried in a fixed order (most blocks first) with backtracking until every pure width also divides out.
+    Fails (AssertionError) unless every block is used and every bank is full; there is no padding."""
+    blocks = {w: n for w, n in blocks.items() if n}
+    assert all(0 < w <= m for w in blocks)
+    mixed = sorted(x for x in blocks if m % x)
+
+    def search(i, left, out):
+        if i == len(mixed):
+            if any(left[w] % (m // w) for w in left): return None
+            return out + [(tuple([w]*(m // w)), left[w]//(m // w)) for w in sorted(left) if left[w]]
+        w = mixed[i]; n = blocks[w]
+        for f in sorted(left, key=lambda x: (-left[x], x)):
+            a = next((a for a in range(m // w, 0, -1) if (m - w*a) % f == 0), None)
+            if a is None: continue
+            b = (m - w*a)//f; q, r = divmod(n, a)
+            if r and (m - w*r) % f: continue
+            t = (m - w*r)//f if r else 0
+            if q*b + t > left[f]: continue
+            rest = dict(left); rest[f] -= q*b + t
+            found = search(i + 1, rest, out + ([(tuple([w]*a + [f]*b), q)] if q else []) + ([(tuple([w]*r + [f]*t), 1)] if r else []))
+            if found is not None: return found
+        return None
+    out = search(0, {w: n for w, n in blocks.items() if not m % w}, [])
+    if out is None: out = economy_tile(blocks, m)
+    assert all(sum(widths) == m and count > 0 for widths, count in out)
+    used = Counter()
+    for widths, count in out:
+        for x in widths: used[x] += count
+    assert used == Counter(blocks), 'every block used exactly once'
+    return tuple(out)
+if __name__ == '__main__':
+    c = load_word(sys.argv[1]); m = int(sys.argv[2])
+    L = Lat(c['lines']); M = to_masks(c, L); v = c['v']; n = 2 * v + c['R']
+    res = Counter(8 - L.dim(M[c['start'][r]]) for r in range(2 * v, n)); tot = sum(k * x for k, x in res.items())
+    reps = [int(sys.argv[3])] if len(sys.argv) > 3 else [t for t in range(1, 200) if t * tot % m == 0]
+    for T in reps:
+        try: pat = tile({r: T * k for r, k in res.items() if r > 0}, m); break
+        except AssertionError: pat = None
+    assert pat, 'no tiling'
+    print('   residual census', dict(sorted(res.items())), 'sum', tot)
+    print('   PASS exact width-%d tiling with %d replicas: %d banks' % (m, T, sum(k for _, k in pat)), pat)
diff --git a/research/e8-joint-frame-retiming/verify.py b/research/e8-joint-frame-retiming/verify.py
new file mode 100644
index 0000000000..36a698beaa
--- /dev/null
+++ b/research/e8-joint-frame-retiming/verify.py
@@ -0,0 +1,50 @@
+"""Verify the selected two-supplier composition using Python's standard library."""
+import argparse,gzip,hashlib,json,os,shutil,subprocess,sys
+from pathlib import Path
+assert __debug__, 'Assertions must remain enabled'
+ROOT=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser(description=__doc__)
+ap.add_argument('output',type=Path,help='A new output directory outside this package')
+ap.add_argument('--replay-phases',action='store_true',help='Recompute all selected Gaussian phase pairs instead of reusing their source-bound evidence')
+a=ap.parse_args();out=a.output.resolve()
+assert not out.exists() and not out.is_relative_to(ROOT)
+def snapshot():
+ return {p.relative_to(ROOT).as_posix():hashlib.sha256(p.read_bytes()).hexdigest() for p in ROOT.rglob('*') if p.is_file() and p.name!='MANIFEST.json'}
+manifest=json.loads((ROOT/'MANIFEST.json').read_text());assert snapshot()==manifest['files'],'Source manifest mismatch'
+sources=json.loads((ROOT/'SOURCES.json').read_text())
+for z in sources['imported_files']:
+ data=(ROOT/z['path']).read_bytes();assert hashlib.sha256(data).hexdigest()==z['sha256']
+ if 'source_sha256' in z:assert hashlib.sha256(gzip.decompress(data)).hexdigest()==z['source_sha256']
+out.mkdir(parents=True)
+def copy(src,dst):
+ p=out/dst;p.parent.mkdir(parents=True,exist_ok=True)
+ data=(ROOT/src).read_bytes();p.write_bytes(gzip.decompress(data) if src.endswith('.gz') and not dst.endswith('.gz') else data)
+for src,dst in [
+ ('inputs/e8-r865.json.gz','work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz'),
+ ('inputs/complex-ports.json.gz','work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz'),
+ ('inputs/complex-template.json.gz','work/complex-nine-native/GLOBAL-TEMPLATE.json.gz'),
+ ('inputs/complex-data-phases.json.gz','work/complex-nine-native/DATA-PHASES.json'),
+ ('inputs/bit-geometry.json.gz','inherited/bit-geometry.json.gz'),
+ ('vendor/clifford_exact.py','work/odd-stages/clifford_exact.py')]:copy(src,dst)
+for name in ('moment','base_two_moment','outer'):copy('vendor/engines/'+name+'.py','work/pr361/code/engines/'+name+'.py')
+p=out/'bit426-source-centres';p.mkdir()
+env=dict(os.environ,E8_OUTPUT=str(out),E8_REPLAY_PHASES=str(int(a.replay_phases)),PYTHONDONTWRITEBYTECODE='1');env.pop('PYTHONOPTIMIZE',None)
+steps=[]
+def run(name,file,*args):
+ with (out/(name+'.log')).open('w') as log:
+  r=subprocess.run([sys.executable,'-B',str(ROOT/file),*map(str,args)],cwd=out,env=env,stdout=log,stderr=subprocess.STDOUT)
+ assert r.returncode==0,(name,str(out/(name+'.log')))
+ steps.append(name);print('PASS',name,flush=True)
+run('hamming_packets','vendor/hamming_packets.py')
+for name in ('complex_construct','complex_audit','complex_emit','complex_phases','bit_construct','bit_kernel'):run(name,'code/'+name+'.py')
+run('bit_export','vendor/export_records.py',p/'bit-source-centres.json',p/'records')
+run('bit_global','code/bit_global.py','--source',p,'--local-check',p,'--out',p/'global')
+run('bit_audit','code/bit_audit.py','--local-check',p,'--out',p/'global')
+for name in ('bit_price','complex_integrate','complex_replay','combined'):run(name,'code/'+name+'.py')
+run('independent_audit','code/independent_audit.py',ROOT,out,out/'INDEPENDENT-AUDIT.json')
+assert snapshot()==manifest['files'],'Package modified during verification'
+r=json.loads((out/'RESULT.json').read_text());expected=json.loads((ROOT/'EXPECTED.json').read_text())
+for key,value in expected.items():assert r[key]==value,(key,r[key],value)
+r['verification_steps']=steps;r['phase_mode']='full replay' if a.replay_phases else 'source-bound unchanged evidence';r['manifest_sha256']=hashlib.sha256((ROOT/'MANIFEST.json').read_bytes()).hexdigest()
+(out/'RESULT.json').write_text(json.dumps(r,indent=2)+'\n')
+print('PASS conditional kappa',r['kappa_decimal'])
diff --git a/research/e8-r740-idle-hosting/AUDIT-CHANGED.json b/research/e8-r740-idle-hosting/AUDIT-CHANGED.json
new file mode 100644
index 0000000000..4ebab1c89c
--- /dev/null
+++ b/research/e8-r740-idle-hosting/AUDIT-CHANGED.json
@@ -0,0 +1,41 @@
+{
+  "status": "PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT",
+  "bit_template_sha256": "c256c1c11027d32d5d800dd8dc3c0c50189ab71157c6c06301bb4283ff23bab1",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f",
+  "bit_profile": {
+    "1": 182016,
+    "2": 76128,
+    "3": 20512,
+    "4": 27896,
+    "5": 8496,
+    "6": 2176,
+    "7": 4208,
+    "8": 648
+  },
+  "complex_profile": {
+    "1": 138384,
+    "2": 56448,
+    "3": 15936,
+    "4": 16128,
+    "5": 32064,
+    "7": 3840,
+    "8": 7488
+  },
+  "bit_live": 9376,
+  "complex_live": 8400,
+  "bit_hosted_residuals": 39712,
+  "complex_hosted_residuals": 34560,
+  "bit_maxchild": 8,
+  "complex_maxchild": 8,
+  "mutations_rejected": [
+    "bit: hosted residual outside its window",
+    "bit: overlapping hosted coordinates",
+    "bit: understated live stock",
+    "bit: hosted owner on the active pair",
+    "bit: missing remainder child",
+    "complex: hosted residual outside its window",
+    "complex: remainder child understated",
+    "complex: dropped bank",
+    "complex: duplicated hosted residual"
+  ]
+}
diff --git a/research/e8-r740-idle-hosting/CERTIFICATE.json b/research/e8-r740-idle-hosting/CERTIFICATE.json
new file mode 100644
index 0000000000..2613e82a26
--- /dev/null
+++ b/research/e8-r740-idle-hosting/CERTIFICATE.json
@@ -0,0 +1,116 @@
+{
+  "status": "PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY",
+  "kappa": "124529313073387/100000000000000000",
+  "kappa_decimal": "0.001245293130733870",
+  "bit_lower": "249369163853537814231/200000000000000000000000",
+  "complex_lower": "1267453159029119/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr434_percent": 9.901378851439578,
+  "bit": {
+    "live": 9376,
+    "physical": 9385,
+    "maxchild": 8,
+    "rank_mass": 597568,
+    "hosted_residuals": 39712,
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 282,
+    "charged_two_level_coefficient_bits": 320,
+    "row_coefficient": 18355
+  },
+  "complex": {
+    "live": 8400,
+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
+  },
+  "strict_outer_constraints": {
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+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
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+      "cutoff_log2": "15858630557976"
+    },
+    {
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+      "cutoff_log2": "10200939576290109046"
+    },
+    {
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+      "cutoff_log2": "6561674279421831238677946"
+    },
+    {
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+      "cutoff_log2": "4220745454595125991404220610916"
+    },
+    {
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+      "cutoff_log2": "2714961370203082164321471435033117471"
+    },
+    {
+      "gap": "35470899911366145532969229267939587198707853200424307949633800426071501554290773399554138981060821463706191785706225360964099272884388120768133353/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1746377582109381257242684594400020974931554"
+    }
+  ],
+  "bit_template_sha256": "c256c1c11027d32d5d800dd8dc3c0c50189ab71157c6c06301bb4283ff23bab1",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f"
+}
diff --git a/research/e8-r740-idle-hosting/EXPECTED.json b/research/e8-r740-idle-hosting/EXPECTED.json
new file mode 100644
index 0000000000..fc0a332a96
--- /dev/null
+++ b/research/e8-r740-idle-hosting/EXPECTED.json
@@ -0,0 +1,10 @@
+{
+  "status": "PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY",
+  "kappa": "124529313073387/100000000000000000",
+  "kappa_decimal": "0.001245293130733870",
+  "bit_lower": "249369163853537814231/200000000000000000000000",
+  "complex_lower": "1267453159029119/1000000000000000000",
+  "binding_component": "bit",
+  "bit_template_sha256": "c256c1c11027d32d5d800dd8dc3c0c50189ab71157c6c06301bb4283ff23bab1",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f"
+}
diff --git a/research/e8-r740-idle-hosting/LICENSE b/research/e8-r740-idle-hosting/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-r740-idle-hosting/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
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diff --git a/research/e8-r740-idle-hosting/MANIFEST.json b/research/e8-r740-idle-hosting/MANIFEST.json
new file mode 100644
index 0000000000..53374e4cb3
--- /dev/null
+++ b/research/e8-r740-idle-hosting/MANIFEST.json
@@ -0,0 +1,40 @@
+{
+  "parent_manifest_sha256": "344d58298774e9e2bbfd0af6332507c3b3d2172bc70d88a79853e679bdaaa33f",
+  "files": {
+    "AUDIT-CHANGED.json": "6320b6fba321cbde5648ca5d07d79d1e05095003cd20c11cee044df54d684842",
+    "CERTIFICATE.json": "f738a33bf7f079a3ea275a555807f0a6d491a65201859953eac7edeebb5e1fe3",
+    "EXPECTED.json": "feee5ada0067f1c83f7b21972fb4351b99a3ca24c020a43434b84ca20c48d14d",
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE.md": "e2bcab601208891189f33c257eb7cfee9261b420c6eceebf96c986135ae65a4c",
+    "PROOF.md": "4f06d1dead63c62b076f0a6c1521c68c0b0544aa2c5df5e74a408fdfc34f91c4",
+    "README.md": "d20e8b023a6c87fefbd24d88fe4b8656cc9d2e230da563547b839350a49ee630",
+    "SELECTION.json": "6e3a436ef9e926019751fd40b08586d695d888f16542f9c8a24ec4d6be8cffae",
+    "SOURCE442-PINS.json": "489716866ad1d368a5f29a3d37e8d76a40474f5709e4ad593f18f9cd89dc9096",
+    "VALIDATION.json": "0194fc0b213d43296551349dc163644dfb59459bd52282e8cc2639856747b3c4",
+    "assemble.py": "fb31ef3d1633effe3a8abeb48bf9bbc0508bfac2a37af101ea89dbb5f622be51",
+    "audit.py": "8792956a1aab64812cb030dc57456d68c5e90c570594f4d2d7fcf9ab14c89c40",
+    "bit_hosted.py": "300227c826ea07951738644975915ea11c1c53295440f93b3a7b19f635ce2061",
+    "complex_hosted.py": "829c5c4f4bdfccedadd31505f1f0a394f7a208d1446b7bbf9cc92d3aa1530c0c",
+    "hosting_core.py": "d8b90cd5d152df3c7c351230863d9e61816ad5e1f21d69bea1a86a5daad559a3",
+    "local-evidence/TESTED-MANIFEST.json": "aac568b890323ced6d856c0477a4761b6f106a5051ee0811ffd1d97d7ca09ca6",
+    "local-evidence/full311/RECEIPT.json": "e76d942a92d48129c91dacaf0c743f47ba2e3ab8289d359164eb1267a144591a",
+    "local-evidence/full311/RESULT.json": "f738a33bf7f079a3ea275a555807f0a6d491a65201859953eac7edeebb5e1fe3",
+    "local-evidence/full311/bit-hosting.log": "0b2dd019350260407d9d99fe7be94f02ff031997fbf6a4976229b27c6cd7d788",
+    "local-evidence/full311/complex-hosting.log": "3b42f65586cb5c37e06df560fae4dcde1c42526238697a73d103f9895df24fcd",
+    "local-evidence/full311/exact-assembly.log": "1d2c62b500f91f48ada95c0b4c811169705b762098c81f7458dbc8194652b8e9",
+    "local-evidence/full311/independent-audit.log": "e55ea84119d6b17d16be29a67e8158e357838aec1a3c2d17aa966d8843afe345",
+    "local-evidence/full311/parent/RESULT.json": "244786938e4901842ce110a450bef6529627c67e3f931134149420c1c8de1568",
+    "local-evidence/full311/parent-r740-full.log": "b6b21746622747ea37b7423dd7600953185f3da7c5cca1019526ab4d9cfb06f1",
+    "local-evidence/full314/RECEIPT.json": "381b19bd5ff1c180d643c6f8b3ef2949b362d542ea038d1bdd7aa6ea623c74e1",
+    "local-evidence/full314/RESULT.json": "f738a33bf7f079a3ea275a555807f0a6d491a65201859953eac7edeebb5e1fe3",
+    "local-evidence/full314/bit-hosting.log": "0b2dd019350260407d9d99fe7be94f02ff031997fbf6a4976229b27c6cd7d788",
+    "local-evidence/full314/complex-hosting.log": "3b42f65586cb5c37e06df560fae4dcde1c42526238697a73d103f9895df24fcd",
+    "local-evidence/full314/exact-assembly.log": "1d2c62b500f91f48ada95c0b4c811169705b762098c81f7458dbc8194652b8e9",
+    "local-evidence/full314/independent-audit.log": "e55ea84119d6b17d16be29a67e8158e357838aec1a3c2d17aa966d8843afe345",
+    "local-evidence/full314/parent/RESULT.json": "244786938e4901842ce110a450bef6529627c67e3f931134149420c1c8de1568",
+    "local-evidence/full314/parent-r740-full.log": "b6b21746622747ea37b7423dd7600953185f3da7c5cca1019526ab4d9cfb06f1",
+    "local-evidence/hosting442-exact-cost.json": "a60c72865bbeb7dc8b6fb0ef453944dc6fdd548f74fdd2a14bd2f0b128eb7260",
+    "local-evidence/hosting442-flexbanks.json": "39b89e7dd5e3179c18670c85b0dda36a369816fc39a13d1f49aad0107fe2dcbb",
+    "verify.py": "094fab9efc8ce362007f4da9e00beee1867d8503e073eab4a622199bcd3d8ae9"
+  }
+}
diff --git a/research/e8-r740-idle-hosting/NOTICE.md b/research/e8-r740-idle-hosting/NOTICE.md
new file mode 100644
index 0000000000..64ffcc9af8
--- /dev/null
+++ b/research/e8-r740-idle-hosting/NOTICE.md
@@ -0,0 +1,20 @@
+R740 composition and exact integration: Rohan Arun with substantial OpenAI Codex assistance. Hosting mechanism, generators and audit from PR442 (Claude-assisted), preserved below. R740 producer/kernel/retiming attribution is retained in the pinned parent package, including PR436, PR440, PR441 and earlier contributors.
+
+# Notice
+
+This package adds idle-axis hosting on top of the following work. Their packages are used unchanged and run fresh by
+`verify.py`; their notices remain in their own directories.
+
+- #434, Rohan Arun with OpenAI Codex: early resets and the shared-donor kernel. This is the parent composition and its
+  verifier.
+- #433, icekylinx with Codex: split centres (complex supplier) and source-centre bit composition, together with their
+  engines and invoices.
+- #435 / #417, chafreaky: the response kernel and mixed-width banks.
+- #426, ai-nanachi: clean-reset reuse.
+- #425 and #386, Zhihao Chen with OpenAI Codex: the mutable-basis complex interface and the compressed nine-stage
+  geometry, routes and banks.
+- #370, Dylan Crow with Anthropic Claude: the Hamming E8 bit producer.
+- Jacob Sussman: the E8 unit and the frame/compiler interfaces.
+
+The hosting construction, its generators, audit and assembly scripts are new here, and were prepared with assistance
+from Claude. They are released under the Apache-2.0 license in `LICENSE`.
diff --git a/research/e8-r740-idle-hosting/PROOF.md b/research/e8-r740-idle-hosting/PROOF.md
new file mode 100644
index 0000000000..ff3eba6770
--- /dev/null
+++ b/research/e8-r740-idle-hosting/PROOF.md
@@ -0,0 +1,109 @@
+# Idle-axis hosting: helper residuals on pending idle coordinates
+
+This package changes only the global nine-stage templates of #434's two suppliers. Both local words are unchanged:
+
+- the complex word is #433's split-centre word, R = 560, m = 73;
+- the bit word is #434's early-reset kernel word, R = 747, m = 64.
+
+So are their local programs, scalar replays, data routes, bridges, terminal exchange and cover correction. What
+changes is where whole dirty-helper residuals live. Many of them move from bank streams onto coordinates of *idle*
+data families that would otherwise be advanced later by an idle child.
+
+## 1. The two inherited facts used
+
+**(a) Dirty invocations act on a helper stream as its residual.** The complete dirty local invocation is block
+diagonal on helpers at its endpoint and admits arbitrary correlated helper values (#425/#433, #386/#434). On the
+physical stream that owns a helper residual of width w, it acts as an exact coordinate factor on w coordinates:
+
+- complex: P_g C_block P_g⁻¹ (PR425-COMPLEX §5, INHERITED-COMPLEX-GEOMETRY);
+- bit: D_P with P the width-w coordinate projector (PR386-BIT-GEOMETRY; mixed widths 8 − entrance rank, #434).
+
+This holds whatever the stream held before. Banks rely on exactly this: eight sequential residuals and a pad tile a
+bank stream.
+
+**(b) An idle child is a product of coordinate factors.** Advancing a data pair from level a to level b applies, on
+every physical data stream (F, g) of that pair, the commuting product of coordinate factors on its pending set S:
+
+- complex: C over S, in the basis U_q ⊕ I used by the inherited idle factorisation;
+- bit: D_{P_V−P_U}, an orthogonal coordinate projector difference.
+
+Factors on disjoint coordinate sets commute and multiply:
+
+- complex: C_{S'}·C_{S∖S'} = C_S;
+- bit: D_{P'}·D_{P−P'} = D_P for P' ≤ P (the parent's identity D_I·D_P = D_{I−P}).
+
+## 2. Hosting lemma
+
+Fix a data family F (replica r, pair j, side, port) and an idle child Γ that advances pair j at recipe position τ.
+Let λ be the position of the last local invocation or bridge that names pair j before τ; idle children do not
+count as touches, since they act on other coordinates or on the other member. Let ι be any local invocation with
+λ < ι < τ. Then:
+
+1. ι is an invocation on another pair, and nothing touches F between ι and τ.
+2. A helper residual of ι, of width w, may be owned by stream (F, d·σ⁻¹) instead of a bank slot. Here d is the
+   invocation's cover class, and σ is a coordinate isometry carrying the local residual block onto a set S' ⊂ S of
+   w pending coordinates. When S' meets the local block of a level −1 advance, σ is composed with U_q ⊕ I.
+3. Γ is replaced by Γ' acting on S ∖ ⋃S' over all hosted residuals of F, which have pairwise disjoint S'.
+
+The complete program's operator is unchanged:
+
+- By (a), ι applies exactly the factor on S' to (F, d·σ⁻¹), for any prior contents.
+- Nothing else acts on F between ι and τ, so this factor may be moved to τ.
+- By (b), the moved factors times Γ' equal Γ.
+
+Distinct slots of one invocation have distinct σ, so distinct physical classes for every d. They are also disjoint
+from the invocation's own data owners, because pair j is not active, and from bank owners, because the families
+differ. Residuals of different invocations on F occupy disjoint coordinates. They are sequential, exactly as the
+parent's banks are co-owned sequentially by different cover classes.
+
+Two further points:
+
+- **Phases.** The stored Z₄ translations after Γ remain valid, because Γ'·∏(hosted factors) = Γ as exact operators.
+  The final X_δ(g) correction still applies to every live family; hosting changes no data endpoint.
+- **Reflection.** The inverse-transpose program reverses chronology and reflects each factor. The window condition
+  (no touch strictly between ι and τ) is symmetric, so hosting commutes with reflection.
+
+## 3. What is checked here
+
+- `bit_hosted.py` and `complex_hosted.py` read #434's freshly regenerated templates and compute windows from each
+  recipe. They apply a frozen integer-programme selection (`SELECTION.json`; `--discover` recomputes it with scipy)
+  and emit new owners, remainder children and banks.
+  - Bit: unhosted residuals keep an exact width-64 tiling with no padding.
+  - Complex: eight per bank plus one paid pad; a final partial bank pays the larger pad.
+- `audit.py` shares no code with the generators. It re-derives every window from the template schedule. For every
+  replica and invocation it checks that:
+  - each helper has exactly one owner;
+  - each hosted slot is inside its child's pending set, disjoint from other slots, outside the active pair, and in
+    window;
+  - every remainder child is exact, and the bank tiling is exact.
+
+  It also recomputes the paid profile and the rank deficit 2496, and rejects nine mutations.
+- `assemble.py` prices both suppliers with the two inherited rational moment engines and recomputes both finite
+  invoices with the hosted stock. Route charging is conservative: two extra route factors per helper selector, and
+  the parent's larger complex per-vertex bill is kept. It then runs #434's strict outer assembly: six bootstrap
+  levels and 47 inequalities. The next grid point and the zero-η, zero-β and unit-β controls are rejected.
+
+## 4. Result
+
+| | live stock | max child | hosted residuals | certified saving |
+| --- | ---: | ---: | ---: | --- |
+| bit | 14,259 → 9,457 | 42 → 8 | 39,568 of 53,784 | c = 1239085165241180038597/10²⁴ |
+| complex | 12,720 → 8,400 | 48 → 8 | 34,560 of 40,320 | b = 1267453159029119/10¹⁸ |
+
+κ = 618775866623647/(5·10¹⁷) ≈ 1.237551733247294·10⁻³, bit-bound, +9.218% over #434.
+
+## 5. Scope
+
+This is a written finite extension of the inherited correlated dirty-bank and compressed-window interfaces. The
+streams that own residuals now include data streams during idle windows. It is the principal new review point.
+
+All other interfaces remain inherited assumptions: the all-size compiler, restored-work, tape/common-grid, precision
+and analytic interfaces.
+
+No Lean proof and no unconditional integer-multiplication theorem is claimed. The global operator identity is argued
+from (a) and (b) and checked combinatorially. It is not replayed numerically on the 2⁷³- and 2⁶⁴-point address
+spaces; neither parent does that either.
+
+## R740 composition and additional scope
+
+The above argument is inherited from PR442 and remains an explicit additional hosting assumption. Here the bit local word has R740 and matches PR441 after two joint B-frame sweeps. The assignment is regenerated for its actual residual-width census, rather than transferred by helper index. Parent residual isometries remain checked, and the finite selector invoice retains the parent extra-helper-route bound of 144 in addition to the two hosting factors. All host windows, owners, disjoint intervals, remainders and bank coverage are independently rechecked. Original PR442 numerical values above describe its historical R747 construction; EXPECTED.json and CERTIFICATE.json describe this R740 composition.
diff --git a/research/e8-r740-idle-hosting/README.md b/research/e8-r740-idle-hosting/README.md
new file mode 100644
index 0000000000..292d2e93a3
--- /dev/null
+++ b/research/e8-r740-idle-hosting/README.md
@@ -0,0 +1,9 @@
+# R740 joint retiming with idle-data hosting
+
+Conditional kappa = 0.001245293130733870. Compose the fully reconstructed R740 word (the same final word as PR441) with PR442's idle-data hosting construction. The bit side has 9,376 live and 9,385 physical families, with 39,712 hosted residuals; the complex side remains PR442's 8,400 live families. Both rank deficits are 2,496.
+
+This uses the additional hosting extension stated in PR442's PROOF.md. Its global operator argument is inherited as an additional mathematical assumption; finite placement checks do not independently prove that extension. All earlier all-size compiler, dirty-bank, restored-work, tape/common-grid, precision and analytic obligations remain.
+
+Run `python -B research/e8-r740-idle-hosting/verify.py /absolute/new/output`. Standard library only for replay. The wrapper first freshly rebuilds the R740 producer, kernel, both joint retiming sweeps and every selected complex phase. It then regenerates the frozen hosting assignment, independently audits the windows, owners, remainders and full banks, and recomputes both moments, invoices and strict assembly. Discovery used scipy; replay uses frozen exact integers without scipy.
+
+Full uninterrupted Python 3.11.15 and 3.14.8 wrappers PASS at commit `5702ed7fc47bc43333da0ccbcc013791c21aaa08`. Both freshly replay the final two-sweep parent and produce identical hashes for all five top-level logs. Receipts, logs and the exact tested manifest are in `local-evidence/`. GitHub CI remains pending. Executable code and witnesses are unchanged by this evidence publication. Exact moment-cost optimization and more general complete-bank constraints found no additional gain; their negative results are retained.
diff --git a/research/e8-r740-idle-hosting/SELECTION.json b/research/e8-r740-idle-hosting/SELECTION.json
new file mode 100644
index 0000000000..41918cc490
--- /dev/null
+++ b/research/e8-r740-idle-hosting/SELECTION.json
@@ -0,0 +1,553 @@
+{
+ "bit": {
+  "patterns": [
+   [
+    0,
+    [
+     7,
+     7
+    ],
+    104
+   ],
+   [
+    0,
+    [
+     8
+    ],
+    136
+   ],
+   [
+    1,
+    [],
+    136
+   ],
+   [
+    1,
+    [
+     7
+    ],
+    104
+   ],
+   [
+    2,
+    [
+     7,
+     7,
+     7,
+     7
+    ],
+    26
+   ],
+   [
+    2,
+    [
+     8,
+     8,
+     8
+    ],
+    182
+   ],
+   [
+    2,
+    [
+     8,
+     8,
+     8,
+     4
+    ],
+    32
+   ],
+   [
+    3,
+    [],
+    128
+   ],
+   [
+    3,
+    [
+     4
+    ],
+    8
+   ],
+   [
+    3,
+    [
+     7
+    ],
+    104
+   ],
+   [
+    4,
+    [
+     8,
+     8,
+     8,
+     8,
+     8
+    ],
+    240
+   ],
+   [
+    5,
+    [],
+    136
+   ],
+   [
+    5,
+    [
+     7
+    ],
+    104
+   ],
+   [
+    6,
+    [
+     8,
+     8,
+     8,
+     8,
+     8
+    ],
+    240
+   ],
+   [
+    7,
+    [
+     7,
+     7,
+     7,
+     7
+    ],
+    26
+   ],
+   [
+    7,
+    [
+     8,
+     8,
+     8
+    ],
+    182
+   ],
+   [
+    7,
+    [
+     8,
+     8,
+     8,
+     4
+    ],
+    32
+   ],
+   [
+    8,
+    [
+     7,
+     7
+    ],
+    104
+   ],
+   [
+    8,
+    [
+     8
+    ],
+    136
+   ]
+  ],
+  "proxy_saving": 23471.92403393749,
+  "stages": [
+   [
+    0,
+    7,
+    0,
+    104
+   ],
+   [
+    0,
+    7,
+    1,
+    104
+   ],
+   [
+    0,
+    8,
+    1,
+    136
+   ],
+   [
+    1,
+    7,
+    2,
+    104
+   ],
+   [
+    2,
+    4,
+    0,
+    8
+   ],
+   [
+    2,
+    4,
+    1,
+    8
+   ],
+   [
+    2,
+    4,
+    2,
+    8
+   ],
+   [
+    2,
+    4,
+    3,
+    8
+   ],
+   [
+    2,
+    7,
+    3,
+    104
+   ],
+   [
+    2,
+    8,
+    1,
+    14
+   ],
+   [
+    2,
+    8,
+    2,
+    628
+   ],
+   [
+    3,
+    4,
+    4,
+    8
+   ],
+   [
+    3,
+    7,
+    4,
+    104
+   ],
+   [
+    4,
+    8,
+    3,
+    628
+   ],
+   [
+    4,
+    8,
+    5,
+    572
+   ],
+   [
+    5,
+    7,
+    6,
+    104
+   ],
+   [
+    6,
+    8,
+    4,
+    572
+   ],
+   [
+    6,
+    8,
+    6,
+    628
+   ],
+   [
+    7,
+    4,
+    5,
+    8
+   ],
+   [
+    7,
+    4,
+    6,
+    8
+   ],
+   [
+    7,
+    4,
+    7,
+    8
+   ],
+   [
+    7,
+    4,
+    8,
+    8
+   ],
+   [
+    7,
+    7,
+    5,
+    104
+   ],
+   [
+    7,
+    8,
+    7,
+    492
+   ],
+   [
+    7,
+    8,
+    8,
+    150
+   ],
+   [
+    8,
+    7,
+    7,
+    104
+   ],
+   [
+    8,
+    7,
+    8,
+    104
+   ],
+   [
+    8,
+    8,
+    7,
+    136
+   ]
+  ]
+ },
+ "complex": {
+  "patterns": [
+   [
+    0,
+    [
+     9
+    ],
+    120
+   ],
+   [
+    2,
+    [
+     9
+    ],
+    120
+   ],
+   [
+    4,
+    [
+     9,
+     9,
+     9
+    ],
+    120
+   ],
+   [
+    6,
+    [
+     9,
+     9,
+     9
+    ],
+    120
+   ],
+   [
+    8,
+    [
+     9,
+     9,
+     9,
+     9,
+     9
+    ],
+    120
+   ],
+   [
+    10,
+    [
+     9,
+     9,
+     9,
+     9,
+     9
+    ],
+    120
+   ],
+   [
+    12,
+    [
+     9,
+     9,
+     9,
+     9,
+     9
+    ],
+    120
+   ],
+   [
+    13,
+    [
+     9,
+     9,
+     9,
+     9,
+     9
+    ],
+    120
+   ],
+   [
+    14,
+    [
+     9,
+     9,
+     9
+    ],
+    120
+   ],
+   [
+    15,
+    [
+     9,
+     9,
+     9
+    ],
+    120
+   ],
+   [
+    16,
+    [
+     9
+    ],
+    120
+   ],
+   [
+    17,
+    [
+     9
+    ],
+    120
+   ]
+  ],
+  "proxy_saving": 17393.16581129622,
+  "stages": [
+   [
+    0,
+    9,
+    0,
+    120
+   ],
+   [
+    2,
+    9,
+    0,
+    80
+   ],
+   [
+    2,
+    9,
+    1,
+    40
+   ],
+   [
+    4,
+    9,
+    3,
+    360
+   ],
+   [
+    6,
+    9,
+    0,
+    360
+   ],
+   [
+    8,
+    9,
+    1,
+    520
+   ],
+   [
+    8,
+    9,
+    5,
+    80
+   ],
+   [
+    10,
+    9,
+    2,
+    560
+   ],
+   [
+    10,
+    9,
+    3,
+    40
+   ],
+   [
+    12,
+    9,
+    4,
+    560
+   ],
+   [
+    12,
+    9,
+    7,
+    40
+   ],
+   [
+    13,
+    9,
+    5,
+    360
+   ],
+   [
+    13,
+    9,
+    6,
+    200
+   ],
+   [
+    13,
+    9,
+    7,
+    40
+   ],
+   [
+    14,
+    9,
+    6,
+    360
+   ],
+   [
+    15,
+    9,
+    7,
+    360
+   ],
+   [
+    16,
+    9,
+    8,
+    120
+   ],
+   [
+    17,
+    9,
+    7,
+    120
+   ]
+  ]
+ }
+}
diff --git a/research/e8-r740-idle-hosting/SOURCE442-PINS.json b/research/e8-r740-idle-hosting/SOURCE442-PINS.json
new file mode 100644
index 0000000000..d47fc03335
--- /dev/null
+++ b/research/e8-r740-idle-hosting/SOURCE442-PINS.json
@@ -0,0 +1,70 @@
+{
+  "head": "4e16d001d505d4f21dd2bcfc44591f9be4c279bd",
+  "files": [
+    {
+      "path": "research/idle-axis-hosting/EXPECTED.json",
+      "git_blob": "1b0811df29bc2eabdabb51219e9b2382da9a48f6",
+      "sha256": "ed83c1bf1ca2d01eaab5149a34520806a07ef375dfa9e3ed69d123f4be4c9960"
+    },
+    {
+      "path": "research/idle-axis-hosting/LICENSE",
+      "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64",
+      "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4"
+    },
+    {
+      "path": "research/idle-axis-hosting/MANIFEST.json",
+      "git_blob": "542ee2f988de429e8fd94c9940a17c35ec65b16d",
+      "sha256": "f68b82604363329618529313ac9c3796dc1e88b176eaee4a7b0dec9be428e987"
+    },
+    {
+      "path": "research/idle-axis-hosting/NOTICE.md",
+      "git_blob": "391e865e06f77efa9ec0aa3ee9c048673b1f24ab",
+      "sha256": "027a868628d0408602dbeae688b031ed9b4abfd6e5401f6e8106a3eb25ebc4ca"
+    },
+    {
+      "path": "research/idle-axis-hosting/PROOF.md",
+      "git_blob": "4468a00349b4f68dce103e785a8392099435e1d6",
+      "sha256": "cfe34bf0b64259661312dae22c3a23adc5bf6f6326951eee5c1488ccfc347542"
+    },
+    {
+      "path": "research/idle-axis-hosting/README.md",
+      "git_blob": "9d9b80cc3bff337db6f3f0c7c70a57efe8532d82",
+      "sha256": "1151f74cad54ac4937282b7a8b5d1108ed4ce35944ef9b7bb7d17abfce1fe4a0"
+    },
+    {
+      "path": "research/idle-axis-hosting/SELECTION.json",
+      "git_blob": "e3303cd97d132e66145d2fb7e957fd6e5808dd80",
+      "sha256": "315d54be472842707cce879618be477d8b897050e873bc136d114eec6a232f97"
+    },
+    {
+      "path": "research/idle-axis-hosting/assemble.py",
+      "git_blob": "f07a59864346dc622aa5c8d3619473c53ba529d8",
+      "sha256": "f9a2e6a42aadcf971702a5a867760a092566ed03356f4f34387d38f4093ad1a6"
+    },
+    {
+      "path": "research/idle-axis-hosting/audit.py",
+      "git_blob": "bd40b9b7914deeced02d5364162060d8130ab08e",
+      "sha256": "38594423a401110bd430b734037c6ecba422ee6a94d71709984e0afa9cd1edf8"
+    },
+    {
+      "path": "research/idle-axis-hosting/bit_hosted.py",
+      "git_blob": "e2f015dbb78a95c121e187b3c20e0f8d59b60586",
+      "sha256": "6dfbf26213e8adf87563b3575cfb722bd07ecd65627f056b3293411dd3d89a61"
+    },
+    {
+      "path": "research/idle-axis-hosting/complex_hosted.py",
+      "git_blob": "56e15c15aeebf571e60ab2c89e55e4624ecac2d3",
+      "sha256": "829c5c4f4bdfccedadd31505f1f0a394f7a208d1446b7bbf9cc92d3aa1530c0c"
+    },
+    {
+      "path": "research/idle-axis-hosting/hosting_core.py",
+      "git_blob": "68b536daa9e6546c0aa046934bf840aaa3c3fde3",
+      "sha256": "d8b90cd5d152df3c7c351230863d9e61816ad5e1f21d69bea1a86a5daad559a3"
+    },
+    {
+      "path": "research/idle-axis-hosting/verify.py",
+      "git_blob": "0aa6cefd0237146967f8e26c540c99e3afca2ffc",
+      "sha256": "737a974d79fdd232b6c4b9e059c56835079971447342ed7ca3b82a614e30cb53"
+    }
+  ]
+}
diff --git a/research/e8-r740-idle-hosting/VALIDATION.json b/research/e8-r740-idle-hosting/VALIDATION.json
new file mode 100644
index 0000000000..5fed6bd833
--- /dev/null
+++ b/research/e8-r740-idle-hosting/VALIDATION.json
@@ -0,0 +1,14 @@
+{
+  "status": "FULL_LOCAL_PYTHON_311_AND_314_PASSED_CI_PENDING",
+  "kappa": "0.001245293130733870",
+  "source_pr442": "4e16d001d505d4f21dd2bcfc44591f9be4c279bd",
+  "new_assumption": "PR442 idle-data hosting extension of the dirty-bank and compressed-window interface is inherited, not independently discharged by combinatorial audits.",
+  "retained_extra_route_factor_bound": 144,
+  "tested_code_commit": "5702ed7fc47bc43333da0ccbcc013791c21aaa08",
+  "tested_manifest_sha256": "aac568b890323ced6d856c0477a4761b6f106a5051ee0811ffd1d97d7ca09ca6",
+  "full_receipts": {
+    "311": "local-evidence/full311/RECEIPT.json",
+    "314": "local-evidence/full314/RECEIPT.json"
+  },
+  "publication_change": "Only documentation and evidence changed after the full runs; executable code, frozen witnesses and parent manifest remain byte-identical."
+}
diff --git a/research/e8-r740-idle-hosting/assemble.py b/research/e8-r740-idle-hosting/assemble.py
new file mode 100644
index 0000000000..77e6e4a0ca
--- /dev/null
+++ b/research/e8-r740-idle-hosting/assemble.py
@@ -0,0 +1,82 @@
+"""Two exact moments for both hosted suppliers, fresh finite invoices with the hosted stock, and the strict outer
+assembly of #434 (six bootstrap levels, 47 inequalities, next-grid and parameter controls).
+usage: assemble.py PARENT_CHANGED_DIR BIT_DIR COMPLEX_DIR AUDIT.json OUT.json"""
+import gzip, hashlib, importlib.util, json, math, sys
+from fractions import Fraction as Q
+from pathlib import Path
+par, bd, cd, ap, outp = map(Path, sys.argv[1:6])
+def load(name):
+    sp = importlib.util.spec_from_file_location('hosted_' + name, par / 'work/pr361/code/engines' / (name + '.py'))
+    mod = importlib.util.module_from_spec(sp); sp.loader.exec_module(mod); return mod
+M, Other, Outer = load('moment'), load('base_two_moment'), load('outer')
+audit = json.loads(ap.read_text()); bg = json.loads((bd / 'GLOBAL.json').read_text()); ch = json.loads((cd / 'HOSTED.json').read_text())
+assert audit['bit_template_sha256'] == bg['template_sha256'] and audit['complex_template_sha256'] == ch['template_sha256']
+# ---------------- bit: two moments and the parent's invoice formulas with the hosted stock
+P = {int(r): n for r, n in audit['bit_profile'].items()}; m, W = 64, audit['bit_live']; E = sum(P.values())
+geo = json.loads((par / 'bit426-source-centres/global/GEOMETRY.json').read_text())
+pg = json.loads((par / 'bit426-source-centres/global/GLOBAL.json').read_text())
+T, L, R, V, K = 8, 9, pg['R'], 120, 4
+mass = sum(r * z for r, z in P.items()); assert m * W - mass == 2496
+physical = W + 9; d = m * m; N = 2 * m
+unit = L * T * pg['local_additions'] + pg['bridge_additions']
+J = 8 * T * L * (2 * V + R) + 8 * (2 * K * V * T) + 2 * L * T * R + 2 * pg['copy_erase_episodes']   # every helper route charged (bank or hosted)
+high = 16 * (d + 1) ** 2; good = 8 * m * m + 8; compiler = 128 * N ** 3
+selectors = 2 * L * T * ((W - 1) + R * m * (geo['max_route_factors'] + pg.get('extra_helper_route_factor_bound', 0) + 2 + (m - 1) + m))   # +2: hosted route may add a slot permutation and U_q
+prefix = int(pg['global_prefix_bound']); charged_prefix = 64 * ((prefix.bit_length() + 63) // 64)
+coefficient = unit + J * high + J * physical + E * (good + compiler) + 16 * m ** 3 + pg['copy_erase_episodes'] + selectors + prefix + 1
+two = (coefficient + 1) ** 2 * (E + 1) ** 2; charged_two = 64 * ((two.bit_length() + 63) // 64)
+assert two < 1 << charged_two and 2 * max(P) ** 2 < m * m
+row = 2 * (m * m + 1) + 9909 + 252; assert row == 18355 < 20161
+root = M.certify(P, m, W, True); c = Q(root['lower']); chi = Q(root['upper'])
+fb = 32 * m * m * E
+lo, hi = Other.moment(m, W, list(P.items()), c); bl, bh = Other.moment(m, W, [(1, fb)], c); assert hi + bh / 10 ** 16 < 1
+lo2, hi2 = Other.moment(m, W, list(P.items()), chi); bl2, bh2 = Other.moment(m, W, [(1, fb)], chi); assert lo2 + bl2 / 10 ** 16 > 1
+# ---------------- complex: two moments and the parent's invoice with the hosted stock
+PC = {int(r): n for r, n in audit['complex_profile'].items()}; mc, WC = 73, audit['complex_live']; EC = sum(PC.values())
+massc = sum(r * z for r, z in PC.items()); assert mc * WC - massc == 2496
+rc = M.certify(PC, mc, WC, True); b = Q(int(Q(rc['lower']) * 10 ** 18), 10 ** 18)
+fbc = 32 * mc * mc * EC
+l3, h3 = Other.moment(mc, WC, list(PC.items()), b); b3, bh3 = Other.moment(mc, WC, [(1, fbc)], b); assert h3 + bh3 / 10 ** 16 < 1
+integ = json.loads((par / 'split-centres/INTEGRATION.json').read_text()); inv = integ['finite_invoice']
+physc = ch['physical']; Rc = 560; v = 120
+compilerc = 64 * (mc + 1) ** 3
+pervertex = inv['pervertex'] - integ['physical'] * (64 + 1) + physc * (64 + 1) - integ['live'] + WC   # stock-dependent terms re-based
+r_ = mc // 2; group = 2 ** (r_ * r_) * math.prod(2 ** (2 * i) - 1 for i in range(1, r_ + 1)); stock = group * physc
+smass = group * massc; logical = group * max(pervertex, inv['pervertex']) + 64; router = compilerc * (logical + 1) * (stock + 1) ** 2
+GG, EE, C0 = 1 << 30000, 1 << 100000, 1 << 210000; BB = smass + EE
+literal = 2 * GG * stock ** 2 + 8 * smass + 4 * stock + 4 + 32 * mc
+assert logical < 1 << 6050 and router < GG and literal < EE and BB < 1 << 100001 and 32 * mc * BB * BB < C0 and 2 * BB + 18 < C0
+depth = 2; assert mc ** depth > 2 * max(PC) ** depth
+rowc = depth * stock.bit_length() + 9909 + 252; assert rowc < 20161
+# ---------------- outer assembly exactly as #434's combined.py
+eta = beta = Q(1, 10 ** 18); grid = Q(1, 10 ** 18); s = min(c, (1 - beta) * b) - Q(1, 10 ** 24)
+assert 0 < s < c and s < (1 - beta) * b
+chain = [Q(384599, 10 ** 10)]; cutoffs = []
+def ceil(x): return -((-x.numerator) // x.denominator)
+for j in range(6):
+    old = chain[-1]; a = (1 - s) * s + s * old
+    gap = min(s - a, 1 - a - s, 1 - a - s * (1 - old), 1 - s); assert old < a < s < 1 - a and gap > 0
+    cutoff = max(ceil(36 / gap ** 2), ceil(2 * (4 + charged_two) / gap)); assert cutoff * gap ** 2 >= 36 and cutoff * gap >= 2 * (4 + charged_two)
+    cutoffs.append(dict(gap=str(gap), cutoff_log2=str(cutoff))); chain.append(a)
+q = chain[-1] * (1 - 2 * eta); margin = (1 - eta) * q / (1 + q); ticks = margin / grid; k = grid * ((ticks.numerator - 1) // ticks.denominator)
+bridge = {'semantic': {'C0': {'base': 2, 'exponent': 210000}, 'strict_literal_gap': 1}, 'rows': {'degree_gap': Q(10 ** 6) - Q(51 * 20161, 25)}}
+a = Outer.assembly(chain[-1], b, bridge, k, eta=eta, beta=beta)
+assert len(a['strict_constraints']) == 47 and all(x > 0 for x in a['strict_constraints'].values())
+controls = []
+for name, kk, ee, bb in [('next_grid', k + grid, eta, beta), ('zero_eta', k, Q(0), beta), ('zero_beta', k, eta, Q(0)), ('unit_beta', k, eta, Q(1))]:
+    try: Outer.assembly(chain[-1], b, bridge, kk, eta=ee, beta=bb)
+    except AssertionError: controls.append(name)
+    else: raise AssertionError(name)
+parent_k = Q(566550276142217, 500000000000000000)
+res = dict(status='PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY', kappa=str(k), kappa_decimal=format(float(k), '.18f'),
+           bit_lower=str(c), complex_lower=str(b), binding_component='bit' if c < (1 - beta) * b else 'complex',
+           gain_over_pr434_percent=float(100 * (k / parent_k - 1)),
+           bit=dict(live=W, physical=physical, maxchild=max(P), rank_mass=mass, hosted_residuals=audit['bit_hosted_residuals'],
+                    prefix_bits=prefix.bit_length(), charged_prefix_bits=charged_prefix, coefficient_bits=coefficient.bit_length(),
+                    two_level_coefficient_bits=two.bit_length(), charged_two_level_coefficient_bits=charged_two, row_coefficient=row),
+           complex=dict(live=WC, physical=physc, maxchild=max(PC), rank_mass=massc, hosted_residuals=audit['complex_hosted_residuals'],
+                        physical_stock_bits=stock.bit_length(), router_bits=router.bit_length(), literal_bits=literal.bit_length(), row_coefficient=rowc),
+           strict_outer_constraints={n: str(x) for n, x in a['strict_constraints'].items()}, outer_controls=controls, bootstrap=cutoffs,
+           bit_template_sha256=bg['template_sha256'], complex_template_sha256=ch['template_sha256'])
+outp.write_text(json.dumps(res, indent=2) + '\n')
+print(res['status'], res['kappa_decimal'], 'binding', res['binding_component'], 'gain over #434 %.4f%%' % res['gain_over_pr434_percent'])
diff --git a/research/e8-r740-idle-hosting/audit.py b/research/e8-r740-idle-hosting/audit.py
new file mode 100644
index 0000000000..1932612d9b
--- /dev/null
+++ b/research/e8-r740-idle-hosting/audit.py
@@ -0,0 +1,159 @@
+"""Independent audit of the two idle-axis-hosted templates (no code shared with the generators).
+Re-derives hosting windows from each template's own schedule and checks, for every replica and invocation:
+  * every helper residual has exactly one owner: a bank slot or a hosted slot;
+  * a hosted slot lies on the data family of the idle child it names, inside that child's pending coordinates,
+    disjoint from every other hosted slot of the family, and its invocation lies strictly between the last
+    local invocation or bridge naming that pair and the child (the window);
+  * the child keeps exactly the remaining coordinates; banks are tiled exactly (bit) or padded (complex);
+  * the emitted paid profile, live stock and rank deficit 2496 are recomputed from scratch.
+Mutation controls must be rejected.  usage: audit.py PARENT_CHANGED_DIR BIT_DIR COMPLEX_DIR OUT.json"""
+import copy, gzip, hashlib, json, sys
+from collections import Counter, defaultdict
+from pathlib import Path
+V, K, T, L = 120, 4, 8, 9
+DATA = 2 * K * V * T
+
+def wins(events):
+    """events: ('local', stage, pair) | ('bridge', a, b) | ('idle', idx, pair); window = local stages after the last
+    local/bridge touch of the pair and before the child"""
+    last = {}; seen = []; w = {}
+    for pos, e in enumerate(events):
+        if e[0] == 'local': seen.append((pos, e[1], e[2])); last[e[2]] = pos
+        elif e[0] == 'bridge': last[e[1]] = pos; last[e[2]] = pos
+        else:
+            lo = last.get(e[2], -1); w[e[1]] = {s for q, s, p in seen if lo < q < pos and p != e[2]}
+    return w
+
+def audit_bit(t, parent_t, widths):
+    assert t['local_programs'] == parent_t['local_programs'] and len(t['calls']) == 72
+    ev = []; rank = {}; pair = {}
+    for e in t['schedule']:
+        if e['kind'] == 'local_cover_sweep': ev.append(('local', e['stage'], e['pair']))
+        elif e['kind'] == 'bridge': ev.append(('bridge', e['dst'], e['src']))
+        elif e['kind'] == 'idle':
+            ev.append(('idle', e['idx'], e['pair'])); rank[e['idx']] = e['rank']; pair[e['idx']] = e['pair']
+    W = wins(ev); hs = t['hosting']
+    used = defaultdict(set); hosted = {}
+    for i, cp, off, w, s, h in hs['slots']:
+        assert s in W[i], ('window', i, s)
+        assert w == widths[h] and 0 <= off and off + w <= rank[i]
+        cells = set(range(off, off + w)); assert not cells & used[i, cp], ('overlap', i, cp); used[i, cp] |= cells
+        assert (s, h) not in hosted; hosted[s, h] = (i, cp, off, w)
+    rem = {}
+    for i in rank:
+        if rank[i] == 0: continue
+        for cp in range(2 * V): rem[i, cp] = rank[i] - len(used[i, cp])
+        rr = Counter(rem[i, cp] for cp in range(2 * V))
+        if str(i) in hs['remainders']: assert {int(k): v for k, v in hs['remainders'][str(i)].items()} == dict(rr)
+        else: assert rr == Counter({rank[i]: 2 * V})
+    occ = defaultdict(set); LIVE = t['live']; bank_lo = {}
+    for c in t['calls']:
+        s, rep, p = c['stage'], c['replica'], c['pair']; own = c['owners']; assert len(own) == 2 * V + len(widths)
+        assert own[:2 * V] == next(q for q in parent_t['calls'] if (q['stage'], q['replica']) == (s, rep))['owners'][:2 * V]
+        for h, (f, r) in enumerate(own[2 * V:]):
+            if (s, h) in hosted:
+                i, cp, off, w = hosted[s, h]; side, port = divmod(cp, V)
+                assert r == ['hosted', i, off, w] and f == rep * 960 + (2 * pair[i] + side) * V + port
+                assert pair[i] != p
+                occ['h', f, i, s, rep, h] = True
+            else:
+                assert r[0] == 'bank' and r[2] == widths[h] and DATA <= f < LIVE
+                cells = set(range(r[1], r[1] + r[2])); assert cells <= set(range(64)) and not cells & occ[f]; occ[f] |= cells
+                bank_lo[f] = s
+    banks = [f for f in occ if isinstance(f, int)]
+    assert sorted(banks) == list(range(DATA, LIVE)) and all(occ[f] == set(range(64)) for f in banks)
+    paid = Counter()
+    for c in t['calls']:
+        for z in t['local_programs'][c['orientation']]:
+            if z[0] == 0 and z[4]: paid[z[4]] += 1
+            if z[0] == 2: paid[z[5]] += 1
+    for (i, cp), r_ in rem.items():
+        if r_: paid[r_] += T
+    mass = sum(r * n for r, n in paid.items()); assert 64 * LIVE - mass == 2496
+    assert 64 * 64 > 2 * max(paid) ** 2
+    return paid, sum(1 for _ in hosted) * T
+
+def audit_complex(t, parent_t, local_checks):
+    R = 560; m = 73
+    assert t['local_programs'] == parent_t['local_programs'] and len(t['calls']) == 72
+    prank = {}
+    for it in parent_t['idle_children']: prank.setdefault(it['child'], it['rank'])
+    stage_pair = {e['stage']: e['pair'] for e in t['recipe'] if e['kind'] == 'local'}
+    ev = []; side = {}; pairs = {}
+    for e in t['execution_schedule']:
+        if e['kind'] == 'local_cover_sweep': ev.append(('local', e['stage'], stage_pair[e['stage']]))
+        elif e['kind'] == 'bridge': ev.append(('bridge', e['dst'], e['src']))
+        elif e['kind'] == 'idle_cover_sweep':
+            for sd, ch in enumerate(e['child_indices']):
+                if ch in prank: ev.append(('idle', ch, e['pair'])); side[ch] = sd; pairs[ch] = e['pair']
+    W = wins(ev); hs = t['hosting']
+    used = defaultdict(set); hosted = {}
+    for i, port, off, w, s, h in hs['slots']:
+        assert w == 9 and s in W[i] and 0 <= off and off + 9 <= prank[i]
+        cells = set(range(off, off + 9)); assert not cells & used[i, port]; used[i, port] |= cells
+        assert (s, h) not in hosted; hosted[s, h] = (i, port, off)
+    rem = {}
+    for it in parent_t['idle_children']: rem[it['child'], it['port']] = it['rank'] - len(used[it['child'], it['port']])
+    got = {(it['child'], it['port']): it['rank'] for it in t['idle_children']}
+    assert got == {k: r for k, r in rem.items() if r} and all(it['replicas'] == T for it in t['idle_children'])
+    LIVE = t['live']; occ = defaultdict(set)
+    for c in t['calls']:
+        s, rep, p = c['stage'], c['replica'], c['pair']; own = c['owners']; assert len(own) == 2 * V + R
+        assert own[:2 * V] == next(q for q in parent_t['calls'] if (q['stage'], q['replica']) == (s, rep))['owners'][:2 * V]
+        for h, (f, r) in enumerate(own[2 * V:]):
+            if (s, h) in hosted:
+                i, port, off = hosted[s, h]
+                assert r == [3, i, off] and f == rep * 960 + (2 * pairs[i] + side[i]) * V + port and pairs[i] != p
+            else:
+                assert r[0] == 2 and 0 <= r[1] < 8 and DATA <= f < LIVE and r[1] not in occ[f]; occ[f].add(r[1])
+    banks = sorted(occ); assert banks == list(range(DATA, LIVE))
+    paid = Counter()
+    for c in t['calls']:
+        for r_, z in local_checks[c['orientation']]['paid_profile'].items(): paid[int(r_)] += z
+    for (ch, port), r_ in rem.items():
+        if r_: paid[r_] += T
+    for f in banks: paid[m - 9 * len(occ[f])] += 1
+    mass = sum(r * n for r, n in paid.items()); assert m * LIVE - mass == 2496
+    assert m * m > 2 * max(paid) ** 2
+    return paid, len(hosted) * T
+
+def main():
+    par, bd, cd, outp = map(Path, sys.argv[1:5])
+    pbt = json.loads(gzip.decompress((par / 'bit426-source-centres/global/GLOBAL-TEMPLATE.json.gz').read_bytes()))
+    bt = json.loads(gzip.decompress((bd / 'GLOBAL-TEMPLATE.json.gz').read_bytes()))
+    bg = json.loads((bd / 'GLOBAL.json').read_text())
+    assert hashlib.sha256(gzip.decompress((bd / 'GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest() == bg['template_sha256']
+    st = json.loads((par / 'bit426-source-centres/records/249-states.json').read_text())
+    fs = json.loads((par / 'bit426-source-centres/records/frames.json').read_text())['frames']
+    widths = [8 - fs[str(st['initial'][str(i)])]['dim'] for i in range(240, st['n'])]
+    pct = json.loads(gzip.decompress((par / 'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes()))
+    ct = json.loads(gzip.decompress((cd / 'GLOBAL-TEMPLATE.json.gz').read_bytes()))
+    ch = json.loads((cd / 'HOSTED.json').read_text())
+    assert hashlib.sha256(gzip.decompress((cd / 'GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest() == ch['template_sha256']
+    lc = json.loads((par / 'split-centres/LOCAL-CHECKS.json').read_text())
+    bp, bh = audit_bit(bt, pbt, widths); assert bp == Counter({int(k): v for k, v in bg['profile'].items()})
+    cp, chh = audit_complex(ct, pct, lc); assert cp == Counter({int(k): v for k, v in ch['global_profile'].items()})
+    controls = []
+    def reject(name, fn, which):
+        q = copy.deepcopy(bt if which == 'bit' else ct); fn(q)
+        try:
+            (audit_bit(q, pbt, widths) if which == 'bit' else audit_complex(q, pct, lc))
+        except (AssertionError, KeyError, IndexError, StopIteration): controls.append(name)
+        else: raise AssertionError('mutation accepted: ' + name)
+    def outside(q):           # move one hosted residual to a stage outside its window
+        sl = q['hosting']['slots'][0]; i = sl[0]; s_bad = next(s for s in range(9) if s not in q['hosting']['windows'][str(i)][2]); sl[4] = s_bad
+    reject('bit: hosted residual outside its window', outside, 'bit')
+    reject('bit: overlapping hosted coordinates', lambda q: q['hosting']['slots'][1].__setitem__(2, q['hosting']['slots'][0][2]) if q['hosting']['slots'][1][:2] == q['hosting']['slots'][0][:2] else q['hosting']['slots'][1].__setitem__(1, q['hosting']['slots'][0][1]) or q['hosting']['slots'][1].__setitem__(2, q['hosting']['slots'][0][2]), 'bit')
+    reject('bit: understated live stock', lambda q: q.__setitem__('live', q['live'] - 1), 'bit')
+    reject('bit: hosted owner on the active pair', lambda q: q['calls'][0]['owners'].__setitem__(240 + next(h for h in range(len(widths)) if q['calls'][0]['owners'][240 + h][1][0] == 'hosted'), [0, ['hosted', 0, 0, 8]]), 'bit')
+    reject('bit: missing remainder child', lambda q: q['hosting']['slots'].pop(), 'bit')
+    reject('complex: hosted residual outside its window', lambda q: q['hosting']['slots'][0].__setitem__(4, next(s for s in range(9) if s not in q['hosting']['windows'][str(q['hosting']['slots'][0][0])][2])), 'complex')
+    reject('complex: remainder child understated', lambda q: q['idle_children'][0].__setitem__('rank', q['idle_children'][0]['rank'] - 1), 'complex')
+    reject('complex: dropped bank', lambda q: q.__setitem__('live', q['live'] - 1), 'complex')
+    reject('complex: duplicated hosted residual', lambda q: q['hosting']['slots'].append(list(q['hosting']['slots'][0])), 'complex')
+    res = dict(status='PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT', bit_template_sha256=bg['template_sha256'], complex_template_sha256=ch['template_sha256'],
+               bit_profile={str(k): v for k, v in sorted(bp.items())}, complex_profile={str(k): v for k, v in sorted(cp.items())},
+               bit_live=bt['live'], complex_live=ct['live'], bit_hosted_residuals=bh, complex_hosted_residuals=chh,
+               bit_maxchild=max(bp), complex_maxchild=max(cp), mutations_rejected=controls)
+    outp.write_text(json.dumps(res, indent=2) + '\n'); print(json.dumps({k: v for k, v in res.items() if 'profile' not in k}))
+if __name__ == '__main__': main()
diff --git a/research/e8-r740-idle-hosting/bit_hosted.py b/research/e8-r740-idle-hosting/bit_hosted.py
new file mode 100644
index 0000000000..19225d9c74
--- /dev/null
+++ b/research/e8-r740-idle-hosting/bit_hosted.py
@@ -0,0 +1,116 @@
+"""Idle-axis hosting for #434's compressed nine-stage bit template (m=64).
+Reads the emitted parent template, keeps every local program and scalar replay unchanged, and moves whole helper
+residuals from banks onto pending idle-advance coordinates of untouched data families.  Emits a new template,
+GLOBAL.json with the new live stock and paid profile.  usage: bit_hosted.py PARENT_GLOBAL_DIR LOCAL_CHECK_DIR OUT"""
+import gzip, hashlib, importlib.util, json, sys, time
+from collections import Counter
+from pathlib import Path
+HERE = Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE))
+import hosting_core as HC
+H, V, L, K, T, M = 8, 120, 9, 4, 8, 64
+DATA = 2 * K * V * T
+DISCOVER = False
+sha = lambda p: hashlib.sha256(Path(p).read_bytes()).hexdigest()
+def main(parent, local, out):
+    t0 = time.monotonic(); out.mkdir(parents=True, exist_ok=False)
+    blob = gzip.decompress((parent / 'GLOBAL-TEMPLATE.json.gz').read_bytes()); t = json.loads(blob)
+    g = json.loads((parent / 'GLOBAL.json').read_text())
+    assert hashlib.sha256(blob).hexdigest() == g['template_sha256']
+    st = json.loads((local / 'records/249-states.json').read_text()); R = st['n'] - 2 * V; assert R == g['R']
+    fs = json.loads((local / 'records/frames.json').read_text())['frames']; dims = {int(f): z['dim'] for f, z in fs.items()}
+    width = [H - dims[st['initial'][str(i)]] for i in range(2 * V, 2 * V + R)]
+    # schedule with indexed idle children
+    sched = []; idx = 0
+    for e in t['schedule']:
+        if e['kind'] == 'local_cover_sweep': sched.append(dict(kind='local', stage=e['stage'], pair=e['pair']))
+        elif e['kind'] == 'bridge': sched.append(dict(kind='bridge', dst=e['dst'], src=e['src']))
+        elif e['kind'] == 'idle':
+            sched.append(dict(kind='idle', pair=e['pair'], rank=e['rank'], idx=idx)); e['idx'] = idx; idx += 1
+    win = {k: x for k, x in HC.windows(sched).items() if x[1] > 0 and x[2]}
+    avail = Counter()
+    for s in range(L):
+        for w in width: avail[s, w] += 1
+    sel = HERE / 'SELECTION.json'; key = 'bit'
+    if DISCOVER:
+        ys, zs, val = HC.solve(win, 2 * V, dict(avail), M, group={7: 8, 4: 2}); HC.save_selection(sel, key, ys, zs, val)
+    ys, zs, val = HC.load_selection(sel, key)
+    helpers = {s: [(h, width[h]) for h in range(R)] for s in range(L)}
+    slots, rem = HC.expand(win, ys, zs, helpers, 2 * V)
+    hosted = {(s, h): (i, c, off, w) for i, c, off, w, s, h in slots}
+    # remaining helpers -> exact width-64 banks (per stage, same set of helpers in every replica)
+    left = {s: [h for h in range(R) if (s, h) not in hosted] for s in range(L)}
+    nb = {}; place = {}
+    for s in range(L):
+        wl = {h: width[h] for h in left[s]}
+        slotsS = sorted(((wl[h], rep, h) for rep in range(T) for h in left[s]), key=lambda x: (-x[0], x[1], x[2]))
+        by = {}
+        for w_, rep, h in slotsS: by.setdefault(w_, []).append((rep, h))
+        bins = []
+        def take(w_): return by[w_].pop(0)
+        for w_ in sorted(by, reverse=True):
+            if w_ == 8: continue
+            while by.get(w_):
+                cont = []; off = 0
+                if w_ == 7:
+                    for _ in range(8): rep, h = take(7); cont.append((rep, h, off, 7)); off += 7
+                    rep, h = take(8); cont.append((rep, h, off, 8)); off += 8
+                else:
+                    for _ in range(64 // w_): rep, h = take(w_); cont.append((rep, h, off, w_)); off += w_
+                assert off == 64; bins.append(cont)
+        while by.get(8):
+            cont = []; off = 0
+            for _ in range(8): rep, h = take(8); cont.append((rep, h, off, 8)); off += 8
+            bins.append(cont)
+        nb[s] = len(bins)
+        for b, cont in enumerate(bins):
+            for rep, h, off, w_ in cont: place[s, rep, h] = (b, off, w_)
+    base = [DATA]
+    for s in range(L): base.append(base[-1] + nb[s])
+    LIVE = base[-1]
+    # owners
+    for c in t['calls']:
+        s, rep, p = c['stage'], c['replica'], c['pair']; own = c['owners'][:2 * V]
+        for h in range(R):
+            if (s, h) in hosted:
+                i, cp, off, w = hosted[s, h]; pair = win[i][0]; side, port = divmod(cp, V)
+                own.append([rep * 960 + (2 * pair + side) * V + port, ['hosted', i, off, w]])
+            else:
+                b, off, w = place[s, rep, h]; own.append([base[s] + b, ['bank', off, w]])
+        assert len({(f, tuple(r)) for f, r in own}) == 2 * V + R and all(0 <= f < LIVE for f, r in own)
+        c['owners'] = own
+    # profile: local programs unchanged; idle children replaced by remainders
+    paid = Counter()
+    for c in t['calls']:
+        for z in t['local_programs'][c['orientation']]:
+            if z[0] == 0 and z[4]: paid[z[4]] += 1
+            if z[0] == 2: paid[z[5]] += 1
+    remainder = {}
+    for e in t['schedule']:
+        if e['kind'] == 'idle' and e['rank']:
+            i = e['idx']
+            if i in win:
+                rr = Counter(rem[i, cp] for cp in range(2 * V)); remainder[i] = {str(k): v for k, v in sorted(rr.items())}
+                for r_, n in rr.items():
+                    if r_: paid[r_] += n * T
+            else:
+                paid[e['rank']] += 2 * V * T
+    mass = sum(r * n for r, n in paid.items()); assert M * LIVE - mass == 2496, M * LIVE - mass
+    t.update(version='compressed-nine-e8-bit-v1+idle-axis-hosting', live=LIVE,
+             hosting=dict(windows={str(i): [w[0], w[1], sorted(w[2])] for i, w in win.items()},
+                          slots=[list(x) for x in slots], remainders=remainder, banks_per_stage=nb,
+                          rule='helper (stage s, helper h) of replica r owns coordinates [off, off+w) of the pending idle-child '
+                               'projector of data family r*960+(2*pair+side)*120+port (copy = side*120+port); s lies strictly between '
+                               'the last local/bridge touch of that pair and the child; the child keeps the remaining coordinates.'),
+             helper_route='bank owner (exact width-64 tiling of the unhosted residuals of each stage) or hosted owner (data family, pending idle coordinates)')
+    tb = json.dumps(t, separators=(',', ':'), sort_keys=True).encode(); (out / 'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(tb, mtime=0))
+    res = dict(g); res.update(status='PASS_IDLE_AXIS_HOSTED_BIT_TEMPLATE', live=LIVE, physical=LIVE + 9, template_sha256=hashlib.sha256(tb).hexdigest(),
+               parent_template_sha256=g['template_sha256'], profile=dict(sorted(paid.items())), paid_calls=sum(paid.values()), rank_mass=mass,
+               maxchild=max(paid), banks_per_stage_hosted=nb, hosted_residuals_per_replica=len(slots), hosted_residuals=len(slots) * T,
+               hosted_coordinates_per_replica=sum(x[3] for x in slots), saved_idle_cost_proxy=val, seconds=time.monotonic() - t0)
+    res['bank_assignments'] = sum(1 for c in t['calls'] for f, r in c['owners'][2 * V:] if r[0] == 'bank')
+    (out / 'GLOBAL.json').write_text(json.dumps(res, indent=2) + '\n')
+    print(json.dumps({k: res[k] for k in ('live', 'maxchild', 'hosted_residuals', 'banks_per_stage_hosted', 'rank_mass')}), flush=True)
+if __name__ == '__main__':
+    DISCOVER = '--discover' in sys.argv; args = [a for a in sys.argv[1:] if a != '--discover']
+    main(Path(args[0]), Path(args[1]), Path(args[2]))
diff --git a/research/e8-r740-idle-hosting/complex_hosted.py b/research/e8-r740-idle-hosting/complex_hosted.py
new file mode 100644
index 0000000000..56e15c15ae
--- /dev/null
+++ b/research/e8-r740-idle-hosting/complex_hosted.py
@@ -0,0 +1,87 @@
+"""Idle-axis hosting for #433's compressed nine-stage complex template (m=73, R=560, whole rank-nine residuals).
+Local programs, data routes and the cover correction are unchanged; bank slots of hosted residuals move onto pending
+idle-child coordinates of untouched data families; unhosted residuals are re-tiled eight per bank with one paid pad
+(a final partial bank pays the larger pad).  usage: complex_hosted.py SPLIT_CENTRES_DIR OUT"""
+import gzip, hashlib, json, math, sys, time
+from collections import Counter
+from pathlib import Path
+HERE = Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE))
+import hosting_core as HC
+V, K, T, L, M, R = 120, 4, 8, 9, 73, 560
+DATA = 2 * K * V * T
+DISCOVER = False
+def main(src, out):
+    t0 = time.monotonic(); out.mkdir(parents=True, exist_ok=False)
+    blob = gzip.decompress((src / 'GLOBAL-TEMPLATE.json.gz').read_bytes()); t = json.loads(blob)
+    integ = json.loads((src / 'INTEGRATION.json').read_text()); checks = json.loads((src / 'LOCAL-CHECKS.json').read_text())
+    assert hashlib.sha256(blob).hexdigest() == integ['global_template_sha256'] and t['live'] == integ['live']
+    rank = {}
+    for it in t['idle_children']:
+        assert it['replicas'] == T; rank.setdefault(it['child'], it['rank']); assert rank[it['child']] == it['rank']
+    pair_of_stage = {e['stage']: e['pair'] for e in t['recipe'] if e['kind'] == 'local'}
+    sched = []; side_of = {}; pair_of = {}
+    for e in t['execution_schedule']:
+        if e['kind'] == 'local_cover_sweep': sched.append(dict(kind='local', stage=e['stage'], pair=pair_of_stage[e['stage']]))
+        elif e['kind'] == 'bridge': sched.append(dict(kind='bridge', dst=e['dst'], src=e['src']))
+        elif e['kind'] == 'idle_cover_sweep':
+            for sd, ch in enumerate(e['child_indices']):
+                if ch in rank:
+                    sched.append(dict(kind='idle', pair=e['pair'], rank=rank[ch], idx=ch)); side_of[ch] = sd; pair_of[ch] = e['pair']
+    win = {k: x for k, x in HC.windows(sched).items() if x[1] >= 9 and x[2]}
+    avail = {(s, 9): R for s in range(L)}
+    sel = HERE / 'SELECTION.json'; key = 'complex'
+    if DISCOVER:
+        ys, zs, val = HC.solve(win, V, avail, M, pad_value=HC.cost(1, M) / 8); HC.save_selection(sel, key, ys, zs, val)
+    ys, zs, val = HC.load_selection(sel, key)
+    slots, rem = HC.expand(win, ys, zs, {s: [(h, 9) for h in range(R)] for s in range(L)}, V)
+    hosted = {(s, h): (i, port, off) for i, port, off, w, s, h in slots}
+    # re-tile unhosted residuals: per stage, z = rank among (replica, helper) unhosted pairs; eight per bank
+    base = [DATA]; tile = {}; partial = Counter()
+    for s in range(L):
+        left = [(rep, h) for rep in range(T) for h in range(R) if (s, h) not in hosted]
+        for z, (rep, h) in enumerate(left): tile[s, rep, h] = divmod(z, 8)
+        nb = -(-len(left) // 8); base.append(base[-1] + nb)
+        if len(left) % 8: partial[M - 9 * (len(left) % 8)] += 1
+        full = len(left) // 8
+        partial[M - 72] += full
+    W = base[-1]
+    for c in t['calls']:
+        s, rep, p = c['stage'], c['replica'], c['pair']; own = c['owners'][:2 * V]
+        for h in range(R):
+            if (s, h) in hosted:
+                i, port, off = hosted[s, h]; own.append([rep * 960 + (2 * pair_of[i] + side_of[i]) * V + port, [3, i, off]])
+            else:
+                b, sl = tile[s, rep, h]; own.append([base[s] + b, [2, sl]])
+        assert len({(f, tuple(r)) for f, r in own}) == 2 * V + R and all(f < W for f, r in own)
+        c['owners'] = own
+    paid = Counter()
+    for c in t['calls']:
+        for r_, z in checks[c['orientation']]['paid_profile'].items(): paid[int(r_)] += z
+    newidle = []
+    for it in t['idle_children']:
+        ch, port = it['child'], it['port']; rr = rem.get((ch, port), it['rank']) if ch in win else it['rank']
+        if rr: newidle.append(dict(child=ch, port=port, rank=rr, hosted=it['rank'] - rr, replicas=T)); paid[rr] += T
+    for r_, n in partial.items(): paid[r_] += L * n if False else n * 1
+    # padding: one pad child per bank per stage (already per-stage counted above), the template replays all stages
+    mass = sum(r * n for r, n in paid.items()); D = M * W - mass
+    assert D == 2496, D
+    t.update(version='hamming-mutable-basis-nine-v1+idle-axis-hosting', live=W, idle_children=newidle,
+             physical=W + R + (integ['physical'] - integ['live'] - R),
+             hosting=dict(windows={str(i): [w[0], w[1], sorted(w[2])] for i, w in win.items()}, sides=side_of, pairs=pair_of,
+                          slots=[list(x) for x in slots], banks=[base[s + 1] - base[s] for s in range(L)]))
+    t['bank_padding']['families'] = list(range(DATA, W)); t['cover_final_correction']['families'] = [0, W]
+    t['cover_final_correction']['charged_calls_per_cover'] = W
+    for e in t['execution_schedule']:
+        if e['kind'] == 'bank_padding_cover_sweep': e['families'] = [DATA, W]
+        elif e['kind'] == 'translate_every_live_family': e.update(t['cover_final_correction'])
+    tb = json.dumps(t, sort_keys=True, separators=(',', ':')).encode(); (out / 'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(tb, mtime=0))
+    res = dict(status='PASS_IDLE_AXIS_HOSTED_COMPLEX_TEMPLATE', parent_template_sha256=integ['global_template_sha256'],
+               template_sha256=hashlib.sha256(tb).hexdigest(), live=W, physical=t['physical'], global_profile=dict(sorted(paid.items())),
+               rank_mass=mass, deficit=D, maxchild=max(paid), hosted_residuals=len(slots) * T, banks_per_stage=t['hosting']['banks'],
+               saved_cost_proxy=val, seconds=time.monotonic() - t0)
+    (out / 'HOSTED.json').write_text(json.dumps(res, indent=2) + '\n')
+    print(json.dumps({k: res[k] for k in ('live', 'maxchild', 'hosted_residuals', 'banks_per_stage', 'deficit')}))
+if __name__ == '__main__':
+    DISCOVER = '--discover' in sys.argv; args = [a for a in sys.argv[1:] if a != '--discover']
+    main(Path(args[0]), Path(args[1]))
diff --git a/research/e8-r740-idle-hosting/hosting_core.py b/research/e8-r740-idle-hosting/hosting_core.py
new file mode 100644
index 0000000000..68b536daa9
--- /dev/null
+++ b/research/e8-r740-idle-hosting/hosting_core.py
@@ -0,0 +1,138 @@
+"""Idle-axis hosting: place whole dirty-helper residuals on the pending coordinates of an idle data family.
+
+A data family that is advanced by an idle child from level a to level b receives the commuting coordinate factors of
+that child.  If the family is untouched (no local invocation on its pair and no bridge naming its pair) during an
+interval of local invocations ending at the child, a helper residual of width w from an invocation inside that
+interval may own w of those pending coordinates instead of a bank slot.  The child keeps only the remaining
+coordinates.  This module computes the windows from the recipe and chooses, per replica, how many residuals of each
+width each child hosts (exact integer programme), then expands that choice into explicit slot assignments.
+Standard library plus scipy for the integer programme; the emitted assignment is re-checked without scipy."""
+import math
+from collections import Counter, defaultdict
+
+def windows(schedule):
+    """schedule: ordered events dict(kind='local',stage,pair) | dict(kind='bridge',dst,src) | dict(kind='idle',pair,rank,idx).
+    Returns {idx: (pair, rank, frozenset(stages))} - stages whose invocation lies strictly between the last touch of
+    the pair and the idle child."""
+    last = {}; out = {}; locals_ = []
+    for pos, e in enumerate(schedule):
+        k = e['kind']
+        if k == 'local':
+            locals_.append((pos, e['stage'], e['pair'])); last[e['pair']] = pos
+        elif k == 'bridge':
+            last[e['dst']] = pos; last[e['src']] = pos
+        elif k == 'idle':
+            p = e['pair']; lo = last.get(p, -1)
+            st = frozenset(s for q, s, pp in locals_ if lo < q < pos and pp != p)
+            out[e['idx']] = (p, e['rank'], st)      # an idle child acts on other coordinates (or the other member): not a touch
+    return out
+
+def patterns(rank, widths, maxk=12):
+    """multisets of widths with sum <= rank (as sorted tuples)"""
+    ws = sorted(set(widths), reverse=True); res = []
+    def rec(i, cur, s):
+        if i == len(ws): res.append(tuple(cur)); return
+        w = ws[i]; k = 0
+        while s + k * w <= rank and len(cur) + k <= maxk:
+            rec(i + 1, cur + [w] * k, s + k * w); k += 1
+    rec(0, [], 0)
+    return res
+
+def cost(r, m):
+    return r * math.log(m / r) if r else 0.0
+
+def solve(win, copies, avail, m, pad_value=0.0, group=None):
+    """win: {idx: (pair, rank, stages)}; copies: piece copies per replica of each idx (2V);
+    avail: {(stage, width): count per replica}; maximise saved idle cost (+ pad_value per hosted residual).
+    group: optional {width: g} - remaining count of that width per stage must be a multiple of g (exact bank tiling).
+    Returns {(idx, pattern): copies} and {(idx, width, stage): count}."""
+    import numpy as np
+    from scipy.optimize import milp, LinearConstraint, Bounds
+    widths = sorted({w for (_, w) in avail})
+    var = []; index = {}
+    for idx, (p, r, st) in win.items():
+        for pat in patterns(r, widths):
+            index[('y', idx, pat)] = len(var); var.append(('y', idx, pat))
+        for w in widths:
+            for s in st:
+                if avail.get((s, w), 0):
+                    index[('z', idx, w, s)] = len(var); var.append(('z', idx, w, s))
+    stages = sorted({s for (s, _) in avail})
+    if group:
+        for w, g in group.items():
+            for s in stages:
+                index[('g', w, s)] = len(var); var.append(('g', w, s))
+    n = len(var); c = np.zeros(n); integ = np.ones(n); lb = np.zeros(n); ub = np.full(n, np.inf)
+    for key, j in index.items():
+        if key[0] == 'y':
+            _, idx, pat = key; r = win[idx][1]; c[j] = -(cost(r, m) - cost(r - sum(pat), m) + pad_value * len(pat))
+    rows, lo, hi = [], [], []
+    for idx in win:
+        row = np.zeros(n)
+        for key, j in index.items():
+            if key[0] == 'y' and key[1] == idx: row[j] = 1
+        rows.append(row); lo.append(copies); hi.append(copies)
+        for w in widths:
+            row = np.zeros(n)
+            for key, j in index.items():
+                if key[0] == 'y' and key[1] == idx: row[j] = key[2].count(w)
+                if key[0] == 'z' and key[1] == idx and key[2] == w: row[j] = -1
+            rows.append(row); lo.append(0); hi.append(0)
+    for (s, w), a in avail.items():
+        row = np.zeros(n)
+        for key, j in index.items():
+            if key[0] == 'z' and key[2] == w and key[3] == s: row[j] = 1
+        if group and w in group:
+            row[index[('g', w, s)]] = group[w]; rows.append(row); lo.append(a); hi.append(a)   # used + g*k = avail
+        else:
+            rows.append(row); lo.append(0); hi.append(a)
+    res = milp(c, constraints=LinearConstraint(np.array(rows), lo, hi), integrality=integ, bounds=Bounds(lb, ub),
+               options=dict(time_limit=600, disp=False))
+    assert res.x is not None, res.message
+    x = [int(round(t)) for t in res.x]
+    ys = {(k[1], k[2]): x[j] for k, j in index.items() if k[0] == 'y' and x[j]}
+    zs = {(k[1], k[2], k[3]): x[j] for k, j in index.items() if k[0] == 'z' and x[j]}
+    return ys, zs, -res.fun
+
+def expand(win, ys, zs, helpers, V2):
+    """helpers: {stage: [(helper, width), ...]} for ONE replica; returns list of
+    (idx, copy, offset, width, stage, helper) and the remainder rank of every (idx, copy).
+    Copies of a piece are the 2V (side, port) data families; residuals packed from offset 0 in decreasing width."""
+    pool = defaultdict(list)                    # (stage, width) -> helpers
+    for s, hs in helpers.items():
+        for h, w in hs: pool[s, w].append(h)
+    for k in pool: pool[k].sort()
+    need = defaultdict(list)                    # (idx, width) -> stages multiset in deterministic order
+    for (idx, w, s), cnt in sorted(zs.items()): need[idx, w] += [s] * cnt
+    out = []; rem = {}
+    for idx in sorted(win):
+        pats = sorted([(pat, cnt) for (i, pat), cnt in ys.items() if i == idx], key=lambda t: (-sum(t[0]), t[0]))
+        copy = 0; ptr = Counter()
+        r = win[idx][1]
+        for pat, cnt in pats:
+            for _ in range(cnt):
+                off = 0
+                for w in sorted(pat, reverse=True):
+                    s = need[idx, w][ptr[idx, w]]; ptr[idx, w] += 1
+                    h = pool[s, w].pop(0)
+                    out.append((idx, copy, off, w, s, h)); off += w
+                rem[idx, copy] = r - off; copy += 1
+        while copy < V2: rem[idx, copy] = r; copy += 1
+    return out, rem
+
+def save_selection(path, key, ys, zs, val):
+    """freeze the integer-programme choice (patterns per child, residual stages per child) for stdlib-only replay"""
+    import json
+    from pathlib import Path
+    p = Path(path); d = json.loads(p.read_text()) if p.exists() else {}
+    d[key] = dict(patterns=sorted([[i, list(pat), n] for (i, pat), n in ys.items()]),
+                  stages=sorted([[i, w, s, n] for (i, w, s), n in zs.items()]), proxy_saving=val)
+    p.write_text(json.dumps(d, indent=1, sort_keys=True) + '\n')
+
+def load_selection(path, key):
+    import json
+    from pathlib import Path
+    d = json.loads(Path(path).read_text())[key]
+    ys = {(i, tuple(pat)): n for i, pat, n in d['patterns']}
+    zs = {(i, w, s): n for i, w, s, n in d['stages']}
+    return ys, zs, d['proxy_saving']
diff --git a/research/e8-r740-idle-hosting/local-evidence/TESTED-MANIFEST.json b/research/e8-r740-idle-hosting/local-evidence/TESTED-MANIFEST.json
new file mode 100644
index 0000000000..a15f071143
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/TESTED-MANIFEST.json
@@ -0,0 +1,21 @@
+{
+  "parent_manifest_sha256": "344d58298774e9e2bbfd0af6332507c3b3d2172bc70d88a79853e679bdaaa33f",
+  "files": {
+    "assemble.py": "fb31ef3d1633effe3a8abeb48bf9bbc0508bfac2a37af101ea89dbb5f622be51",
+    "AUDIT-CHANGED.json": "6320b6fba321cbde5648ca5d07d79d1e05095003cd20c11cee044df54d684842",
+    "audit.py": "8792956a1aab64812cb030dc57456d68c5e90c570594f4d2d7fcf9ab14c89c40",
+    "bit_hosted.py": "300227c826ea07951738644975915ea11c1c53295440f93b3a7b19f635ce2061",
+    "CERTIFICATE.json": "f738a33bf7f079a3ea275a555807f0a6d491a65201859953eac7edeebb5e1fe3",
+    "complex_hosted.py": "829c5c4f4bdfccedadd31505f1f0a394f7a208d1446b7bbf9cc92d3aa1530c0c",
+    "EXPECTED.json": "feee5ada0067f1c83f7b21972fb4351b99a3ca24c020a43434b84ca20c48d14d",
+    "hosting_core.py": "d8b90cd5d152df3c7c351230863d9e61816ad5e1f21d69bea1a86a5daad559a3",
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE.md": "e2bcab601208891189f33c257eb7cfee9261b420c6eceebf96c986135ae65a4c",
+    "PROOF.md": "4f06d1dead63c62b076f0a6c1521c68c0b0544aa2c5df5e74a408fdfc34f91c4",
+    "README.md": "38da638aa8dbb2139a0e3647ab36dbd360c73975b7456cd763bca9173ba47f79",
+    "SELECTION.json": "6e3a436ef9e926019751fd40b08586d695d888f16542f9c8a24ec4d6be8cffae",
+    "SOURCE442-PINS.json": "489716866ad1d368a5f29a3d37e8d76a40474f5709e4ad593f18f9cd89dc9096",
+    "VALIDATION.json": "57a7ff96c9c568d9ef25fffe1ff4e7c19a1de3b2d9c6a45635e7ab233f01f350",
+    "verify.py": "094fab9efc8ce362007f4da9e00beee1867d8503e073eab4a622199bcd3d8ae9"
+  }
+}
diff --git a/research/e8-r740-idle-hosting/local-evidence/full311/RECEIPT.json b/research/e8-r740-idle-hosting/local-evidence/full311/RECEIPT.json
new file mode 100644
index 0000000000..7f3f6aaf6e
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full311/RECEIPT.json
@@ -0,0 +1,35 @@
+{
+  "status": "PASS_FULL_IDLE_AXIS_HOSTING_COMPOSITION",
+  "kappa": "124529313073387/100000000000000000",
+  "kappa_decimal": "0.001245293130733870",
+  "gain_over_pr434_percent": 9.901378851439578,
+  "manifest_sha256": "aac568b890323ced6d856c0477a4761b6f106a5051ee0811ffd1d97d7ca09ca6",
+  "checks": [
+    {
+      "name": "parent-r740-full",
+      "seconds": 149.4,
+      "log_sha256": "b6b21746622747ea37b7423dd7600953185f3da7c5cca1019526ab4d9cfb06f1"
+    },
+    {
+      "name": "bit-hosting",
+      "seconds": 0.4,
+      "log_sha256": "0b2dd019350260407d9d99fe7be94f02ff031997fbf6a4976229b27c6cd7d788"
+    },
+    {
+      "name": "complex-hosting",
+      "seconds": 0.4,
+      "log_sha256": "3b42f65586cb5c37e06df560fae4dcde1c42526238697a73d103f9895df24fcd"
+    },
+    {
+      "name": "independent-audit",
+      "seconds": 3.3,
+      "log_sha256": "e55ea84119d6b17d16be29a67e8158e357838aec1a3c2d17aa966d8843afe345"
+    },
+    {
+      "name": "exact-assembly",
+      "seconds": 0.2,
+      "log_sha256": "1d2c62b500f91f48ada95c0b4c811169705b762098c81f7458dbc8194652b8e9"
+    }
+  ],
+  "python": "3.11.15"
+}
diff --git a/research/e8-r740-idle-hosting/local-evidence/full311/RESULT.json b/research/e8-r740-idle-hosting/local-evidence/full311/RESULT.json
new file mode 100644
index 0000000000..2613e82a26
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full311/RESULT.json
@@ -0,0 +1,116 @@
+{
+  "status": "PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY",
+  "kappa": "124529313073387/100000000000000000",
+  "kappa_decimal": "0.001245293130733870",
+  "bit_lower": "249369163853537814231/200000000000000000000000",
+  "complex_lower": "1267453159029119/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr434_percent": 9.901378851439578,
+  "bit": {
+    "live": 9376,
+    "physical": 9385,
+    "maxchild": 8,
+    "rank_mass": 597568,
+    "hosted_residuals": 39712,
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 282,
+    "charged_two_level_coefficient_bits": 320,
+    "row_coefficient": 18355
+  },
+  "complex": {
+    "live": 8400,
+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
+  },
+  "strict_outer_constraints": {
+    "bit_positive": "9740982963028820832919725088633854467030770732060412801292146799575692050366199573928498445709226600445861018939178536293808214293774639035900727115611879231866647/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+    "complex_below_one_over32": "29982546840970881/1000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "160994841886171344678297106451153345469229267939587198707853200424307949633800426071501554290773399554138981060821463706191785706225360964099272884388120768133353/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
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+      "cutoff_log2": "15858630557976"
+    },
+    {
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+      "cutoff_log2": "10200939576290109046"
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+      "cutoff_log2": "6561674279421831238677946"
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+      "cutoff_log2": "4220745454595125991404220610916"
+    },
+    {
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+      "cutoff_log2": "2714961370203082164321471435033117471"
+    },
+    {
+      "gap": "35470899911366145532969229267939587198707853200424307949633800426071501554290773399554138981060821463706191785706225360964099272884388120768133353/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1746377582109381257242684594400020974931554"
+    }
+  ],
+  "bit_template_sha256": "c256c1c11027d32d5d800dd8dc3c0c50189ab71157c6c06301bb4283ff23bab1",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f"
+}
diff --git a/research/e8-r740-idle-hosting/local-evidence/full311/bit-hosting.log b/research/e8-r740-idle-hosting/local-evidence/full311/bit-hosting.log
new file mode 100644
index 0000000000..ce65a77978
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full311/bit-hosting.log
@@ -0,0 +1 @@
+{"live": 9376, "maxchild": 8, "hosted_residuals": 39712, "banks_per_stage_hosted": {"0": 628, "1": 478, "2": 0, "3": 0, "4": 56, "5": 56, "6": 0, "7": 0, "8": 478}, "rank_mass": 597568}
diff --git a/research/e8-r740-idle-hosting/local-evidence/full311/complex-hosting.log b/research/e8-r740-idle-hosting/local-evidence/full311/complex-hosting.log
new file mode 100644
index 0000000000..b8925ed69d
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full311/complex-hosting.log
@@ -0,0 +1 @@
+{"live": 8400, "maxchild": 8, "hosted_residuals": 34560, "banks_per_stage": [0, 0, 0, 160, 0, 120, 0, 0, 440], "deficit": 2496}
diff --git a/research/e8-r740-idle-hosting/local-evidence/full311/exact-assembly.log b/research/e8-r740-idle-hosting/local-evidence/full311/exact-assembly.log
new file mode 100644
index 0000000000..c09992815d
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full311/exact-assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY 0.001245293130733870 binding bit gain over #434 9.9014%
diff --git a/research/e8-r740-idle-hosting/local-evidence/full311/independent-audit.log b/research/e8-r740-idle-hosting/local-evidence/full311/independent-audit.log
new file mode 100644
index 0000000000..868a926873
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full311/independent-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT", "bit_template_sha256": "c256c1c11027d32d5d800dd8dc3c0c50189ab71157c6c06301bb4283ff23bab1", "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f", "bit_live": 9376, "complex_live": 8400, "bit_hosted_residuals": 39712, "complex_hosted_residuals": 34560, "bit_maxchild": 8, "complex_maxchild": 8, "mutations_rejected": ["bit: hosted residual outside its window", "bit: overlapping hosted coordinates", "bit: understated live stock", "bit: hosted owner on the active pair", "bit: missing remainder child", "complex: hosted residual outside its window", "complex: remainder child understated", "complex: dropped bank", "complex: duplicated hosted residual"]}
diff --git a/research/e8-r740-idle-hosting/local-evidence/full311/parent-r740-full.log b/research/e8-r740-idle-hosting/local-evidence/full311/parent-r740-full.log
new file mode 100644
index 0000000000..ee23b611cb
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full311/parent-r740-full.log
@@ -0,0 +1,16 @@
+PASS hamming_packets
+PASS complex_construct
+PASS complex_audit
+PASS complex_emit
+PASS complex_phases
+PASS bit_construct
+PASS bit_kernel
+PASS bit_export
+PASS bit_global
+PASS bit_audit
+PASS bit_price
+PASS complex_integrate
+PASS complex_replay
+PASS combined
+PASS independent_audit
+PASS conditional kappa 0.001138798055343319
diff --git a/research/e8-r740-idle-hosting/local-evidence/full311/parent/RESULT.json b/research/e8-r740-idle-hosting/local-evidence/full311/parent/RESULT.json
new file mode 100644
index 0000000000..655468f65f
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full311/parent/RESULT.json
@@ -0,0 +1,126 @@
+{
+  "status": "PASS_CONDITIONAL_SPLIT_CENTRE_ASSEMBLY",
+  "kappa": "1138798055343319/1000000000000000000",
+  "kappa_decimal": "0.001138798055343319",
+  "bit_lower": "17814006170324008149/15625000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr425_percent": 8.663365470849168,
+  "bit_invoice": {
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "extra_helper_route_factor_bound": 144,
+    "selector_charge": 2375347104,
+    "full_counted_coefficient": "8271410009661736653226855278395470361",
+    "two_level_coefficient": "7323242093316479963924177312150069573045566553609912891292783054664675728289084971684",
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 282,
+    "charged_two_level_coefficient_bits": 512,
+    "row_coefficient": 18355,
+    "live": 14187,
+    "physical": 14196
+  },
+  "strict_outer_constraints": {
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+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "561793975111583740163871249502858784489610640586234796636459037191440313755980151433958329973247989079787120670653922609169116125411859040051524587834320988443/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+      "cutoff_log2": "6150734807365621625035986466966332327804006"
+    }
+  ],
+  "bit_template_sha256": "b87ed8c20819237f2daacdd1383a2776419551a62a7014eb9720af146a9dd9ec",
+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f",
+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim.",
+  "verification_steps": [
+    "hamming_packets",
+    "complex_construct",
+    "complex_audit",
+    "complex_emit",
+    "complex_phases",
+    "bit_construct",
+    "bit_kernel",
+    "bit_export",
+    "bit_global",
+    "bit_audit",
+    "bit_price",
+    "complex_integrate",
+    "complex_replay",
+    "combined",
+    "independent_audit"
+  ],
+  "phase_mode": "full replay",
+  "manifest_sha256": "344d58298774e9e2bbfd0af6332507c3b3d2172bc70d88a79853e679bdaaa33f"
+}
diff --git a/research/e8-r740-idle-hosting/local-evidence/full314/RECEIPT.json b/research/e8-r740-idle-hosting/local-evidence/full314/RECEIPT.json
new file mode 100644
index 0000000000..5750454614
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full314/RECEIPT.json
@@ -0,0 +1,35 @@
+{
+  "status": "PASS_FULL_IDLE_AXIS_HOSTING_COMPOSITION",
+  "kappa": "124529313073387/100000000000000000",
+  "kappa_decimal": "0.001245293130733870",
+  "gain_over_pr434_percent": 9.901378851439578,
+  "manifest_sha256": "aac568b890323ced6d856c0477a4761b6f106a5051ee0811ffd1d97d7ca09ca6",
+  "checks": [
+    {
+      "name": "parent-r740-full",
+      "seconds": 128.9,
+      "log_sha256": "b6b21746622747ea37b7423dd7600953185f3da7c5cca1019526ab4d9cfb06f1"
+    },
+    {
+      "name": "bit-hosting",
+      "seconds": 0.4,
+      "log_sha256": "0b2dd019350260407d9d99fe7be94f02ff031997fbf6a4976229b27c6cd7d788"
+    },
+    {
+      "name": "complex-hosting",
+      "seconds": 0.4,
+      "log_sha256": "3b42f65586cb5c37e06df560fae4dcde1c42526238697a73d103f9895df24fcd"
+    },
+    {
+      "name": "independent-audit",
+      "seconds": 2.0,
+      "log_sha256": "e55ea84119d6b17d16be29a67e8158e357838aec1a3c2d17aa966d8843afe345"
+    },
+    {
+      "name": "exact-assembly",
+      "seconds": 0.2,
+      "log_sha256": "1d2c62b500f91f48ada95c0b4c811169705b762098c81f7458dbc8194652b8e9"
+    }
+  ],
+  "python": "3.14.8"
+}
diff --git a/research/e8-r740-idle-hosting/local-evidence/full314/RESULT.json b/research/e8-r740-idle-hosting/local-evidence/full314/RESULT.json
new file mode 100644
index 0000000000..2613e82a26
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full314/RESULT.json
@@ -0,0 +1,116 @@
+{
+  "status": "PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY",
+  "kappa": "124529313073387/100000000000000000",
+  "kappa_decimal": "0.001245293130733870",
+  "bit_lower": "249369163853537814231/200000000000000000000000",
+  "complex_lower": "1267453159029119/1000000000000000000",
+  "binding_component": "bit",
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+  "bit": {
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+    "maxchild": 8,
+    "rank_mass": 597568,
+    "hosted_residuals": 39712,
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 282,
+    "charged_two_level_coefficient_bits": 320,
+    "row_coefficient": 18355
+  },
+  "complex": {
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+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
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+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "376667732875215341121174631116822818722929/250000000000000000000000000000000000000000000000",
+      "cutoff_log2": "15858630557976"
+    },
+    {
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+      "cutoff_log2": "10200939576290109046"
+    },
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+      "cutoff_log2": "6561674279421831238677946"
+    },
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+      "cutoff_log2": "4220745454595125991404220610916"
+    },
+    {
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+      "cutoff_log2": "2714961370203082164321471435033117471"
+    },
+    {
+      "gap": "35470899911366145532969229267939587198707853200424307949633800426071501554290773399554138981060821463706191785706225360964099272884388120768133353/7812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1746377582109381257242684594400020974931554"
+    }
+  ],
+  "bit_template_sha256": "c256c1c11027d32d5d800dd8dc3c0c50189ab71157c6c06301bb4283ff23bab1",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f"
+}
diff --git a/research/e8-r740-idle-hosting/local-evidence/full314/bit-hosting.log b/research/e8-r740-idle-hosting/local-evidence/full314/bit-hosting.log
new file mode 100644
index 0000000000..ce65a77978
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full314/bit-hosting.log
@@ -0,0 +1 @@
+{"live": 9376, "maxchild": 8, "hosted_residuals": 39712, "banks_per_stage_hosted": {"0": 628, "1": 478, "2": 0, "3": 0, "4": 56, "5": 56, "6": 0, "7": 0, "8": 478}, "rank_mass": 597568}
diff --git a/research/e8-r740-idle-hosting/local-evidence/full314/complex-hosting.log b/research/e8-r740-idle-hosting/local-evidence/full314/complex-hosting.log
new file mode 100644
index 0000000000..b8925ed69d
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full314/complex-hosting.log
@@ -0,0 +1 @@
+{"live": 8400, "maxchild": 8, "hosted_residuals": 34560, "banks_per_stage": [0, 0, 0, 160, 0, 120, 0, 0, 440], "deficit": 2496}
diff --git a/research/e8-r740-idle-hosting/local-evidence/full314/exact-assembly.log b/research/e8-r740-idle-hosting/local-evidence/full314/exact-assembly.log
new file mode 100644
index 0000000000..c09992815d
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full314/exact-assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY 0.001245293130733870 binding bit gain over #434 9.9014%
diff --git a/research/e8-r740-idle-hosting/local-evidence/full314/independent-audit.log b/research/e8-r740-idle-hosting/local-evidence/full314/independent-audit.log
new file mode 100644
index 0000000000..868a926873
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full314/independent-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT", "bit_template_sha256": "c256c1c11027d32d5d800dd8dc3c0c50189ab71157c6c06301bb4283ff23bab1", "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f", "bit_live": 9376, "complex_live": 8400, "bit_hosted_residuals": 39712, "complex_hosted_residuals": 34560, "bit_maxchild": 8, "complex_maxchild": 8, "mutations_rejected": ["bit: hosted residual outside its window", "bit: overlapping hosted coordinates", "bit: understated live stock", "bit: hosted owner on the active pair", "bit: missing remainder child", "complex: hosted residual outside its window", "complex: remainder child understated", "complex: dropped bank", "complex: duplicated hosted residual"]}
diff --git a/research/e8-r740-idle-hosting/local-evidence/full314/parent-r740-full.log b/research/e8-r740-idle-hosting/local-evidence/full314/parent-r740-full.log
new file mode 100644
index 0000000000..ee23b611cb
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full314/parent-r740-full.log
@@ -0,0 +1,16 @@
+PASS hamming_packets
+PASS complex_construct
+PASS complex_audit
+PASS complex_emit
+PASS complex_phases
+PASS bit_construct
+PASS bit_kernel
+PASS bit_export
+PASS bit_global
+PASS bit_audit
+PASS bit_price
+PASS complex_integrate
+PASS complex_replay
+PASS combined
+PASS independent_audit
+PASS conditional kappa 0.001138798055343319
diff --git a/research/e8-r740-idle-hosting/local-evidence/full314/parent/RESULT.json b/research/e8-r740-idle-hosting/local-evidence/full314/parent/RESULT.json
new file mode 100644
index 0000000000..655468f65f
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/full314/parent/RESULT.json
@@ -0,0 +1,126 @@
+{
+  "status": "PASS_CONDITIONAL_SPLIT_CENTRE_ASSEMBLY",
+  "kappa": "1138798055343319/1000000000000000000",
+  "kappa_decimal": "0.001138798055343319",
+  "bit_lower": "17814006170324008149/15625000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr425_percent": 8.663365470849168,
+  "bit_invoice": {
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "extra_helper_route_factor_bound": 144,
+    "selector_charge": 2375347104,
+    "full_counted_coefficient": "8271410009661736653226855278395470361",
+    "two_level_coefficient": "7323242093316479963924177312150069573045566553609912891292783054664675728289084971684",
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 282,
+    "charged_two_level_coefficient_bits": 512,
+    "row_coefficient": 18355,
+    "live": 14187,
+    "physical": 14196
+  },
+  "strict_outer_constraints": {
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+    "complex_below_one_over32": "30066013450793671/1000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "561793975111583740163871249502858784489610640586234796636459037191440313755980151433958329973247989079787120670653922609169116125411859040051524587834320988443/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+    "alpha_positive": "14593233854729433808198016283832561418400870912502867609268668484930276693345556800958407657780243352313668390506485898656340355577974958403084145055041404002516695344173943431055975412165679011557/12814593233854729427415494633211197275126148187518101505172342762243981029279516937922948922297538712313788129539275842055550405125215895986178286707662989397091660049175668641976886000000000000000000",
+    "alpha_below_one": "12799999999999999993607296616927364713707747316605598637563074093759050752586171381121990514639758468961474461148769356156894064769637921027775202562607947993089143353831494698545830024587834320988443/12814593233854729427415494633211197275126148187518101505172342762243981029279516937922948922297538712313788129539275842055550405125215895986178286707662989397091660049175668641976886000000000000000000",
+    "alpha_below_one_fourth": "3189055074608952923045675642018966757363136175967022508683817022076064980626533677679778822916604434726133363994312474615231260925725999038141487531860705945270398316949743217063165524587834320988443/12814593233854729427415494633211197275126148187518101505172342762243981029279516937922948922297538712313788129539275842055550405125215895986178286707662989397091660049175668641976886000000000000000000",
+    "delta_positive": "1/8000000000000000000",
+    "delta_below_one_eighth": "999999999999999999/8000000000000000000",
+    "short_record_fallback": "81826496822092562171882315893595751752399902690116486852838304432755607303153150619225216237579156329475548128864912385926260879534056410653826445668927928937673680050034015948260296943169395903763640168091395592402062955133096133288079820489374838549015828583026644692484032808774556966449204475165761360629808686214538063881707838504539564249/82013396696670268335459165652551662560807348400115849633102993678361478587388908402706873102704247758808244029051365389155522592801381734311541034929043132141386624314724279308652070400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "small_field_exposure": "1/1000000000000000000",
+    "artificial_boundary": "358866983483351341747717718113540406945159983950396044078204190673084545194703056156900337057440514200925643528703135014248295158315822434641030782333039504686200551635115880638897842073763502962965329/51258372935418917709661978532844789100504592750072406020689371048975924117118067751691795689190154849255152518157103368222201620500863583944713146830651957588366640196702674567907544000000000000000000",
+    "literal_scalar_guard": "1",
+    "row_product_gap": "23971789/25",
+    "balanced_prefix_above_kappa": "10428274416196871282531516897522607540915684699387944996351562842329855748924675580097931857187250784626831881239543084291418480285841495843978289147099063037268827644742874203737683/6407296616927364713707747316605598637563074093759050752586171381121990514639758468961474461148769356156894064769637921027775202562607947993089143353831494698545830024587834320988443000000000000000000",
+    "coordinate_movement_above_kappa": "16618746334944244681100920656130015510389359413765203363540962808559686244019848566041670026752010920212879329346077390830883874588140959948475412165679011557/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_phase_layer_above_kappa": "100524444981737664220594239522925222583815265140722356094134786530196630857122927778411434900962035711748445411747629081591081943080838696272228644831689208468074940503875997068731/160182415423184117842693682915139965939076852343976268814654284528049762865993961724036861528719233903922351619240948025694380064065198699827228583845787367463645750614695858024711075000000000000000",
+    "bulk_exposure_above_kappa": "16618746334944244681100920656130015510389359413765203363540962808559686244019848566041670026752010920212879329346077390830883874588140959948475412165679011557/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "Gaussian_arithmetic_above_kappa": "51389712244938146691713398597152867139510107126308306207881645833028893418198612295976082551754159496230184726068155069192471829473692226786380596407635030805421471035003822024959249/51258372935418917709661978532844789100504592750072406020689371048975924117118067751691795689190154849255152518157103368222201620500863583944713146830651957588366640196702674567907544000000000000000000",
+    "scalar_work_above_kappa": "77018898712647605546544387863575261689762403501344509218226331357516855476757646171821980396349236920857760985146706753303572639724124018758737169822961009599604791133355159308913021/51258372935418917709661978532844789100504592750072406020689371048975924117118067751691795689190154849255152518157103368222201620500863583944713146830651957588366640196702674567907544000000000000000000",
+    "dimension_above_kappa": "6392703383072635283920527099591272644968442803763556788329513318265954481711804373368381287775906223941037792417612863599056678676935136298329336932010001145432459122511228716280384644742874203737683/6407296616927364713707747316605598637563074093759050752586171381121990514639758468961474461148769356156894064769637921027775202562607947993089143353831494698545830024587834320988443000000000000000000"
+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "50238871853096532822362240972278860750249/40000000000000000000000000000000000000000000000",
+      "cutoff_log2": "22821423299056"
+    },
+    {
+      "gap": "11455431336719088296695724797447540819776987379259584929022443/8000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "17557374861114977035"
+    },
+    {
+      "gap": "2612059193805271546589956973717711376230817511984641822790221508429225435153562001/1600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "13507545431071750093791293"
+    },
+    {
+      "gap": "595599854024942868145937931074452609889067823826597234111825602004869306469267614758018107869138838307/320000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "10391860116659867549821478467986"
+    },
+    {
+      "gap": "135808249275448458154076421829336450566886398980362416351705509454393700941063236129602722212894374934350058630123597688249/64000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "7994846823599212441742710007613379908"
+    },
+    {
+      "gap": "30966899079343869984489610640586234796636459037191440313755980151433958329973247989079787120670653922609169116125411859040051524587834320988443/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "6150734807365621625035986466966332327804006"
+    }
+  ],
+  "bit_template_sha256": "b87ed8c20819237f2daacdd1383a2776419551a62a7014eb9720af146a9dd9ec",
+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f",
+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim.",
+  "verification_steps": [
+    "hamming_packets",
+    "complex_construct",
+    "complex_audit",
+    "complex_emit",
+    "complex_phases",
+    "bit_construct",
+    "bit_kernel",
+    "bit_export",
+    "bit_global",
+    "bit_audit",
+    "bit_price",
+    "complex_integrate",
+    "complex_replay",
+    "combined",
+    "independent_audit"
+  ],
+  "phase_mode": "full replay",
+  "manifest_sha256": "344d58298774e9e2bbfd0af6332507c3b3d2172bc70d88a79853e679bdaaa33f"
+}
diff --git a/research/e8-r740-idle-hosting/local-evidence/hosting442-exact-cost.json b/research/e8-r740-idle-hosting/local-evidence/hosting442-exact-cost.json
new file mode 100644
index 0000000000..fe39db44f5
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/hosting442-exact-cost.json
@@ -0,0 +1,8 @@
+{
+  "status": "MILP_NOMINATION_REQUIRES_EXACT_REPLAY",
+  "reference_bit_lower": "249369163853537814231/200000000000000000000000",
+  "prior_score": 23476.37893908448,
+  "new_score": 23476.37893908448,
+  "same_patterns": true,
+  "same_stages": true
+}
diff --git a/research/e8-r740-idle-hosting/local-evidence/hosting442-flexbanks.json b/research/e8-r740-idle-hosting/local-evidence/hosting442-flexbanks.json
new file mode 100644
index 0000000000..ef0d170aab
--- /dev/null
+++ b/research/e8-r740-idle-hosting/local-evidence/hosting442-flexbanks.json
@@ -0,0 +1,8 @@
+{
+  "status": "MILP_NOMINATION_REQUIRES_EXACT_REPLAY",
+  "reference_bit_lower": "249369163853537814231/200000000000000000000000",
+  "prior_score": 23476.37893908448,
+  "new_score": 23476.37893908448,
+  "same_patterns": true,
+  "same_stages": false
+}
diff --git a/research/e8-r740-idle-hosting/verify.py b/research/e8-r740-idle-hosting/verify.py
new file mode 100644
index 0000000000..fa399bf90c
--- /dev/null
+++ b/research/e8-r740-idle-hosting/verify.py
@@ -0,0 +1,38 @@
+"""Fresh replay: #434 in full, then idle-axis hosting of both suppliers, independent audit and exact assembly.
+usage: python -B research/idle-axis-hosting/verify.py /absolute/new/output   (Python 3.11+, standard library only)"""
+from pathlib import Path
+import gzip, hashlib, json, os, subprocess, sys, time
+assert __debug__
+ROOT = Path(__file__).resolve().parent; PARENT = ROOT.parent / 'e8-joint-frame-retiming'
+out = Path(sys.argv[1]).resolve(); assert not out.exists() and not out.is_relative_to(ROOT.parent)
+read = lambda p: json.loads(Path(p).read_text()); sha = lambda p: hashlib.sha256(Path(p).read_bytes()).hexdigest()
+def integrity():
+    files = {p.relative_to(ROOT).as_posix(): sha(p) for p in ROOT.rglob('*') if p.is_file() and p.name != 'MANIFEST.json' and '__pycache__' not in p.parts}
+    assert files == read(ROOT / 'MANIFEST.json')['files'], 'manifest mismatch'
+    assert sha(PARENT / 'MANIFEST.json') == read(ROOT / 'MANIFEST.json')['parent_manifest_sha256'], 'parent package changed'
+integrity(); out.mkdir(parents=True)
+env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONINTMAXSTRDIGITS='0'); env.pop('PYTHONOPTIMIZE', None); steps = []
+def run(name, file, *args, cwd=None):
+    t = time.monotonic(); log = out / (name + '.log'); print('RUN', name, flush=True)
+    with log.open('w') as f: q = subprocess.run([sys.executable, '-B', str(file), *map(str, args)], cwd=cwd, env=env, stdout=f, stderr=subprocess.STDOUT)
+    if q.returncode: raise RuntimeError((name, q.returncode, log.read_text()[-3000:]))
+    steps.append(dict(name=name, seconds=round(time.monotonic() - t, 1), log_sha256=sha(log))); print('PASS', name, flush=True)
+try:
+    run('parent-r740-full', PARENT / 'verify.py', out / 'parent', '--replay-phases')
+    changed = out / 'parent'
+    run('bit-hosting', ROOT / 'bit_hosted.py', 'bit426-source-centres/global', 'bit426-source-centres', out / 'bit', cwd=changed)
+    run('complex-hosting', ROOT / 'complex_hosted.py', 'split-centres', out / 'complex', cwd=changed)
+    run('independent-audit', ROOT / 'audit.py', changed, out / 'bit', out / 'complex', out / 'AUDIT.json')
+    run('exact-assembly', ROOT / 'assemble.py', changed, out / 'bit', out / 'complex', out / 'AUDIT.json', out / 'RESULT.json')
+    actual = read(out / 'RESULT.json'); expected = read(ROOT / 'EXPECTED.json')
+    for k, v in expected.items(): assert actual[k] == v, (k, actual[k], v)
+    for side, d in (('bit', 'bit'), ('complex', 'complex')):
+        h = hashlib.sha256(gzip.decompress((out / d / 'GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest()
+        assert h == expected[side + '_template_sha256'], (side, h)
+    integrity()
+    receipt = dict(status='PASS_FULL_IDLE_AXIS_HOSTING_COMPOSITION', kappa=actual['kappa'], kappa_decimal=actual['kappa_decimal'],
+                   gain_over_pr434_percent=actual['gain_over_pr434_percent'], manifest_sha256=sha(ROOT / 'MANIFEST.json'), checks=steps,
+                   python=sys.version.split()[0])
+    (out / 'RECEIPT.json').write_text(json.dumps(receipt, indent=2) + '\n'); print(json.dumps(receipt, indent=2))
+except BaseException as e:
+    (out / 'FAILURE.json').write_text(json.dumps(dict(error=repr(e), completed=steps), indent=2) + '\n'); raise
diff --git a/research/e8-rank138-idle-hosting/AUDIT.json b/research/e8-rank138-idle-hosting/AUDIT.json
new file mode 100644
index 0000000000..0519d52555
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/AUDIT.json
@@ -0,0 +1,41 @@
+{
+  "status": "PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT",
+  "bit_template_sha256": "50d9302688535aee7196ddba537c99620195b39ec096b3cfde8c2d6b2e691ef7",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f",
+  "bit_profile": {
+    "1": 728640,
+    "2": 305600,
+    "3": 80832,
+    "4": 111584,
+    "5": 33984,
+    "6": 8576,
+    "7": 16704,
+    "8": 2592
+  },
+  "complex_profile": {
+    "1": 138384,
+    "2": 56448,
+    "3": 15936,
+    "4": 16128,
+    "5": 32064,
+    "7": 3840,
+    "8": 7488
+  },
+  "bit_live": 37464,
+  "complex_live": 8400,
+  "bit_hosted_residuals": 159168,
+  "complex_hosted_residuals": 34560,
+  "bit_maxchild": 8,
+  "complex_maxchild": 8,
+  "mutations_rejected": [
+    "bit: hosted residual outside its window",
+    "bit: overlapping hosted coordinates",
+    "bit: understated live stock",
+    "bit: hosted owner on the active pair",
+    "bit: missing remainder child",
+    "complex: hosted residual outside its window",
+    "complex: remainder child understated",
+    "complex: dropped bank",
+    "complex: duplicated hosted residual"
+  ]
+}
diff --git a/research/e8-rank138-idle-hosting/CERTIFICATE.json b/research/e8-rank138-idle-hosting/CERTIFICATE.json
new file mode 100644
index 0000000000..79f353344d
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/CERTIFICATE.json
@@ -0,0 +1,116 @@
+{
+  "status": "PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY",
+  "kappa": "623036752743971/500000000000000000",
+  "kappa_decimal": "0.001246073505487942",
+  "bit_lower": "1247628141860215921989/1000000000000000000000000",
+  "complex_lower": "1267453159029119/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr434_percent": 9.97024959309606,
+  "bit": {
+    "live": 37464,
+    "physical": 37473,
+    "maxchild": 8,
+    "rank_mass": 2387712,
+    "hosted_residuals": 159168,
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 286,
+    "charged_two_level_coefficient_bits": 320,
+    "row_coefficient": 18355
+  },
+  "complex": {
+    "live": 8400,
+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
+  },
+  "strict_outer_constraints": {
+    "bit_positive": "76149178580335444178934016814246485348104726063359519287252627776452954618443174044033128392250851780720284666136895050656759211998894561371080237426335078260687/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "1210023020562932285909733185753514651895273936640480712747372223547045381556825955966871607749148219279715333863104949343240788001105438628919762573664921739313/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "29982546840970881/1000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "1210023020562932208550531584855138187051523936640480712747372223547045381556825955966871607749148219279715333863104949343240788001105438628919762573664921739313/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_positive": "38074589290167722013317829826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313/30517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_internal": "76149178580335444178934016814246485348104726063359519287252627776452954618443174044033128392250851780720284666136895050656759211998894561371080237426335078260687/30517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_leaf": "605011510281466180424444372763013272459778782566725704478412175133041978031040754436390422317748153672986059182404255391905060137447769971219093285727022240736737426335078260687/30517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_positive": "38074589290167729642712361076787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313/30517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_below_one": "30479503535709832270357287638923212201504881653782566725704478412175133041978031040754436390422317748153672986059182404255391905060137447769971219093285727022240736737426335078260687/30517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_reservations": "1/4000000000000000000",
+    "lambda_above_tau": "76149178580335444178934016814246485348104726063359519287252627776452954618443174044033128392250851780720284666136895050656759211998894561371080237426335078260687/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_sigma": "1210023020562932362058911766088958830829290750886966060852098286906564668809453732419826226192322263312843726113956730063525454138000489285678974572559483110393237426335078260687/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_internal": "76149178580335444178934016814246485348104726063359519287252627776452954618443174044033128392250851780720284666136895050656759211998894561371080237426335078260687/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_prime_above_lambda": "76149178580335444178934016814246485348104726063359519287252627776452954618443174044033128392250851780720284666136895050656759211998894561371080237426335078260687/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_leaf": "605011510281466180424444372763013272459778782566725704478412175133041978031040754436390422317748153672986059182404255391905060137447769971219093285727022240736737426335078260687/30517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_reservations": "1/4000000000000000000",
+    "lambda_prime_below_one": "38074589290167722013317829826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313/30517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "epsilon_positive": "30517578124999999969482421875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/30555652714290167722013317829826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313",
+    "epsilon_below_one": "38074589290167752530895954826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313/30555652714290167722013317829826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313",
+    "guard_width": "38074589290167752530895954826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313/30555652714290167722013317829826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313",
+    "K_geometry": "22926258183040167729642712361076787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313/30555652714290167722013317829826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313000000000000000000",
+    "K_dominates_log": "1228212557747346116278637799568389317819547907762757283883975535723667216982173271635375856635912664540754979455978835428421967711127628561957611833926475733241366318044901418711281852462421879377/985666216590005410387526381607315735435326398265078492719210373800802159936192547072437535792828459736978290772284438572406712739995566200968670351829492676701911718147537578120623000000000000000000",
+    "record_suffix": "38074589290167752530895954826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313/30555652714290167722013317829826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313",
+    "phase_local": "304596714321341989691514924324134665947628939912678395869054356381502389880230086139641918599489055525052501948858514110537745578082822095622152313851631592045325193875046396155240737426335078260687/244445221714321341776106542638614302387960946769739466194364172702598935664175751673964508876621458014770616111526540765956864759518900417840230247253714183822074106100589319373914504000000000000000000",
+    "phase_boundary": "60919342864268373493780813432692755578871524121105440377716194302353858539628746968034817302322643708559612727625901345045937962962487823437954510880284534386040313403590897023637537426335078260687/48889044342864268355221308527722860477592189353947893238872834540519787132835150334792901775324291602954123222305308153191372951903780083568046049450742836764414821220117863874782900800000000000000000",
+    "gamma_sublinear": "1/2000000000000000000",
+    "cell_above_band": "61035156249999999908409191035709832277986682170173212201504881653782566725704478412175133041978031040754436390422317748153672986059182404255391905060137447769971219093285727022240736737426335078260687/122222610857160670888053271319307151193980473384869733097182086351299467832087875836982254438310729007385308055763270382978432379759450208920115123626857091911037053050294659686957252000000000000000000",
+    "prime_interval_packing": "38074589290167752530895954826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313/30555652714290167722013317829826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313",
+    "alpha_positive": "76149178580335474506139195363407874976918862608078750095924829432300641748416330666260261133395544447090418303952939642889175938907508715449466873565993725489745618433056865719362737426335078260687/61111305428580335444026635659653575596990236692434866548591043175649733916043937918491127219155364503692654027881635191489216189879725104460057561813428545955518526525147329843478626000000000000000000",
+    "alpha_below_one": "61035156249999999969520496464290167722013317829826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313/61111305428580335444026635659653575596990236692434866548591043175649733916043937918491127219155364503692654027881635191489216189879725104460057561813428545955518526525147329843478626000000000000000000",
+    "alpha_below_one_fourth": "15201677178564748386500519719549986024270640310500637887051835964480132837262568148956521543655445581476073088666455858229414871531023767399564923579791142763389886012853775595150293762573664921739313/61111305428580335444026635659653575596990236692434866548591043175649733916043937918491127219155364503692654027881635191489216189879725104460057561813428545955518526525147329843478626000000000000000000",
+    "delta_positive": "1/8000000000000000000",
+    "delta_below_one_eighth": "999999999999999999/8000000000000000000",
+    "short_record_fallback": "1860318361375777835971716568804910774470137061740509136531467936075974298045185231681041481622566244818294714959773011087729104800121343747530183249547614769575520090772329979864591831490202963442824158881097379776855533337218759204748132801963088395741865976055068446531008216776203112366217673904999457051939926327280789302456684109025129711969/1864969037737436994751789418324388903716743063123622636370576268788138852418333066360202857029887832754292420284473730209021490169669345228883592584638322325302689408116068415633502990722656250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "small_field_exposure": "1/1000000000000000000",
+    "artificial_boundary": "1711421148714570734544659924251784922269727527647396092950398736659443785136292578155190671887037570995901619720945372883193899117973656129955666262849301127266679191524857373924593821787720994765217939/244445221714321341776106542638614302387960946769739466194364172702598935664175751673964508876621458014770616111526540765956864759518900417840230247253714183822074106100589319373914504000000000000000000",
+    "literal_scalar_guard": "1",
+    "row_product_gap": "23971789/25",
+    "balanced_prefix_above_kappa": "26676886390601640958575817478941199504343613257003698277665410697642142066198541569477104007541924888402338313813423324686146058481989370871091578007284269104667359512172277305568077/15277826357145083861006658914913393899247559173108716637147760793912433479010984479622781804788841125923163506970408797872304047469931276115014390453357136488879631631286832460869656500000000000000000",
+    "coordinate_movement_above_kappa": "94887473893671717996516814246485348104726063359519287252627776452954618443174044033128392250851780720284666136895050656759211998894561371080237426335078260687/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_phase_layer_above_kappa": "22798120066913114195138317128055611210192108167789963281035299807459417174375114179708644405506167524958349613686029053627684022024116189512154375107854265231575455761770889689396841/30555652714290167722013317829826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313000000000000000000",
+    "bulk_exposure_above_kappa": "94887473893671717996516814246485348104726063359519287252627776452954618443174044033128392250851780720284666136895050656759211998894561371080237426335078260687/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "Gaussian_arithmetic_above_kappa": "274051918678175416727146490513925253077022220380972006071168963223149938269066820315405846072782386955205777951310685216255296461012517172787321343582976940785881435881888112280392667/244445221714321341776106542638614302387960946769739466194364172702598935664175751673964508876621458014770616111526540765956864759518900417840230247253714183822074106100589319373914504000000000000000000",
+    "scalar_work_above_kappa": "396274529535336087615199761833232404271002693765841739168351049574449406101154696152388100511093115962591086007073955599233728840771967381707436467209834032696918488932182771967349919/244445221714321341776106542638614302387960946769739466194364172702598935664175751673964508876621458014770616111526540765956864759518900417840230247253714183822074106100589319373914504000000000000000000",
+    "dimension_above_kappa": "15239751767854916135152649350688247059328258305832482867195852463091264798654426218019360261409700443553940500571516090530034266343492048571131668028632234382211946375997436643797703012172277305568077/15277826357145083861006658914913393899247559173108716637147760793912433479010984479622781804788841125923163506970408797872304047469931276115014390453357136488879631631286832460869656500000000000000000"
+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "94287020424277834163680254991104056367009/62500000000000000000000000000000000000000000000",
+      "cutoff_log2": "15818260083840"
+    },
+    {
+      "gap": "29408785023369495427727557576784775208283541746515592160223473/15625000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "10162215197593843554"
+    },
+    {
+      "gap": "9172806953268257565007102287437866302700738375134023268194695915019528111703606081/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "6528569967547151436395053"
+    },
+    {
+      "gap": "2861063023687136162665647272462448282050413362534253607940694932308513294882957767367031894837944602257/976562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "4194186502884772884117694502077"
+    },
+    {
+      "gap": "892385685996938155756805007131692738674820820957983219861627580057577912447454106275234926512117420246977622028593300181729/244140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "2694495197022448340895066350774684894"
+    },
+    {
+      "gap": "278341373810753514651895273936640480712747372223547045381556825955966871607749148219279715333863104949343240788001105438628919762573664921739313/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1731039943451104430442680727076306832163430"
+    }
+  ],
+  "bit_template_sha256": "50d9302688535aee7196ddba537c99620195b39ec096b3cfde8c2d6b2e691ef7",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f"
+}
diff --git a/research/e8-rank138-idle-hosting/EXPECTED.json b/research/e8-rank138-idle-hosting/EXPECTED.json
new file mode 100644
index 0000000000..2906256d6b
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/EXPECTED.json
@@ -0,0 +1,33 @@
+{
+  "kappa": "623036752743971/500000000000000000",
+  "kappa_decimal": "0.001246073505487942",
+  "bit_lower": "1247628141860215921989/1000000000000000000000000",
+  "complex_lower": "1267453159029119/1000000000000000000",
+  "binding_component": "bit",
+  "bit": {
+    "live": 37464,
+    "physical": 37473,
+    "maxchild": 8,
+    "rank_mass": 2387712,
+    "hosted_residuals": 159168,
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 286,
+    "charged_two_level_coefficient_bits": 320,
+    "row_coefficient": 18355
+  },
+  "complex": {
+    "live": 8400,
+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
+  },
+  "bit_template_sha256": "50d9302688535aee7196ddba537c99620195b39ec096b3cfde8c2d6b2e691ef7",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f"
+}
diff --git a/research/e8-rank138-idle-hosting/INHERITED-HOSTING-PROOF.md b/research/e8-rank138-idle-hosting/INHERITED-HOSTING-PROOF.md
new file mode 100644
index 0000000000..ff3eba6770
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/INHERITED-HOSTING-PROOF.md
@@ -0,0 +1,109 @@
+# Idle-axis hosting: helper residuals on pending idle coordinates
+
+This package changes only the global nine-stage templates of #434's two suppliers. Both local words are unchanged:
+
+- the complex word is #433's split-centre word, R = 560, m = 73;
+- the bit word is #434's early-reset kernel word, R = 747, m = 64.
+
+So are their local programs, scalar replays, data routes, bridges, terminal exchange and cover correction. What
+changes is where whole dirty-helper residuals live. Many of them move from bank streams onto coordinates of *idle*
+data families that would otherwise be advanced later by an idle child.
+
+## 1. The two inherited facts used
+
+**(a) Dirty invocations act on a helper stream as its residual.** The complete dirty local invocation is block
+diagonal on helpers at its endpoint and admits arbitrary correlated helper values (#425/#433, #386/#434). On the
+physical stream that owns a helper residual of width w, it acts as an exact coordinate factor on w coordinates:
+
+- complex: P_g C_block P_g⁻¹ (PR425-COMPLEX §5, INHERITED-COMPLEX-GEOMETRY);
+- bit: D_P with P the width-w coordinate projector (PR386-BIT-GEOMETRY; mixed widths 8 − entrance rank, #434).
+
+This holds whatever the stream held before. Banks rely on exactly this: eight sequential residuals and a pad tile a
+bank stream.
+
+**(b) An idle child is a product of coordinate factors.** Advancing a data pair from level a to level b applies, on
+every physical data stream (F, g) of that pair, the commuting product of coordinate factors on its pending set S:
+
+- complex: C over S, in the basis U_q ⊕ I used by the inherited idle factorisation;
+- bit: D_{P_V−P_U}, an orthogonal coordinate projector difference.
+
+Factors on disjoint coordinate sets commute and multiply:
+
+- complex: C_{S'}·C_{S∖S'} = C_S;
+- bit: D_{P'}·D_{P−P'} = D_P for P' ≤ P (the parent's identity D_I·D_P = D_{I−P}).
+
+## 2. Hosting lemma
+
+Fix a data family F (replica r, pair j, side, port) and an idle child Γ that advances pair j at recipe position τ.
+Let λ be the position of the last local invocation or bridge that names pair j before τ; idle children do not
+count as touches, since they act on other coordinates or on the other member. Let ι be any local invocation with
+λ < ι < τ. Then:
+
+1. ι is an invocation on another pair, and nothing touches F between ι and τ.
+2. A helper residual of ι, of width w, may be owned by stream (F, d·σ⁻¹) instead of a bank slot. Here d is the
+   invocation's cover class, and σ is a coordinate isometry carrying the local residual block onto a set S' ⊂ S of
+   w pending coordinates. When S' meets the local block of a level −1 advance, σ is composed with U_q ⊕ I.
+3. Γ is replaced by Γ' acting on S ∖ ⋃S' over all hosted residuals of F, which have pairwise disjoint S'.
+
+The complete program's operator is unchanged:
+
+- By (a), ι applies exactly the factor on S' to (F, d·σ⁻¹), for any prior contents.
+- Nothing else acts on F between ι and τ, so this factor may be moved to τ.
+- By (b), the moved factors times Γ' equal Γ.
+
+Distinct slots of one invocation have distinct σ, so distinct physical classes for every d. They are also disjoint
+from the invocation's own data owners, because pair j is not active, and from bank owners, because the families
+differ. Residuals of different invocations on F occupy disjoint coordinates. They are sequential, exactly as the
+parent's banks are co-owned sequentially by different cover classes.
+
+Two further points:
+
+- **Phases.** The stored Z₄ translations after Γ remain valid, because Γ'·∏(hosted factors) = Γ as exact operators.
+  The final X_δ(g) correction still applies to every live family; hosting changes no data endpoint.
+- **Reflection.** The inverse-transpose program reverses chronology and reflects each factor. The window condition
+  (no touch strictly between ι and τ) is symmetric, so hosting commutes with reflection.
+
+## 3. What is checked here
+
+- `bit_hosted.py` and `complex_hosted.py` read #434's freshly regenerated templates and compute windows from each
+  recipe. They apply a frozen integer-programme selection (`SELECTION.json`; `--discover` recomputes it with scipy)
+  and emit new owners, remainder children and banks.
+  - Bit: unhosted residuals keep an exact width-64 tiling with no padding.
+  - Complex: eight per bank plus one paid pad; a final partial bank pays the larger pad.
+- `audit.py` shares no code with the generators. It re-derives every window from the template schedule. For every
+  replica and invocation it checks that:
+  - each helper has exactly one owner;
+  - each hosted slot is inside its child's pending set, disjoint from other slots, outside the active pair, and in
+    window;
+  - every remainder child is exact, and the bank tiling is exact.
+
+  It also recomputes the paid profile and the rank deficit 2496, and rejects nine mutations.
+- `assemble.py` prices both suppliers with the two inherited rational moment engines and recomputes both finite
+  invoices with the hosted stock. Route charging is conservative: two extra route factors per helper selector, and
+  the parent's larger complex per-vertex bill is kept. It then runs #434's strict outer assembly: six bootstrap
+  levels and 47 inequalities. The next grid point and the zero-η, zero-β and unit-β controls are rejected.
+
+## 4. Result
+
+| | live stock | max child | hosted residuals | certified saving |
+| --- | ---: | ---: | ---: | --- |
+| bit | 14,259 → 9,457 | 42 → 8 | 39,568 of 53,784 | c = 1239085165241180038597/10²⁴ |
+| complex | 12,720 → 8,400 | 48 → 8 | 34,560 of 40,320 | b = 1267453159029119/10¹⁸ |
+
+κ = 618775866623647/(5·10¹⁷) ≈ 1.237551733247294·10⁻³, bit-bound, +9.218% over #434.
+
+## 5. Scope
+
+This is a written finite extension of the inherited correlated dirty-bank and compressed-window interfaces. The
+streams that own residuals now include data streams during idle windows. It is the principal new review point.
+
+All other interfaces remain inherited assumptions: the all-size compiler, restored-work, tape/common-grid, precision
+and analytic interfaces.
+
+No Lean proof and no unconditional integer-multiplication theorem is claimed. The global operator identity is argued
+from (a) and (b) and checked combinatorially. It is not replayed numerically on the 2⁷³- and 2⁶⁴-point address
+spaces; neither parent does that either.
+
+## R740 composition and additional scope
+
+The above argument is inherited from PR442 and remains an explicit additional hosting assumption. Here the bit local word has R740 and matches PR441 after two joint B-frame sweeps. The assignment is regenerated for its actual residual-width census, rather than transferred by helper index. Parent residual isometries remain checked, and the finite selector invoice retains the parent extra-helper-route bound of 144 in addition to the two hosting factors. All host windows, owners, disjoint intervals, remainders and bank coverage are independently rechecked. Original PR442 numerical values above describe its historical R747 construction; EXPECTED.json and CERTIFICATE.json describe this R740 composition.
diff --git a/research/e8-rank138-idle-hosting/LICENSE b/research/e8-rank138-idle-hosting/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
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+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
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+      of this License, Derivative Works shall not include works that remain
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+      the Work and Derivative Works thereof.
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+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
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diff --git a/research/e8-rank138-idle-hosting/MANIFEST.json b/research/e8-rank138-idle-hosting/MANIFEST.json
new file mode 100644
index 0000000000..a8cc841d35
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/MANIFEST.json
@@ -0,0 +1,200 @@
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+}
diff --git a/research/e8-rank138-idle-hosting/NOTICE.md b/research/e8-rank138-idle-hosting/NOTICE.md
new file mode 100644
index 0000000000..62327dd3e1
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/NOTICE.md
@@ -0,0 +1,7 @@
+# Attribution and scope
+
+Rohan Arun with substantial OpenAI Codex assistance: composition of the rank-138 kernel with idle-data hosting, frozen assignment, standard-library wrapper, replication-aware emitter, independent audit and fresh invoice.
+
+Credit chafreaky PR443 for the rank-138 local word and 32-replica admission, PR417/PR439 kernel and residual routes; eumemic PR436/PR440/PR441 for R740 and joint retiming; PR442 for idle-data hosting with disclosed Claude assistance; and Rohan Arun PR434/PR435/PR438, icekylinx PR433, the retained PR426/PR389/PR376/PR370, PR425/PR386 and Jacob Sussman lineage. All upstream licenses, notices and source-specific disclosures remain in upstream443 and the sibling pinned parent. Apache-2.0.
+
+The immutable upstream443 source is pinned to 5a514e94f156edcc5fd827b87494d962f79d0f6c. Its shell wrapper is retained for provenance; our Python wrapper avoids its unquoted-space-path failure and independently reconstructs the bit program using the retained exact audit code. Its upstream full shell wrapper was not passed locally. The unchanged complex supplier is replayed by our parent wrapper rather than merely cited.
diff --git a/research/e8-rank138-idle-hosting/PROOF.md b/research/e8-rank138-idle-hosting/PROOF.md
new file mode 100644
index 0000000000..a0c76b3056
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/PROOF.md
@@ -0,0 +1,11 @@
+# Rank-138 kernel with idle-data hosting
+
+Use PR443's exactly pinned local word, reconstructed by its unchanged rebuild.py: 57 A-frame changes, 114 pivots of total entrance rank 138 and 103 donor slots, followed by the two PR441 B-frame witnesses. All local scalar columns and integer source spans are checked. The complete local frame family is identical to the already checked R740 parent.
+
+Repeat the nine-stage identity with 32 independent bit replicas, as in PR443. The unhosted residual coordinates partition 2,891 banks per stage, with no padding. The emitter checks all 7,620 columns of the one-replica global identity and emits every one of 288 local invocations and 213,120 helper assignments. The independent audit reconstructs all local records, exact projector inclusions, reflected streams, data owners and bank intervals. Explicit rational residual isometries and the conservative inherited extra route-factor bound of 144 are retained.
+
+Apply the frozen hosting assignment using PR442's additional idle-data hosting extension. The independent hosting audit re-derives windows, disjoint intervals, owners, remainders and all complete remaining banks. The bit construction has 37,464 live families, 37,473 physical families, 159,168 hosted residuals and rank deficit 9,984. The complex construction stays at eight replicas, 8,400 live families and deficit 2,496. Different suppliers may have different replication counts; each supplies its own certified exponent and finite invoice.
+
+Two rational moment engines certify both suppliers. The bit invoice is recomputed with 32 replicas everywhere, including local invocations, bridge additions, helper routes, copy/erase episodes and physical stock. Prefix/coefficient charges and the two extra hosting route factors are explicit. Six bootstrap levels and all 47 strict outer inequalities produce the stated kappa, rejecting the next grid point.
+
+The hosting operator extension is inherited as an additional mathematical assumption, not proved by the finite interval audit. See INHERITED-HOSTING-PROOF.md for the original PR442 argument, with its historical parameters. All-size compiler, dirty-bank/compressed-window, restored-work, tape/common-grid, precision and analytic interfaces remain conditional. No unconditional theorem or new Lean proof is claimed.
diff --git a/research/e8-rank138-idle-hosting/README.md b/research/e8-rank138-idle-hosting/README.md
new file mode 100644
index 0000000000..b37f1acbf5
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/README.md
@@ -0,0 +1,9 @@
+# Rank-138 idle-data hosting
+
+Conditional kappa = 0.001246073505487942, 0.06266595% above the preceding hosted PR434 result and 0.68859927% above PR442.
+
+Composes PR443's rank-138 kernel / 32 bit replicas with PR442's idle-data hosting. The bit side binds. The extra hosting operator assumption remains explicit; finite combinatorial checks do not discharge it.
+
+Run `python -B research/e8-rank138-idle-hosting/verify.py /absolute/new/output`. Python 3.11 or newer; standard library only for replay. The wrapper freshly rebuilds the full R740 and complex parent, including every selected Gaussian phase, reconstructs the pinned PR443 word, emits and audits all 32 bit replicas, then regenerates and audits both hosted suppliers and strict assembly.
+
+Full uninterrupted Python 3.11.15 and 3.14.8 wrappers PASS at commit `d21614a4e458b99d1d897eebb6c30370f9aa06f1`. Both replay all nine top-level stages including the full parent. Exact tested manifest, terminal receipts, parent receipts, audits and logs are in `local-evidence/`. GitHub CI remains pending. Code and frozen witnesses are unchanged by this evidence update. PR444 independently reports the same bound. This shared numerical lead uses the additional hosting extension and must not be presented as a stronger result under only the pre-hosting assumptions. Research and failure evidence are preserved. The inherited `gain_over_pr434_percent` field in CERTIFICATE.json refers to the historical pre-hosting baseline 566550276142217/500000000000000000; the comparisons above use the immediately preceding hosted result.
diff --git a/research/e8-rank138-idle-hosting/SOURCE442-PINS.json b/research/e8-rank138-idle-hosting/SOURCE442-PINS.json
new file mode 100644
index 0000000000..d47fc03335
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/SOURCE442-PINS.json
@@ -0,0 +1,70 @@
+{
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+  "files": [
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+    },
+    {
+      "path": "research/idle-axis-hosting/LICENSE",
+      "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64",
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+      "git_blob": "4468a00349b4f68dce103e785a8392099435e1d6",
+      "sha256": "cfe34bf0b64259661312dae22c3a23adc5bf6f6326951eee5c1488ccfc347542"
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+      "git_blob": "9d9b80cc3bff337db6f3f0c7c70a57efe8532d82",
+      "sha256": "1151f74cad54ac4937282b7a8b5d1108ed4ce35944ef9b7bb7d17abfce1fe4a0"
+    },
+    {
+      "path": "research/idle-axis-hosting/SELECTION.json",
+      "git_blob": "e3303cd97d132e66145d2fb7e957fd6e5808dd80",
+      "sha256": "315d54be472842707cce879618be477d8b897050e873bc136d114eec6a232f97"
+    },
+    {
+      "path": "research/idle-axis-hosting/assemble.py",
+      "git_blob": "f07a59864346dc622aa5c8d3619473c53ba529d8",
+      "sha256": "f9a2e6a42aadcf971702a5a867760a092566ed03356f4f34387d38f4093ad1a6"
+    },
+    {
+      "path": "research/idle-axis-hosting/audit.py",
+      "git_blob": "bd40b9b7914deeced02d5364162060d8130ab08e",
+      "sha256": "38594423a401110bd430b734037c6ecba422ee6a94d71709984e0afa9cd1edf8"
+    },
+    {
+      "path": "research/idle-axis-hosting/bit_hosted.py",
+      "git_blob": "e2f015dbb78a95c121e187b3c20e0f8d59b60586",
+      "sha256": "6dfbf26213e8adf87563b3575cfb722bd07ecd65627f056b3293411dd3d89a61"
+    },
+    {
+      "path": "research/idle-axis-hosting/complex_hosted.py",
+      "git_blob": "56e15c15aeebf571e60ab2c89e55e4624ecac2d3",
+      "sha256": "829c5c4f4bdfccedadd31505f1f0a394f7a208d1446b7bbf9cc92d3aa1530c0c"
+    },
+    {
+      "path": "research/idle-axis-hosting/hosting_core.py",
+      "git_blob": "68b536daa9e6546c0aa046934bf840aaa3c3fde3",
+      "sha256": "d8b90cd5d152df3c7c351230863d9e61816ad5e1f21d69bea1a86a5daad559a3"
+    },
+    {
+      "path": "research/idle-axis-hosting/verify.py",
+      "git_blob": "0aa6cefd0237146967f8e26c540c99e3afca2ffc",
+      "sha256": "737a974d79fdd232b6c4b9e059c56835079971447342ed7ca3b82a614e30cb53"
+    }
+  ]
+}
diff --git a/research/e8-rank138-idle-hosting/SOURCE443-PINS.json b/research/e8-rank138-idle-hosting/SOURCE443-PINS.json
new file mode 100644
index 0000000000..f668d2b93d
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/SOURCE443-PINS.json
@@ -0,0 +1,42 @@
+{
+  "head": "5a514e94f156edcc5fd827b87494d962f79d0f6c",
+  "files": {
+    "EXPECTED.json": {
+      "sha256": "02f3fd3ac40f17f25822fa49d01ae6e84c2e02e2fafbf24f02845f24e02ec931",
+      "git_blob": "bab80135968c7f27931d297dd1de7aa46e208af2"
+    },
+    "PROOF.md": {
+      "sha256": "380a5269e012cb7d54cdf13289b7187aa82c16d23ed1689c5986485398f5cdca",
+      "git_blob": "ae1ad94af0f62456d6fb424da4ff0166d5bf3c6c"
+    },
+    "code/replica_kernel.py": {
+      "sha256": "780e08ad63983d0256271e8c7803c74bb1623d15cc202d98177c440ff3726aad",
+      "git_blob": "b61f1d98f27b0dd1d5ca8ad2c0bcf88b1d9094fa"
+    },
+    "code/global_kernel.py": {
+      "sha256": "01cf4be0ab9affe48598062c4ae3610882aa77a9e18e75c4e596e2f08d8b2173",
+      "git_blob": "72856bf507250ee0ce83fcbba5698c5283387858"
+    },
+    "code/rebuild.py": {
+      "sha256": "3efb6c81a247ac6d5cab87c47030a332292c2c46d482ff996588858f41cdad4d",
+      "git_blob": "f7239ea69f1de840100e249846ea139607fa2f6b"
+    },
+    "code/config.py": {
+      "sha256": "283d7fad45155ee91e704d63ec947cf4a60aeff5cc43510bc0e835f7da7d8767",
+      "git_blob": "c6824d9c4ea37d58c0d24cb7a3021c4dfcc6f3bb"
+    },
+    "data/selection.json": {
+      "sha256": "1a96e47f1889bc690316f95a3858b0062ce212ea876dd15e5123ed89d09a9c39",
+      "git_blob": "ef068005b1422ac3cc459232e20108b74568122a"
+    },
+    "data/word.json.gz": {
+      "sha256": "d8d6d3d3f336720302bc40b3c1504fe3c3583a7a8d707bb9bd7b21f85e5e69c6",
+      "git_blob": "85390b07e4747feddbf2e16f94b5e0a8a308c191"
+    },
+    "MANIFEST.json": {
+      "sha256": "11f8fc7eb52127b078c1d29029ba71a2e1bd3340e9f4d76c92fae1e22511d550",
+      "git_blob": "5b72d8bc17fc7e473331ac95373302e1c7c291f8"
+    }
+  },
+  "manifest_files_verified": 117
+}
diff --git a/research/e8-rank138-idle-hosting/VALIDATION.json b/research/e8-rank138-idle-hosting/VALIDATION.json
new file mode 100644
index 0000000000..70aeb0e1f9
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/VALIDATION.json
@@ -0,0 +1,17 @@
+{
+  "status": "FULL_LOCAL_PYTHON_311_AND_314_PASS_CI_PENDING",
+  "kappa": "0.001246073505487942",
+  "bit_replicas": 32,
+  "complex_replicas": 8,
+  "source443_head": "5a514e94f156edcc5fd827b87494d962f79d0f6c",
+  "gain_over_previous_hosted_percent": 0.06266594866801468,
+  "gain_over442_percent": 0.6885992732026771,
+  "tested_commit": "d21614a4e458b99d1d897eebb6c30370f9aa06f1",
+  "tested_manifest_sha256": "cf742207a00951e991a3ed667ee015449dedcd3fc41f3f857f36ed60a77fa7a8",
+  "full_receipts": {
+    "311": "local-evidence/full311/RECEIPT.json",
+    "314": "local-evidence/full314/RECEIPT.json"
+  },
+  "comparison_scope": "PR434 and PR444 tie at this kappa under the additional PR442 hosting extension. This is not a stronger bound under only the pre-hosting assumptions.",
+  "publication_change": "Documentation and evidence only; all executable code, frozen witnesses, upstream files and parent manifest are byte-identical to the tested versions."
+}
diff --git a/research/e8-rank138-idle-hosting/code/SELECTION.json b/research/e8-rank138-idle-hosting/code/SELECTION.json
new file mode 100644
index 0000000000..8dc4956837
--- /dev/null
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diff --git a/research/e8-rank138-idle-hosting/code/assemble.py b/research/e8-rank138-idle-hosting/code/assemble.py
new file mode 100644
index 0000000000..a6fd3e0926
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/code/assemble.py
@@ -0,0 +1,82 @@
+"""Two exact moments for both hosted suppliers, fresh finite invoices with the hosted stock, and the strict outer
+assembly of #434 (six bootstrap levels, 47 inequalities, next-grid and parameter controls).
+usage: assemble.py PARENT_CHANGED_DIR BIT_DIR COMPLEX_DIR AUDIT.json OUT.json"""
+import gzip, hashlib, importlib.util, json, math, sys
+from fractions import Fraction as Q
+from pathlib import Path
+par, bd, cd, ap, outp = map(Path, sys.argv[1:6])
+def load(name):
+    sp = importlib.util.spec_from_file_location('hosted_' + name, par / 'work/pr361/code/engines' / (name + '.py'))
+    mod = importlib.util.module_from_spec(sp); sp.loader.exec_module(mod); return mod
+M, Other, Outer = load('moment'), load('base_two_moment'), load('outer')
+audit = json.loads(ap.read_text()); bg = json.loads((bd / 'GLOBAL.json').read_text()); ch = json.loads((cd / 'HOSTED.json').read_text())
+assert audit['bit_template_sha256'] == bg['template_sha256'] and audit['complex_template_sha256'] == ch['template_sha256']
+# ---------------- bit: two moments and the parent's invoice formulas with the hosted stock
+P = {int(r): n for r, n in audit['bit_profile'].items()}; m, W = 64, audit['bit_live']; E = sum(P.values())
+geo = json.loads((par / 'bit426-source-centres/global/GEOMETRY.json').read_text())
+pg = json.loads((par / 'bit426-source-centres/global/GLOBAL.json').read_text())
+T, L, R, V, K = pg['replicas'], 9, pg['R'], 120, 4
+mass = sum(r * z for r, z in P.items()); assert m * W - mass == 312*T
+physical = W + 9; d = m * m; N = 2 * m
+unit = L * T * pg['local_additions'] + pg['bridge_additions']
+J = 8 * T * L * (2 * V + R) + 8 * (2 * K * V * T) + 2 * L * T * R + 2 * pg['copy_erase_episodes']   # every helper route charged (bank or hosted)
+high = 16 * (d + 1) ** 2; good = 8 * m * m + 8; compiler = 128 * N ** 3
+selectors = 2 * L * T * ((W - 1) + R * m * (geo['max_route_factors'] + pg.get('extra_helper_route_factor_bound', 0) + 2 + (m - 1) + m))   # +2: hosted route may add a slot permutation and U_q
+prefix = int(pg['global_prefix_bound']); charged_prefix = 64 * ((prefix.bit_length() + 63) // 64)
+coefficient = unit + J * high + J * physical + E * (good + compiler) + 16 * m ** 3 + pg['copy_erase_episodes'] + selectors + prefix + 1
+two = (coefficient + 1) ** 2 * (E + 1) ** 2; charged_two = 64 * ((two.bit_length() + 63) // 64)
+assert two < 1 << charged_two and 2 * max(P) ** 2 < m * m
+row = 2 * (m * m + 1) + 9909 + 252; assert row == 18355 < 20161
+root = M.certify(P, m, W, True); c = Q(root['lower']); chi = Q(root['upper'])
+fb = 32 * m * m * E
+lo, hi = Other.moment(m, W, list(P.items()), c); bl, bh = Other.moment(m, W, [(1, fb)], c); assert hi + bh / 10 ** 16 < 1
+lo2, hi2 = Other.moment(m, W, list(P.items()), chi); bl2, bh2 = Other.moment(m, W, [(1, fb)], chi); assert lo2 + bl2 / 10 ** 16 > 1
+# ---------------- complex: two moments and the parent's invoice with the hosted stock
+PC = {int(r): n for r, n in audit['complex_profile'].items()}; mc, WC = 73, audit['complex_live']; EC = sum(PC.values())
+massc = sum(r * z for r, z in PC.items()); assert mc * WC - massc == 2496
+rc = M.certify(PC, mc, WC, True); b = Q(int(Q(rc['lower']) * 10 ** 18), 10 ** 18)
+fbc = 32 * mc * mc * EC
+l3, h3 = Other.moment(mc, WC, list(PC.items()), b); b3, bh3 = Other.moment(mc, WC, [(1, fbc)], b); assert h3 + bh3 / 10 ** 16 < 1
+integ = json.loads((par / 'split-centres/INTEGRATION.json').read_text()); inv = integ['finite_invoice']
+physc = ch['physical']; Rc = 560; v = 120
+compilerc = 64 * (mc + 1) ** 3
+pervertex = inv['pervertex'] - integ['physical'] * (64 + 1) + physc * (64 + 1) - integ['live'] + WC   # stock-dependent terms re-based
+r_ = mc // 2; group = 2 ** (r_ * r_) * math.prod(2 ** (2 * i) - 1 for i in range(1, r_ + 1)); stock = group * physc
+smass = group * massc; logical = group * max(pervertex, inv['pervertex']) + 64; router = compilerc * (logical + 1) * (stock + 1) ** 2
+GG, EE, C0 = 1 << 30000, 1 << 100000, 1 << 210000; BB = smass + EE
+literal = 2 * GG * stock ** 2 + 8 * smass + 4 * stock + 4 + 32 * mc
+assert logical < 1 << 6050 and router < GG and literal < EE and BB < 1 << 100001 and 32 * mc * BB * BB < C0 and 2 * BB + 18 < C0
+depth = 2; assert mc ** depth > 2 * max(PC) ** depth
+rowc = depth * stock.bit_length() + 9909 + 252; assert rowc < 20161
+# ---------------- outer assembly exactly as #434's combined.py
+eta = beta = Q(1, 10 ** 18); grid = Q(1, 10 ** 18); s = min(c, (1 - beta) * b) - Q(1, 10 ** 24)
+assert 0 < s < c and s < (1 - beta) * b
+chain = [Q(384599, 10 ** 10)]; cutoffs = []
+def ceil(x): return -((-x.numerator) // x.denominator)
+for j in range(6):
+    old = chain[-1]; a = (1 - s) * s + s * old
+    gap = min(s - a, 1 - a - s, 1 - a - s * (1 - old), 1 - s); assert old < a < s < 1 - a and gap > 0
+    cutoff = max(ceil(36 / gap ** 2), ceil(2 * (4 + charged_two) / gap)); assert cutoff * gap ** 2 >= 36 and cutoff * gap >= 2 * (4 + charged_two)
+    cutoffs.append(dict(gap=str(gap), cutoff_log2=str(cutoff))); chain.append(a)
+q = chain[-1] * (1 - 2 * eta); margin = (1 - eta) * q / (1 + q); ticks = margin / grid; k = grid * ((ticks.numerator - 1) // ticks.denominator)
+bridge = {'semantic': {'C0': {'base': 2, 'exponent': 210000}, 'strict_literal_gap': 1}, 'rows': {'degree_gap': Q(10 ** 6) - Q(51 * 20161, 25)}}
+a = Outer.assembly(chain[-1], b, bridge, k, eta=eta, beta=beta)
+assert len(a['strict_constraints']) == 47 and all(x > 0 for x in a['strict_constraints'].values())
+controls = []
+for name, kk, ee, bb in [('next_grid', k + grid, eta, beta), ('zero_eta', k, Q(0), beta), ('zero_beta', k, eta, Q(0)), ('unit_beta', k, eta, Q(1))]:
+    try: Outer.assembly(chain[-1], b, bridge, kk, eta=ee, beta=bb)
+    except AssertionError: controls.append(name)
+    else: raise AssertionError(name)
+parent_k = Q(566550276142217, 500000000000000000)
+res = dict(status='PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY', kappa=str(k), kappa_decimal=format(float(k), '.18f'),
+           bit_lower=str(c), complex_lower=str(b), binding_component='bit' if c < (1 - beta) * b else 'complex',
+           gain_over_pr434_percent=float(100 * (k / parent_k - 1)),
+           bit=dict(live=W, physical=physical, maxchild=max(P), rank_mass=mass, hosted_residuals=audit['bit_hosted_residuals'],
+                    prefix_bits=prefix.bit_length(), charged_prefix_bits=charged_prefix, coefficient_bits=coefficient.bit_length(),
+                    two_level_coefficient_bits=two.bit_length(), charged_two_level_coefficient_bits=charged_two, row_coefficient=row),
+           complex=dict(live=WC, physical=physc, maxchild=max(PC), rank_mass=massc, hosted_residuals=audit['complex_hosted_residuals'],
+                        physical_stock_bits=stock.bit_length(), router_bits=router.bit_length(), literal_bits=literal.bit_length(), row_coefficient=rowc),
+           strict_outer_constraints={n: str(x) for n, x in a['strict_constraints'].items()}, outer_controls=controls, bootstrap=cutoffs,
+           bit_template_sha256=bg['template_sha256'], complex_template_sha256=ch['template_sha256'])
+outp.write_text(json.dumps(res, indent=2) + '\n')
+print(res['status'], res['kappa_decimal'], 'binding', res['binding_component'], 'gain over #434 %.4f%%' % res['gain_over_pr434_percent'])
diff --git a/research/e8-rank138-idle-hosting/code/audit.py b/research/e8-rank138-idle-hosting/code/audit.py
new file mode 100644
index 0000000000..4c3c28ac96
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/code/audit.py
@@ -0,0 +1,161 @@
+"""Independent audit of the two idle-axis-hosted templates (no code shared with the generators).
+Re-derives hosting windows from each template's own schedule and checks, for every replica and invocation:
+  * every helper residual has exactly one owner: a bank slot or a hosted slot;
+  * a hosted slot lies on the data family of the idle child it names, inside that child's pending coordinates,
+    disjoint from every other hosted slot of the family, and its invocation lies strictly between the last
+    local invocation or bridge naming that pair and the child (the window);
+  * the child keeps exactly the remaining coordinates; banks are tiled exactly (bit) or padded (complex);
+  * the emitted paid profile, live stock and rank deficit 2496 are recomputed from scratch.
+Mutation controls must be rejected.  usage: audit.py PARENT_CHANGED_DIR BIT_DIR COMPLEX_DIR OUT.json"""
+import copy, gzip, hashlib, json, sys
+from collections import Counter, defaultdict
+from pathlib import Path
+V, K, T, L = 120, 4, 8, 9
+DATA = 2 * K * V * T
+
+def wins(events):
+    """events: ('local', stage, pair) | ('bridge', a, b) | ('idle', idx, pair); window = local stages after the last
+    local/bridge touch of the pair and before the child"""
+    last = {}; seen = []; w = {}
+    for pos, e in enumerate(events):
+        if e[0] == 'local': seen.append((pos, e[1], e[2])); last[e[2]] = pos
+        elif e[0] == 'bridge': last[e[1]] = pos; last[e[2]] = pos
+        else:
+            lo = last.get(e[2], -1); w[e[1]] = {s for q, s, p in seen if lo < q < pos and p != e[2]}
+    return w
+
+def audit_bit(t, parent_t, widths):
+    T=32; DATA=960*T
+    assert t['replicas']==parent_t['replicas']==T
+    assert t['local_programs'] == parent_t['local_programs'] and len(t['calls']) == 9*T
+    ev = []; rank = {}; pair = {}
+    for e in t['schedule']:
+        if e['kind'] == 'local_cover_sweep': ev.append(('local', e['stage'], e['pair']))
+        elif e['kind'] == 'bridge': ev.append(('bridge', e['dst'], e['src']))
+        elif e['kind'] == 'idle':
+            ev.append(('idle', e['idx'], e['pair'])); rank[e['idx']] = e['rank']; pair[e['idx']] = e['pair']
+    W = wins(ev); hs = t['hosting']
+    used = defaultdict(set); hosted = {}
+    for i, cp, off, w, s, h in hs['slots']:
+        assert s in W[i], ('window', i, s)
+        assert w == widths[h] and 0 <= off and off + w <= rank[i]
+        cells = set(range(off, off + w)); assert not cells & used[i, cp], ('overlap', i, cp); used[i, cp] |= cells
+        assert (s, h) not in hosted; hosted[s, h] = (i, cp, off, w)
+    rem = {}
+    for i in rank:
+        if rank[i] == 0: continue
+        for cp in range(2 * V): rem[i, cp] = rank[i] - len(used[i, cp])
+        rr = Counter(rem[i, cp] for cp in range(2 * V))
+        if str(i) in hs['remainders']: assert {int(k): v for k, v in hs['remainders'][str(i)].items()} == dict(rr)
+        else: assert rr == Counter({rank[i]: 2 * V})
+    occ = defaultdict(set); LIVE = t['live']; bank_lo = {}
+    for c in t['calls']:
+        s, rep, p = c['stage'], c['replica'], c['pair']; own = c['owners']; assert len(own) == 2 * V + len(widths)
+        assert own[:2 * V] == next(q for q in parent_t['calls'] if (q['stage'], q['replica']) == (s, rep))['owners'][:2 * V]
+        for h, (f, r) in enumerate(own[2 * V:]):
+            if (s, h) in hosted:
+                i, cp, off, w = hosted[s, h]; side, port = divmod(cp, V)
+                assert r == ['hosted', i, off, w] and f == rep * 960 + (2 * pair[i] + side) * V + port
+                assert pair[i] != p
+                occ['h', f, i, s, rep, h] = True
+            else:
+                assert r[0] == 'bank' and r[2] == widths[h] and DATA <= f < LIVE
+                cells = set(range(r[1], r[1] + r[2])); assert cells <= set(range(64)) and not cells & occ[f]; occ[f] |= cells
+                bank_lo[f] = s
+    banks = [f for f in occ if isinstance(f, int)]
+    assert sorted(banks) == list(range(DATA, LIVE)) and all(occ[f] == set(range(64)) for f in banks)
+    paid = Counter()
+    for c in t['calls']:
+        for z in t['local_programs'][c['orientation']]:
+            if z[0] == 0 and z[4]: paid[z[4]] += 1
+            if z[0] == 2: paid[z[5]] += 1
+    for (i, cp), r_ in rem.items():
+        if r_: paid[r_] += T
+    mass = sum(r * n for r, n in paid.items()); assert 64 * LIVE - mass == 312*T
+    assert 64 * 64 > 2 * max(paid) ** 2
+    return paid, sum(1 for _ in hosted) * T
+
+def audit_complex(t, parent_t, local_checks):
+    R = 560; m = 73
+    assert t['local_programs'] == parent_t['local_programs'] and len(t['calls']) == 72
+    prank = {}
+    for it in parent_t['idle_children']: prank.setdefault(it['child'], it['rank'])
+    stage_pair = {e['stage']: e['pair'] for e in t['recipe'] if e['kind'] == 'local'}
+    ev = []; side = {}; pairs = {}
+    for e in t['execution_schedule']:
+        if e['kind'] == 'local_cover_sweep': ev.append(('local', e['stage'], stage_pair[e['stage']]))
+        elif e['kind'] == 'bridge': ev.append(('bridge', e['dst'], e['src']))
+        elif e['kind'] == 'idle_cover_sweep':
+            for sd, ch in enumerate(e['child_indices']):
+                if ch in prank: ev.append(('idle', ch, e['pair'])); side[ch] = sd; pairs[ch] = e['pair']
+    W = wins(ev); hs = t['hosting']
+    used = defaultdict(set); hosted = {}
+    for i, port, off, w, s, h in hs['slots']:
+        assert w == 9 and s in W[i] and 0 <= off and off + 9 <= prank[i]
+        cells = set(range(off, off + 9)); assert not cells & used[i, port]; used[i, port] |= cells
+        assert (s, h) not in hosted; hosted[s, h] = (i, port, off)
+    rem = {}
+    for it in parent_t['idle_children']: rem[it['child'], it['port']] = it['rank'] - len(used[it['child'], it['port']])
+    got = {(it['child'], it['port']): it['rank'] for it in t['idle_children']}
+    assert got == {k: r for k, r in rem.items() if r} and all(it['replicas'] == T for it in t['idle_children'])
+    LIVE = t['live']; occ = defaultdict(set)
+    for c in t['calls']:
+        s, rep, p = c['stage'], c['replica'], c['pair']; own = c['owners']; assert len(own) == 2 * V + R
+        assert own[:2 * V] == next(q for q in parent_t['calls'] if (q['stage'], q['replica']) == (s, rep))['owners'][:2 * V]
+        for h, (f, r) in enumerate(own[2 * V:]):
+            if (s, h) in hosted:
+                i, port, off = hosted[s, h]
+                assert r == [3, i, off] and f == rep * 960 + (2 * pairs[i] + side[i]) * V + port and pairs[i] != p
+            else:
+                assert r[0] == 2 and 0 <= r[1] < 8 and DATA <= f < LIVE and r[1] not in occ[f]; occ[f].add(r[1])
+    banks = sorted(occ); assert banks == list(range(DATA, LIVE))
+    paid = Counter()
+    for c in t['calls']:
+        for r_, z in local_checks[c['orientation']]['paid_profile'].items(): paid[int(r_)] += z
+    for (ch, port), r_ in rem.items():
+        if r_: paid[r_] += T
+    for f in banks: paid[m - 9 * len(occ[f])] += 1
+    mass = sum(r * n for r, n in paid.items()); assert m * LIVE - mass == 2496
+    assert m * m > 2 * max(paid) ** 2
+    return paid, len(hosted) * T
+
+def main():
+    par, bd, cd, outp = map(Path, sys.argv[1:5])
+    pbt = json.loads(gzip.decompress((par / 'bit426-source-centres/global/GLOBAL-TEMPLATE.json.gz').read_bytes()))
+    bt = json.loads(gzip.decompress((bd / 'GLOBAL-TEMPLATE.json.gz').read_bytes()))
+    bg = json.loads((bd / 'GLOBAL.json').read_text())
+    assert hashlib.sha256(gzip.decompress((bd / 'GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest() == bg['template_sha256']
+    st = json.loads((par / 'bit426-source-centres/records/249-states.json').read_text())
+    fs = json.loads((par / 'bit426-source-centres/records/frames.json').read_text())['frames']
+    widths = [8 - fs[str(st['initial'][str(i)])]['dim'] for i in range(240, st['n'])]
+    pct = json.loads(gzip.decompress((par / 'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes()))
+    ct = json.loads(gzip.decompress((cd / 'GLOBAL-TEMPLATE.json.gz').read_bytes()))
+    ch = json.loads((cd / 'HOSTED.json').read_text())
+    assert hashlib.sha256(gzip.decompress((cd / 'GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest() == ch['template_sha256']
+    lc = json.loads((par / 'split-centres/LOCAL-CHECKS.json').read_text())
+    bp, bh = audit_bit(bt, pbt, widths); assert bp == Counter({int(k): v for k, v in bg['profile'].items()})
+    cp, chh = audit_complex(ct, pct, lc); assert cp == Counter({int(k): v for k, v in ch['global_profile'].items()})
+    controls = []
+    def reject(name, fn, which):
+        q = copy.deepcopy(bt if which == 'bit' else ct); fn(q)
+        try:
+            (audit_bit(q, pbt, widths) if which == 'bit' else audit_complex(q, pct, lc))
+        except (AssertionError, KeyError, IndexError, StopIteration): controls.append(name)
+        else: raise AssertionError('mutation accepted: ' + name)
+    def outside(q):           # move one hosted residual to a stage outside its window
+        sl = q['hosting']['slots'][0]; i = sl[0]; s_bad = next(s for s in range(9) if s not in q['hosting']['windows'][str(i)][2]); sl[4] = s_bad
+    reject('bit: hosted residual outside its window', outside, 'bit')
+    reject('bit: overlapping hosted coordinates', lambda q: q['hosting']['slots'][1].__setitem__(2, q['hosting']['slots'][0][2]) if q['hosting']['slots'][1][:2] == q['hosting']['slots'][0][:2] else q['hosting']['slots'][1].__setitem__(1, q['hosting']['slots'][0][1]) or q['hosting']['slots'][1].__setitem__(2, q['hosting']['slots'][0][2]), 'bit')
+    reject('bit: understated live stock', lambda q: q.__setitem__('live', q['live'] - 1), 'bit')
+    reject('bit: hosted owner on the active pair', lambda q: q['calls'][0]['owners'].__setitem__(240 + next(h for h in range(len(widths)) if q['calls'][0]['owners'][240 + h][1][0] == 'hosted'), [0, ['hosted', 0, 0, 8]]), 'bit')
+    reject('bit: missing remainder child', lambda q: q['hosting']['slots'].pop(), 'bit')
+    reject('complex: hosted residual outside its window', lambda q: q['hosting']['slots'][0].__setitem__(4, next(s for s in range(9) if s not in q['hosting']['windows'][str(q['hosting']['slots'][0][0])][2])), 'complex')
+    reject('complex: remainder child understated', lambda q: q['idle_children'][0].__setitem__('rank', q['idle_children'][0]['rank'] - 1), 'complex')
+    reject('complex: dropped bank', lambda q: q.__setitem__('live', q['live'] - 1), 'complex')
+    reject('complex: duplicated hosted residual', lambda q: q['hosting']['slots'].append(list(q['hosting']['slots'][0])), 'complex')
+    res = dict(status='PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT', bit_template_sha256=bg['template_sha256'], complex_template_sha256=ch['template_sha256'],
+               bit_profile={str(k): v for k, v in sorted(bp.items())}, complex_profile={str(k): v for k, v in sorted(cp.items())},
+               bit_live=bt['live'], complex_live=ct['live'], bit_hosted_residuals=bh, complex_hosted_residuals=chh,
+               bit_maxchild=max(bp), complex_maxchild=max(cp), mutations_rejected=controls)
+    outp.write_text(json.dumps(res, indent=2) + '\n'); print(json.dumps({k: v for k, v in res.items() if 'profile' not in k}))
+if __name__ == '__main__': main()
diff --git a/research/e8-rank138-idle-hosting/code/bit_audit.py b/research/e8-rank138-idle-hosting/code/bit_audit.py
new file mode 100644
index 0000000000..4524163ffe
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/code/bit_audit.py
@@ -0,0 +1,134 @@
+# Adapted with exact rational span checks by icekylinx; Codex assistance.
+"""Independent audit of the emitted bit template, including mutation controls.
+Prepared by Zhihao Chen with OpenAI Codex assistance; Apache-2.0.
+"""
+import argparse, copy, gzip, hashlib, json, struct, time
+from collections import Counter, defaultdict
+from pathlib import Path
+from fractions import Fraction as Q
+from residual_routes import validate_isometries
+
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out
+    blob=gzip.decompress((out/'GLOBAL-TEMPLATE.json.gz').read_bytes()); t=json.loads(blob)
+    g=json.loads((out/'GLOBAL.json').read_text()); geo=json.loads((out/'GEOMETRY.json').read_text())
+    assert hashlib.sha256(blob).hexdigest()==g['template_sha256']
+    assert t['geometry_sha256']==sha(out/'GEOMETRY.json') and t['source_record_sha256']==sha(a.local_check/'records/249-records.bin')
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    records=list(struct.iter_unpack('<6i',(a.local_check/'records/249-records.bin').read_bytes()))
+    word=json.loads((a.local_check/'bit-source-centres.json').read_text())
+    assert g['word_sha256']==sha(a.local_check/'bit-source-centres.json')
+    def rank(rows):
+        piv={}
+        for rr in rows:
+            row=list(map(Q,rr))
+            for k,b in sorted(piv.items()):
+                q=row[k]
+                if q:row=[x-q*y for x,y in zip(row,b)]
+            k=next((j for j,x in enumerate(row) if x),None)
+            if k is not None:
+                q=row[k];piv[k]=[x/q for x in row]
+        return len(piv)
+    dimensions={};proj={}
+    for key,f in fs.items():
+        k=int(key);B=f['B'];roots=[word['lines'][j] for j in word['frames'][k]]
+        assert rank(B)==f['dim']==rank(B+roots)==rank(roots)
+        dimensions[k]=f['dim'];proj[k]=B
+    sets=[set(f) for f in word['frames']];pairs={}
+    for op,x,y,c,r,z in records:
+        if op==0:
+            assert sets[y]<=sets[c] and dimensions[c]-dimensions[y]==r
+            pairs[y,c]=r
+    # Positive definite rational form: exact inclusion implies commuting
+    # orthogonal projectors and rank(P_V-P_U)=dim(V)-dim(U), also in reflection.
+    assert len(proj)==len(word['frames'])
+    expected={}
+    for rev in (False,True):
+        es=[]
+        for op,x,y,c,f,z in (reversed(records) if rev else records):
+            if op==0: es.append([0,x,c if rev else y,y if rev else c,f,int(rev)])
+            elif op==1: es.append([1,x,y,-c if rev else c,f,int(rev)])
+            elif op==(3 if rev else 2): es.append([2,x,y,c,f,abs(dimensions[c]-dimensions[f]),int(rev)])
+            else: es.append([3,x,y,c,f,z,int(rev)])
+        expected['reverse' if rev else 'forward']=es
+    assert t['local_programs']==expected
+
+    st=json.loads((a.local_check/'records/249-states.json').read_text())
+    RR=st['n']-240; width=[8-dimensions[st['initial'][str(i)]] for i in range(240,240+RR)]; ENT=sum(8-x for x in width); T=32; DATA=960*T; assert T*(8*RR-ENT)%64==0
+    NB=T*(8*RR-ENT)//64; LIVE=DATA+9*NB; assert g['live']==LIVE
+    def validate(q,check_profile=True):
+        assert validate_isometries(q['residual_isometries'],word['frames'],word['lines'],dimensions)==set(word['start'][240:])
+        assert (q['m'],q['live'],q['replicas'],q['stages'])==(64,LIVE,T,9)
+        assert q['bank_padding'] is None and q['local_programs']==expected
+        hist=Counter(); occupation=defaultdict(set); calls=set()
+        for c in q['calls']:
+            st,rep,p=c['stage'],c['replica'],c['pair']; rev=c['orientation']=='reverse'
+            assert 0<=st<9 and 0<=rep<T and p==max(0,(st-1)//2)
+            assert rev==(st in (1,3,5,7)) and (st,rep) not in calls; calls.add((st,rep))
+            own=c['owners']; assert len(own)==240+RR
+            assert len({(f,tuple(r)) for f,r in own})==240+RR
+            for i,(family,route) in enumerate(own):
+                assert 0<=family<LIVE
+                if i<240:
+                    side=i//120; side=1-side if rev else side
+                    assert family==rep*960+(2*p+side)*120+i%120 and route==['data',st,i%120]
+                else:
+                    j=i-240; assert len(route)==4 and route[0]=='bank' and route[2]==width[j] and route[3]==word['start'][i] and DATA+st*NB<=family<DATA+(st+1)*NB
+                    cells=set(range(route[1],route[1]+route[2])); assert cells<=set(range(64)) and not (cells & occupation[family])
+                    occupation[family]|=cells
+            for e in q['local_programs'][c['orientation']]:
+                if e[0]==0 and e[4]: hist[e[4]]+=1
+                if e[0]==2: hist[e[5]]+=1
+        assert calls=={(s,r) for s in range(9) for r in range(T)}
+        assert set(occupation)==set(range(DATA,LIVE)) and all(s==set(range(64)) for s in occupation.values())
+        levels=[-1]*4; scalar=[1<<i for i in range(8)]; seen=[]; br=0; exchanged=False
+        for e in q['schedule']:
+            if e['kind']=='local_cover_sweep':
+                s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1 and not exchanged
+                src,dst=(2*p+1,2*p) if rev else (2*p,2*p+1)
+                scalar[dst]^=scalar[src]; levels[p]=s; seen.append(s)
+            elif e['kind']=='idle':
+                p,src,dst,r=e['pair'],e['source_level'],e['target_level'],e['rank']
+                assert levels[p]==src and src<=dst<=8
+                assert r==7*(dst-src); levels[p]=dst
+                if r: hist[r]+=240*T
+            elif e['kind']=='bridge':
+                d,s=e['dst'],e['src']; assert levels[d]==levels[s] and e['coefficient'] in (-1,1)
+                scalar[2*d]^=scalar[2*s]; scalar[2*s+1]^=scalar[2*d+1]; br+=1
+            else:
+                assert e['kind']=='exchange' and levels==[8]*4 and not exchanged
+                for p in range(4): scalar[2*p],scalar[2*p+1]=scalar[2*p+1],scalar[2*p]
+                exchanged=True
+        assert exchanged and scalar==[1<<i for i in range(8)] and seen==list(range(9)) and br==9
+        assert 64*LIVE-sum(r*n for r,n in hist.items())==312*T
+        if check_profile: assert hist==Counter({int(k):v for k,v in g['profile'].items()})
+        return hist
+    hist=validate(t)
+    controls=[]
+    def rejects(name,mutator):
+        q=copy.deepcopy(t); mutator(q)
+        try: validate(q)
+        except (AssertionError,KeyError,IndexError): controls.append(name)
+        else: raise AssertionError('mutation accepted: '+name)
+    rejects('omit an idle child',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='idle')))
+    rejects('omit a bridge',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='bridge')))
+    rejects('omit terminal exchange',lambda q:q['schedule'].pop())
+    rejects('remove a local invocation',lambda q:q['calls'].pop())
+    rejects('re-use a helper bank slot',lambda q:q['calls'][0]['owners'].__setitem__(241,q['calls'][0]['owners'][240]))
+    rejects('understate live stock',lambda q:q.__setitem__('live',LIVE-1))
+    rejects('omit a local paid move',lambda q:q['local_programs']['forward'].pop(next(i for i,e in enumerate(q['local_programs']['forward']) if e[0]==0)))
+    rejects('wrong reflected copy charge',lambda q:q['local_programs']['reverse'][next(i for i,e in enumerate(q['local_programs']['reverse']) if e[0]==2)].__setitem__(5,0))
+    rejects('alter residual orthogonal basis',lambda q:q['residual_isometries'][0]['orthogonal_rows_numerator'][0].__setitem__(0,99))
+    rejects('wrong residual frame',lambda q:q['calls'][0]['owners'][240][1].__setitem__(3,-1))
+    rejects('omit a residual route factor',lambda q:next(r for r in q['residual_isometries'] if r['gaussian_reduction'])['gaussian_reduction'].pop())
+    result=dict(status='PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT',template_sha256=g['template_sha256'],
+                source_frames=len(proj),exact_nested_frame_pairs=len(pairs),exact_reflected_pairs=len(pairs),
+                orthogonal_lift_argument='Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.',
+                exact_bank_families=LIVE-DATA,mixed_width_slots=True,entrance_rank_total=ENT,residual_isometries=len(t['residual_isometries']),mutations_rejected=controls,
+                profile=dict(sorted(hist.items())),seconds=time.monotonic()-start)
+    (out/'AUDIT.json').write_text(json.dumps(result,indent=2)+'\n'); print(json.dumps(result),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-rank138-idle-hosting/code/bit_global.py b/research/e8-rank138-idle-hosting/code/bit_global.py
new file mode 100644
index 0000000000..7a885efcd3
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/code/bit_global.py
@@ -0,0 +1,275 @@
+# Adapted for the PR426/source-centre composition by icekylinx with Codex assistance.
+"""Source-bound compressed nine-stage bit template and exact scalar audits.
+
+Prepared by Zhihao Chen with OpenAI Codex assistance, Apache-2.0.
+The local E8 bit word is Dylan Crow's pinned PR #370 contribution.
+"""
+import argparse, gzip, hashlib, json, struct, time
+from collections import Counter
+from pathlib import Path
+from residual_routes import generate
+
+import sys as _sys
+H,V,L,K,T,M=8,120,9,4,32,64
+R=json.loads((Path(_sys.argv[_sys.argv.index('--source')+1])/'bit-source-centres.json').read_bytes())['R']
+LOCAL=2*V+R; DATA=2*K*V*T
+
+def tile_banks(width):
+    """exact width-64 bank tiling of the per-stage helper slots (8 replicas x R helpers, slot width = 8 - entrance rank);
+    returns {(replica, helper): (bank, offset)} and the bank count; every bank is filled exactly (no padding)."""
+    slots=sorted(((width[h],rep,h) for rep in range(T) for h in range(R)),key=lambda x:(-x[0],x[1],x[2]))
+    bins=[]; place={}
+    by={}
+    for w_,rep,h in slots: by.setdefault(w_,[]).append((rep,h))
+    def take(w_):
+        return by[w_].pop(0) if by.get(w_) else None
+    # Exact mixed widths: eight width-7 slots plus one width-8; divisor-width remainders filled with width-8 slots.
+    for w_ in sorted(by,reverse=True):
+        if w_==8: continue
+        while by.get(w_):
+            b=len(bins); off=0; cont=[]
+            if w_==7:
+                for _ in range(8): rep,h=take(7); cont.append((rep,h,off,7)); off+=7
+                rep,h=take(8); cont.append((rep,h,off,8)); off+=8
+            else:
+                assert 64%w_==0
+                for _ in range(min(64//w_,len(by[w_]))): rep,h=take(w_); cont.append((rep,h,off,w_)); off+=w_
+                assert (64-off)%8==0
+                while off<64: rep,h=take(8); cont.append((rep,h,off,8)); off+=8
+            assert off==64; bins.append(cont)
+    while by.get(8):
+        cont=[]; off=0
+        for _ in range(8): rep,h=take(8); cont.append((rep,h,off,8)); off+=8
+        bins.append(cont)
+    for b,cont in enumerate(bins):
+        for rep,h,off,w_ in cont: place[rep,h]=(b,off,w_)
+    assert len(place)==T*R
+    return place,len(bins)
+
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+def write(p,x): p.write_text(json.dumps(x,indent=2)+'\n')
+
+def recipe():
+    out=[dict(kind='local',stage=0,pair=0,reverse=False)]; stage=1
+    for j in range(K):
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=True)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=1))
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=False)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=-1))
+    for j in reversed(range(K-1)): out.append(dict(kind='bridge',dst=j+1,src=j,coefficient=1))
+    out.append(dict(kind='exchange'))
+    return out
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--source',type=Path,required=True)
+    ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out; out.mkdir(parents=True,exist_ok=True)
+    wp=a.source/'bit-source-centres.json'; w=json.loads(wp.read_bytes())
+    inherited=Path('inherited/bit-geometry.json.gz')
+    geo=json.loads(gzip.decompress(inherited.read_bytes()))
+    base=Path('work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz')
+    original=json.loads(gzip.decompress(base.read_bytes()))
+    assert geo['word_sha256']==sha(base)
+    assert w['lines']==original['lines'] and w['form']==original['form']
+    # PR436 regenerates the same root-closed frame family in a different order.
+    # Bind every actual frame by its exact root set; all record IDs remain actual IDs.
+    original_ids={tuple(sorted(fr)):i for i,fr in enumerate(original['frames'])}
+    actual_keys=[tuple(sorted(fr)) for fr in w['frames']]
+    assert len(original_ids)==len(original['frames'])==len(actual_keys)==len(set(actual_keys))
+    assert set(actual_keys)==set(original_ids)
+    frame_map=[original_ids[k] for k in actual_keys]
+    assert sorted(frame_map)==list(range(len(original['frames'])))
+    geo['actual_frame_to_pinned_frame']=frame_map
+    geo['frame_binding']='Exact bijection of root sets; frame IDs in emitted records are those of the reconstructed PR436 word.'
+    kr=json.loads((a.source/'bit-kernel-receipt.json').read_text()); assert kr['output_sha256'] and len(w['frames'])==len(original['frames'])+kr['new_frames']
+    geo['inherited_geometry_sha256']=sha(inherited);geo['word_sha256']=sha(wp)
+    geo['reuse_scope']='Unchanged ports and compressed windows; nonzero helper entrances use mixed-width residual slots, with every owner and coordinate checked independently.'
+    write(out/'GEOMETRY.json',geo)
+    rp=a.local_check/'records/249-records.bin';raw=rp.read_bytes();rec=list(struct.iter_unpack('<6i',raw))
+    state=json.loads((a.local_check/'records/249-states.json').read_text())
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    dims={int(f):z['dim'] for f,z in fs.items()}
+    assert (state['v'],state['n'])==(V,LOCAL)
+    expected_adds=sum(e[0]==1 for e in rec)
+    initial=[state['initial'][str(i)] for i in range(LOCAL)]
+    final=[state['final'][str(i)] for i in range(LOCAL)]
+    assert all(dims[final[i]]==H for i in range(2*V,LOCAL))
+    width={i-2*V:H-dims[initial[i]] for i in range(2*V,LOCAL)}; ENT=sum(H-x for x in width.values()); assert T*(8*R-ENT)%64==0
+    place,NB=tile_banks(width); assert NB==T*(8*R-ENT)//64
+    isometries=generate(w,dims)
+    LIVE=DATA+L*NB
+    streams={}; checks={}; localH=None
+    for reverse in (False,True):
+        cur=(final if reverse else initial)[:]+[-1]; val=[1<<i for i in range(LOCAL)]+[0]
+        norm=[1]*LOCAL+[0]; maxnorm=1; center=None; hist=Counter(); events=[]; copies=0; adds=0
+        dim=lambda f:H-dims[f] if reverse else dims[f]
+        for op,x,y,c,f,z in (reversed(rec) if reverse else rec):
+            if op==0:
+                oldf,newf=(c,y) if reverse else (y,c)
+                assert cur[x]==oldf and dim(newf)-dim(oldf)==f>=0
+                cur[x]=newf
+                if f: hist[f]+=1
+                events.append([0,x,oldf,newf,f,int(reverse)])
+            elif op==1:
+                assert cur[x]==cur[y]==f and x!=y and x<LOCAL
+                if center is not None: assert x!=center
+                if y==LOCAL: assert center is not None
+                if c&1: val[x]^=val[y]
+                norm[x]+=abs(c)*norm[y]; maxnorm=max(maxnorm,norm[x]); adds+=1
+                events.append([1,x,y,-c if reverse else c,f,int(reverse)])
+            elif op==(3 if reverse else 2):
+                assert center is None and y==LOCAL and cur[x]==c and val[LOCAL]==0
+                copy_rank=abs(dim(c)-dim(f)); assert copy_rank==8
+                assert z==(0 if reverse else copy_rank)
+                center=x; cur[LOCAL]=f; val[LOCAL]=val[x]; norm[LOCAL]=norm[x]
+                hist[copy_rank]+=1; copies+=1; events.append([2,x,LOCAL,c,f,copy_rank,int(reverse)])
+            else:
+                assert op==(2 if reverse else 3)
+                assert center==x and y==LOCAL and cur[x]==c and cur[LOCAL]==f
+                assert val[LOCAL]==val[x]
+                val[LOCAL]=0; norm[LOCAL]=0; cur[LOCAL]=-1; center=None
+                events.append([3,x,LOCAL,c,f,z,int(reverse)])
+        assert center is None and copies==9 and adds==expected_adds
+        assert cur[:LOCAL]==(initial if reverse else final)
+        for i in range(LOCAL):
+            want=(1<<i) ^ ((1<<(i-V)) if V<=i<2*V else 0)
+            assert val[i]==want
+        assert val[LOCAL]==0
+        if localH is None: localH=hist
+        else: assert localH==hist
+        key='reverse' if reverse else 'forward'; streams[key]=events
+        checks[key]=dict(copies=copies,adds=adds,records=len(events),all_columns=LOCAL,
+                         cancellation_free_row_l1=maxnorm,profile=dict(sorted(hist.items())),
+                         sha256=hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest())
+    assert sum(r*n for r,n in localH.items())==H*R-ENT+72+2*V*(H-1)
+
+    events=recipe(); levels=[-1]*K; schedule=[]; bridge_controls=[]
+    # Full scalar replay on separate dirty helpers for all nine stages.
+    # Physical banking then uses the separately checked injective cover owners.
+    n=2*K*V+L*R; vals=[1<<i for i in range(n)]+[0]; temp=n
+    stages=[]
+    for e in events:
+        if e['kind']=='local':
+            s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1
+            def mapper(i):
+                if i==LOCAL: return temp
+                if i<2*V:
+                    side=i//V; side=1-side if rev else side
+                    return (2*p+side)*V+i%V
+                return 2*K*V+s*R+i-2*V
+            before=vals[:]; opened=False
+            for z in streams['reverse' if rev else 'forward']:
+                if z[0]==0: continue
+                x,y=mapper(z[1]),mapper(z[2])
+                if z[0]==1:
+                    if z[3]&1: vals[x]^=vals[y]
+                elif z[0]==2:
+                    assert not opened; vals[temp]=vals[x]; opened=True
+                else:
+                    assert opened and vals[temp]==vals[x]; vals[temp]=0; opened=False
+            assert not opened
+            d=(2*p+(0 if rev else 1))*V; src=(2*p+(1 if rev else 0))*V
+            for t in range(V): before[d+t]^=before[src+t]
+            assert vals==before
+            levels[p]=s; schedule.append(dict(kind='local_cover_sweep',**{k:v for k,v in e.items() if k!='kind'}))
+            if s in (1,3,5):
+                j=(s+1)//2; assert levels[j]==-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7*(s+1),source_level=-1,target_level=s))
+            elif s in (2,4,6):
+                j=s//2; assert levels[j]==s-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7,source_level=s-1,target_level=s))
+            elif s==8:
+                for j in range(4):
+                    oldlevel=levels[j]; assert oldlevel==2*j+2
+                    schedule.append(dict(kind='idle',pair=j,rank=7*(8-oldlevel),source_level=oldlevel,target_level=8))
+                    levels[j]=8
+            stages.append(dict(stage=s,all_columns=n,helper_columns=L*R,reverse=rev))
+        elif e['kind']=='bridge':
+            d,s=e['dst'],e['src']; assert levels[d]==levels[s]
+            for t in range(V): vals[2*d*V+t]^=vals[2*s*V+t]; vals[(2*s+1)*V+t]^=vals[(2*d+1)*V+t]
+            schedule.append(e)
+        else:
+            assert levels==[8]*4
+            for j in range(K):
+                for t in range(V):
+                    x=2*j*V+t; y=(2*j+1)*V+t; vals[x],vals[y]=vals[y],vals[x]
+            schedule.append(e)
+    assert vals==[1<<i for i in range(n)]+[0]
+    # Integer scalar eight-bank matrix, with each individual bridge shear omitted.
+    def small(skip=-1):
+        z=[[int(i==j) for j in range(8)] for i in range(8)]; count=0
+        def add(d,s,c): z[d]=[x+c*y for x,y in zip(z[d],z[s])]
+        for e in events:
+            if e['kind']=='local':
+                p=e['pair']; add(2*p,2*p+1,-1) if e['reverse'] else add(2*p+1,2*p,1)
+            elif e['kind']=='bridge':
+                d,s,c=e['dst'],e['src'],e['coefficient']
+                for x,y,sgn in [(2*d,2*s,c),(2*s+1,2*d+1,-c)]:
+                    if count!=skip: add(x,y,sgn)
+                    count+=1
+            else:
+                for j in range(4): z[2*j],z[2*j+1]=z[2*j+1],[-x for x in z[2*j]]
+        return z,count
+    ident=[[int(i==j) for j in range(8)] for i in range(8)]
+    z,nb=small(); assert z==ident and nb==18
+    for skip in range(nb): assert small(skip)[0]!=ident; bridge_controls.append(skip)
+
+    paid=Counter(); calls=[]; assignment=set(); expanded=hashlib.sha256(); full_event_count=0
+    for e in events:
+        if e['kind']!='local': continue
+        s,p,rev=e['stage'],e['pair'],e['reverse']; ori='reverse' if rev else 'forward'
+        for rep in range(T):
+            owners=[]
+            for i in range(2*V):
+                side=i//V; side=1-side if rev else side
+                owners.append([rep*(2*K*V)+(2*p+side)*V+i%V, ['data',s,i%V]])
+            for r in range(R):
+                bank,off,w_=place[rep,r]
+                owners.append([DATA+s*NB+bank,['bank',off,w_,initial[2*V+r]]])
+                assignment.add((s,rep,r,bank,off))
+            assert len({(f,tuple(route)) for f,route in owners})==LOCAL
+            assert all(0<=f<LIVE for f,route in owners)
+            # Stream one full renamed instruction program into a source-bound
+            # digest, including exact owner route descriptors and reflection.
+            for z in streams[ori]:
+                op=z[0]
+                if op==0: paid[z[4]]+=bool(z[4]); mapped=[op,owners[z[1]],*z[2:]]
+                else:
+                    ox=owners[z[1]]; oy=owners[z[2]] if z[2]<LOCAL else [LIVE,['private',0]]
+                    mapped=[op,ox,oy,*z[3:]]
+                    if op==2: paid[z[5]]+=1
+                expanded.update((json.dumps(mapped,separators=(',',':'))+'\n').encode()); full_event_count+=1
+            calls.append(dict(stage=s,replica=rep,pair=p,orientation=ori,owners=owners,local_hash=checks[ori]['sha256']))
+    paid.pop(0,None)
+    assert len(assignment)==L*T*R and len(calls)==L*T
+    for e in schedule:
+        if e['kind']=='idle' and e['rank']: paid[e['rank']]+=2*V*T
+    mass=sum(r*c for r,c in paid.items()); assert M*LIVE-mass==312*T
+    cf=checks['forward']['cancellation_free_row_l1']; cb=checks['reverse']['cancellation_free_row_l1']
+    prefix=(1<<nb)*cf**5*cb**4; charged_prefix=64*((prefix.bit_length()+63)//64);assert prefix<1<<charged_prefix
+    print('Fresh prefix bits',prefix.bit_length(),'charged',charged_prefix,flush=True)
+    template=dict(version='compressed-nine-e8-bit-v1',m=M,h=H,stages=L,replicas=T,live=LIVE,private_centre_reserve=9,
+                  cover='O(I_64/2,F_q) for admitted odd address primes q',loop_order='Each recipe phase: replicas then all cover classes; finish every local invocation before the next.',
+                  schedule=schedule,local_programs=streams,calls=calls,bank_padding=None,
+                  helper_route='Exact listed residual coordinate isometry, extended by identity on exterior coordinates and permuted to the assigned bank interval.',banks_per_stage=NB,entrance_rank_total=ENT,residual_isometries=isometries,
+                  data_route='owner (replica*960 + (2*pair+side)*120+port, d*rho_stage,port)',
+                  bit_operator='D_U exchanges the two address halves on projector U; D_I D_P = D_(I-P) exactly.',
+                  geometry_sha256=sha(out/'GEOMETRY.json'),source_record_sha256=sha(rp))
+    blob=json.dumps(template,separators=(',',':'),sort_keys=True).encode(); (out/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+    result=dict(status='PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE',h=H,m=M,v=V,R=R,replicas=T,live=LIVE,physical=LIVE+9,
+                word_sha256=sha(wp),source_records_sha256=sha(rp),local_checks=checks,scalar_stages=stages,
+                independent_unbanked_scalar_columns=n,all_scalar_columns_restored=True,
+                geometry_sha256=sha(out/'GEOMETRY.json'),template_sha256=hashlib.sha256(blob).hexdigest(),
+                emitted_program_sha256=expanded.hexdigest(),emitted_events=full_event_count,local_invocations=len(calls),
+                bank_assignments=len(assignment),banks_per_stage=NB,entrance_rank_total=ENT,mixed_width_slots=True,padding_calls=0,residual_isometries=len(isometries),extra_helper_route_factor_bound=144,
+                profile=dict(sorted(paid.items())),paid_calls=sum(paid.values()),rank_mass=mass,deficit=312*T,
+                maxchild=max(paid),halving_depth=2,halving_integer_inequality=[64**2,2*42**2],
+                local_additions=expected_adds,bridge_additions=18*V*T,copy_erase_episodes=9*L*T,
+                global_prefix_bound=str(prefix),global_prefix_bits=prefix.bit_length(),charged_prefix_bits=charged_prefix,
+                omitted_bridge_shears_rejected=bridge_controls,
+                scope='Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.',
+                seconds=time.monotonic()-start)
+    write(out/'GLOBAL.json',result)
+    print(json.dumps({k:v for k,v in result.items() if k not in ('local_checks','scalar_stages','global_prefix_bound')}),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-rank138-idle-hosting/code/bit_hosted.py b/research/e8-rank138-idle-hosting/code/bit_hosted.py
new file mode 100644
index 0000000000..c499db68d5
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/code/bit_hosted.py
@@ -0,0 +1,116 @@
+"""Idle-axis hosting for #434's compressed nine-stage bit template (m=64).
+Reads the emitted parent template, keeps every local program and scalar replay unchanged, and moves whole helper
+residuals from banks onto pending idle-advance coordinates of untouched data families.  Emits a new template,
+GLOBAL.json with the new live stock and paid profile.  usage: bit_hosted.py PARENT_GLOBAL_DIR LOCAL_CHECK_DIR OUT"""
+import gzip, hashlib, importlib.util, json, sys, time
+from collections import Counter
+from pathlib import Path
+HERE = Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE))
+import hosting_core as HC
+H, V, L, K, T, M = 8, 120, 9, 4, 32, 64
+DATA = 2 * K * V * T
+DISCOVER = False
+sha = lambda p: hashlib.sha256(Path(p).read_bytes()).hexdigest()
+def main(parent, local, out):
+    t0 = time.monotonic(); out.mkdir(parents=True, exist_ok=False)
+    blob = gzip.decompress((parent / 'GLOBAL-TEMPLATE.json.gz').read_bytes()); t = json.loads(blob)
+    g = json.loads((parent / 'GLOBAL.json').read_text())
+    assert hashlib.sha256(blob).hexdigest() == g['template_sha256']
+    st = json.loads((local / 'records/249-states.json').read_text()); R = st['n'] - 2 * V; assert R == g['R']
+    fs = json.loads((local / 'records/frames.json').read_text())['frames']; dims = {int(f): z['dim'] for f, z in fs.items()}
+    width = [H - dims[st['initial'][str(i)]] for i in range(2 * V, 2 * V + R)]
+    # schedule with indexed idle children
+    sched = []; idx = 0
+    for e in t['schedule']:
+        if e['kind'] == 'local_cover_sweep': sched.append(dict(kind='local', stage=e['stage'], pair=e['pair']))
+        elif e['kind'] == 'bridge': sched.append(dict(kind='bridge', dst=e['dst'], src=e['src']))
+        elif e['kind'] == 'idle':
+            sched.append(dict(kind='idle', pair=e['pair'], rank=e['rank'], idx=idx)); e['idx'] = idx; idx += 1
+    win = {k: x for k, x in HC.windows(sched).items() if x[1] > 0 and x[2]}
+    avail = Counter()
+    for s in range(L):
+        for w in width: avail[s, w] += 1
+    sel = HERE / 'SELECTION.json'; key = 'bit'
+    if DISCOVER:
+        ys, zs, val = HC.solve(win, 2 * V, dict(avail), M, group={7: 2}); HC.save_selection(sel, key, ys, zs, val)
+    ys, zs, val = HC.load_selection(sel, key)
+    helpers = {s: [(h, width[h]) for h in range(R)] for s in range(L)}
+    slots, rem = HC.expand(win, ys, zs, helpers, 2 * V)
+    hosted = {(s, h): (i, c, off, w) for i, c, off, w, s, h in slots}
+    # remaining helpers -> exact width-64 banks (per stage, same set of helpers in every replica)
+    left = {s: [h for h in range(R) if (s, h) not in hosted] for s in range(L)}
+    nb = {}; place = {}
+    for s in range(L):
+        wl = {h: width[h] for h in left[s]}
+        slotsS = sorted(((wl[h], rep, h) for rep in range(T) for h in left[s]), key=lambda x: (-x[0], x[1], x[2]))
+        by = {}
+        for w_, rep, h in slotsS: by.setdefault(w_, []).append((rep, h))
+        bins = []
+        def take(w_): return by[w_].pop(0)
+        for w_ in sorted(by, reverse=True):
+            if w_ == 8: continue
+            while by.get(w_):
+                cont = []; off = 0
+                if w_ == 7:
+                    for _ in range(8): rep, h = take(7); cont.append((rep, h, off, 7)); off += 7
+                    rep, h = take(8); cont.append((rep, h, off, 8)); off += 8
+                else:
+                    for _ in range(64 // w_): rep, h = take(w_); cont.append((rep, h, off, w_)); off += w_
+                assert off == 64; bins.append(cont)
+        while by.get(8):
+            cont = []; off = 0
+            for _ in range(8): rep, h = take(8); cont.append((rep, h, off, 8)); off += 8
+            bins.append(cont)
+        nb[s] = len(bins)
+        for b, cont in enumerate(bins):
+            for rep, h, off, w_ in cont: place[s, rep, h] = (b, off, w_)
+    base = [DATA]
+    for s in range(L): base.append(base[-1] + nb[s])
+    LIVE = base[-1]
+    # owners
+    for c in t['calls']:
+        s, rep, p = c['stage'], c['replica'], c['pair']; own = c['owners'][:2 * V]
+        for h in range(R):
+            if (s, h) in hosted:
+                i, cp, off, w = hosted[s, h]; pair = win[i][0]; side, port = divmod(cp, V)
+                own.append([rep * 960 + (2 * pair + side) * V + port, ['hosted', i, off, w]])
+            else:
+                b, off, w = place[s, rep, h]; own.append([base[s] + b, ['bank', off, w]])
+        assert len({(f, tuple(r)) for f, r in own}) == 2 * V + R and all(0 <= f < LIVE for f, r in own)
+        c['owners'] = own
+    # profile: local programs unchanged; idle children replaced by remainders
+    paid = Counter()
+    for c in t['calls']:
+        for z in t['local_programs'][c['orientation']]:
+            if z[0] == 0 and z[4]: paid[z[4]] += 1
+            if z[0] == 2: paid[z[5]] += 1
+    remainder = {}
+    for e in t['schedule']:
+        if e['kind'] == 'idle' and e['rank']:
+            i = e['idx']
+            if i in win:
+                rr = Counter(rem[i, cp] for cp in range(2 * V)); remainder[i] = {str(k): v for k, v in sorted(rr.items())}
+                for r_, n in rr.items():
+                    if r_: paid[r_] += n * T
+            else:
+                paid[e['rank']] += 2 * V * T
+    mass = sum(r * n for r, n in paid.items()); assert M * LIVE - mass == 312*T, M * LIVE - mass
+    t.update(version='compressed-nine-e8-bit-v1+idle-axis-hosting', live=LIVE,
+             hosting=dict(windows={str(i): [w[0], w[1], sorted(w[2])] for i, w in win.items()},
+                          slots=[list(x) for x in slots], remainders=remainder, banks_per_stage=nb,
+                          rule='helper (stage s, helper h) of replica r owns coordinates [off, off+w) of the pending idle-child '
+                               'projector of data family r*960+(2*pair+side)*120+port (copy = side*120+port); s lies strictly between '
+                               'the last local/bridge touch of that pair and the child; the child keeps the remaining coordinates.'),
+             helper_route='bank owner (exact width-64 tiling of the unhosted residuals of each stage) or hosted owner (data family, pending idle coordinates)')
+    tb = json.dumps(t, separators=(',', ':'), sort_keys=True).encode(); (out / 'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(tb, mtime=0))
+    res = dict(g); res.update(status='PASS_IDLE_AXIS_HOSTED_BIT_TEMPLATE', live=LIVE, physical=LIVE + 9, template_sha256=hashlib.sha256(tb).hexdigest(),
+               parent_template_sha256=g['template_sha256'], profile=dict(sorted(paid.items())), paid_calls=sum(paid.values()), rank_mass=mass,
+               maxchild=max(paid), banks_per_stage_hosted=nb, hosted_residuals_per_replica=len(slots), hosted_residuals=len(slots) * T,
+               hosted_coordinates_per_replica=sum(x[3] for x in slots), saved_idle_cost_proxy=val, seconds=time.monotonic() - t0)
+    res['bank_assignments'] = sum(1 for c in t['calls'] for f, r in c['owners'][2 * V:] if r[0] == 'bank')
+    (out / 'GLOBAL.json').write_text(json.dumps(res, indent=2) + '\n')
+    print(json.dumps({k: res[k] for k in ('live', 'maxchild', 'hosted_residuals', 'banks_per_stage_hosted', 'rank_mass')}), flush=True)
+if __name__ == '__main__':
+    DISCOVER = '--discover' in sys.argv; args = [a for a in sys.argv[1:] if a != '--discover']
+    main(Path(args[0]), Path(args[1]), Path(args[2]))
diff --git a/research/e8-rank138-idle-hosting/code/complex_hosted.py b/research/e8-rank138-idle-hosting/code/complex_hosted.py
new file mode 100644
index 0000000000..56e15c15ae
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/code/complex_hosted.py
@@ -0,0 +1,87 @@
+"""Idle-axis hosting for #433's compressed nine-stage complex template (m=73, R=560, whole rank-nine residuals).
+Local programs, data routes and the cover correction are unchanged; bank slots of hosted residuals move onto pending
+idle-child coordinates of untouched data families; unhosted residuals are re-tiled eight per bank with one paid pad
+(a final partial bank pays the larger pad).  usage: complex_hosted.py SPLIT_CENTRES_DIR OUT"""
+import gzip, hashlib, json, math, sys, time
+from collections import Counter
+from pathlib import Path
+HERE = Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE))
+import hosting_core as HC
+V, K, T, L, M, R = 120, 4, 8, 9, 73, 560
+DATA = 2 * K * V * T
+DISCOVER = False
+def main(src, out):
+    t0 = time.monotonic(); out.mkdir(parents=True, exist_ok=False)
+    blob = gzip.decompress((src / 'GLOBAL-TEMPLATE.json.gz').read_bytes()); t = json.loads(blob)
+    integ = json.loads((src / 'INTEGRATION.json').read_text()); checks = json.loads((src / 'LOCAL-CHECKS.json').read_text())
+    assert hashlib.sha256(blob).hexdigest() == integ['global_template_sha256'] and t['live'] == integ['live']
+    rank = {}
+    for it in t['idle_children']:
+        assert it['replicas'] == T; rank.setdefault(it['child'], it['rank']); assert rank[it['child']] == it['rank']
+    pair_of_stage = {e['stage']: e['pair'] for e in t['recipe'] if e['kind'] == 'local'}
+    sched = []; side_of = {}; pair_of = {}
+    for e in t['execution_schedule']:
+        if e['kind'] == 'local_cover_sweep': sched.append(dict(kind='local', stage=e['stage'], pair=pair_of_stage[e['stage']]))
+        elif e['kind'] == 'bridge': sched.append(dict(kind='bridge', dst=e['dst'], src=e['src']))
+        elif e['kind'] == 'idle_cover_sweep':
+            for sd, ch in enumerate(e['child_indices']):
+                if ch in rank:
+                    sched.append(dict(kind='idle', pair=e['pair'], rank=rank[ch], idx=ch)); side_of[ch] = sd; pair_of[ch] = e['pair']
+    win = {k: x for k, x in HC.windows(sched).items() if x[1] >= 9 and x[2]}
+    avail = {(s, 9): R for s in range(L)}
+    sel = HERE / 'SELECTION.json'; key = 'complex'
+    if DISCOVER:
+        ys, zs, val = HC.solve(win, V, avail, M, pad_value=HC.cost(1, M) / 8); HC.save_selection(sel, key, ys, zs, val)
+    ys, zs, val = HC.load_selection(sel, key)
+    slots, rem = HC.expand(win, ys, zs, {s: [(h, 9) for h in range(R)] for s in range(L)}, V)
+    hosted = {(s, h): (i, port, off) for i, port, off, w, s, h in slots}
+    # re-tile unhosted residuals: per stage, z = rank among (replica, helper) unhosted pairs; eight per bank
+    base = [DATA]; tile = {}; partial = Counter()
+    for s in range(L):
+        left = [(rep, h) for rep in range(T) for h in range(R) if (s, h) not in hosted]
+        for z, (rep, h) in enumerate(left): tile[s, rep, h] = divmod(z, 8)
+        nb = -(-len(left) // 8); base.append(base[-1] + nb)
+        if len(left) % 8: partial[M - 9 * (len(left) % 8)] += 1
+        full = len(left) // 8
+        partial[M - 72] += full
+    W = base[-1]
+    for c in t['calls']:
+        s, rep, p = c['stage'], c['replica'], c['pair']; own = c['owners'][:2 * V]
+        for h in range(R):
+            if (s, h) in hosted:
+                i, port, off = hosted[s, h]; own.append([rep * 960 + (2 * pair_of[i] + side_of[i]) * V + port, [3, i, off]])
+            else:
+                b, sl = tile[s, rep, h]; own.append([base[s] + b, [2, sl]])
+        assert len({(f, tuple(r)) for f, r in own}) == 2 * V + R and all(f < W for f, r in own)
+        c['owners'] = own
+    paid = Counter()
+    for c in t['calls']:
+        for r_, z in checks[c['orientation']]['paid_profile'].items(): paid[int(r_)] += z
+    newidle = []
+    for it in t['idle_children']:
+        ch, port = it['child'], it['port']; rr = rem.get((ch, port), it['rank']) if ch in win else it['rank']
+        if rr: newidle.append(dict(child=ch, port=port, rank=rr, hosted=it['rank'] - rr, replicas=T)); paid[rr] += T
+    for r_, n in partial.items(): paid[r_] += L * n if False else n * 1
+    # padding: one pad child per bank per stage (already per-stage counted above), the template replays all stages
+    mass = sum(r * n for r, n in paid.items()); D = M * W - mass
+    assert D == 2496, D
+    t.update(version='hamming-mutable-basis-nine-v1+idle-axis-hosting', live=W, idle_children=newidle,
+             physical=W + R + (integ['physical'] - integ['live'] - R),
+             hosting=dict(windows={str(i): [w[0], w[1], sorted(w[2])] for i, w in win.items()}, sides=side_of, pairs=pair_of,
+                          slots=[list(x) for x in slots], banks=[base[s + 1] - base[s] for s in range(L)]))
+    t['bank_padding']['families'] = list(range(DATA, W)); t['cover_final_correction']['families'] = [0, W]
+    t['cover_final_correction']['charged_calls_per_cover'] = W
+    for e in t['execution_schedule']:
+        if e['kind'] == 'bank_padding_cover_sweep': e['families'] = [DATA, W]
+        elif e['kind'] == 'translate_every_live_family': e.update(t['cover_final_correction'])
+    tb = json.dumps(t, sort_keys=True, separators=(',', ':')).encode(); (out / 'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(tb, mtime=0))
+    res = dict(status='PASS_IDLE_AXIS_HOSTED_COMPLEX_TEMPLATE', parent_template_sha256=integ['global_template_sha256'],
+               template_sha256=hashlib.sha256(tb).hexdigest(), live=W, physical=t['physical'], global_profile=dict(sorted(paid.items())),
+               rank_mass=mass, deficit=D, maxchild=max(paid), hosted_residuals=len(slots) * T, banks_per_stage=t['hosting']['banks'],
+               saved_cost_proxy=val, seconds=time.monotonic() - t0)
+    (out / 'HOSTED.json').write_text(json.dumps(res, indent=2) + '\n')
+    print(json.dumps({k: res[k] for k in ('live', 'maxchild', 'hosted_residuals', 'banks_per_stage', 'deficit')}))
+if __name__ == '__main__':
+    DISCOVER = '--discover' in sys.argv; args = [a for a in sys.argv[1:] if a != '--discover']
+    main(Path(args[0]), Path(args[1]))
diff --git a/research/e8-rank138-idle-hosting/code/hosting_core.py b/research/e8-rank138-idle-hosting/code/hosting_core.py
new file mode 100644
index 0000000000..68b536daa9
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/code/hosting_core.py
@@ -0,0 +1,138 @@
+"""Idle-axis hosting: place whole dirty-helper residuals on the pending coordinates of an idle data family.
+
+A data family that is advanced by an idle child from level a to level b receives the commuting coordinate factors of
+that child.  If the family is untouched (no local invocation on its pair and no bridge naming its pair) during an
+interval of local invocations ending at the child, a helper residual of width w from an invocation inside that
+interval may own w of those pending coordinates instead of a bank slot.  The child keeps only the remaining
+coordinates.  This module computes the windows from the recipe and chooses, per replica, how many residuals of each
+width each child hosts (exact integer programme), then expands that choice into explicit slot assignments.
+Standard library plus scipy for the integer programme; the emitted assignment is re-checked without scipy."""
+import math
+from collections import Counter, defaultdict
+
+def windows(schedule):
+    """schedule: ordered events dict(kind='local',stage,pair) | dict(kind='bridge',dst,src) | dict(kind='idle',pair,rank,idx).
+    Returns {idx: (pair, rank, frozenset(stages))} - stages whose invocation lies strictly between the last touch of
+    the pair and the idle child."""
+    last = {}; out = {}; locals_ = []
+    for pos, e in enumerate(schedule):
+        k = e['kind']
+        if k == 'local':
+            locals_.append((pos, e['stage'], e['pair'])); last[e['pair']] = pos
+        elif k == 'bridge':
+            last[e['dst']] = pos; last[e['src']] = pos
+        elif k == 'idle':
+            p = e['pair']; lo = last.get(p, -1)
+            st = frozenset(s for q, s, pp in locals_ if lo < q < pos and pp != p)
+            out[e['idx']] = (p, e['rank'], st)      # an idle child acts on other coordinates (or the other member): not a touch
+    return out
+
+def patterns(rank, widths, maxk=12):
+    """multisets of widths with sum <= rank (as sorted tuples)"""
+    ws = sorted(set(widths), reverse=True); res = []
+    def rec(i, cur, s):
+        if i == len(ws): res.append(tuple(cur)); return
+        w = ws[i]; k = 0
+        while s + k * w <= rank and len(cur) + k <= maxk:
+            rec(i + 1, cur + [w] * k, s + k * w); k += 1
+    rec(0, [], 0)
+    return res
+
+def cost(r, m):
+    return r * math.log(m / r) if r else 0.0
+
+def solve(win, copies, avail, m, pad_value=0.0, group=None):
+    """win: {idx: (pair, rank, stages)}; copies: piece copies per replica of each idx (2V);
+    avail: {(stage, width): count per replica}; maximise saved idle cost (+ pad_value per hosted residual).
+    group: optional {width: g} - remaining count of that width per stage must be a multiple of g (exact bank tiling).
+    Returns {(idx, pattern): copies} and {(idx, width, stage): count}."""
+    import numpy as np
+    from scipy.optimize import milp, LinearConstraint, Bounds
+    widths = sorted({w for (_, w) in avail})
+    var = []; index = {}
+    for idx, (p, r, st) in win.items():
+        for pat in patterns(r, widths):
+            index[('y', idx, pat)] = len(var); var.append(('y', idx, pat))
+        for w in widths:
+            for s in st:
+                if avail.get((s, w), 0):
+                    index[('z', idx, w, s)] = len(var); var.append(('z', idx, w, s))
+    stages = sorted({s for (s, _) in avail})
+    if group:
+        for w, g in group.items():
+            for s in stages:
+                index[('g', w, s)] = len(var); var.append(('g', w, s))
+    n = len(var); c = np.zeros(n); integ = np.ones(n); lb = np.zeros(n); ub = np.full(n, np.inf)
+    for key, j in index.items():
+        if key[0] == 'y':
+            _, idx, pat = key; r = win[idx][1]; c[j] = -(cost(r, m) - cost(r - sum(pat), m) + pad_value * len(pat))
+    rows, lo, hi = [], [], []
+    for idx in win:
+        row = np.zeros(n)
+        for key, j in index.items():
+            if key[0] == 'y' and key[1] == idx: row[j] = 1
+        rows.append(row); lo.append(copies); hi.append(copies)
+        for w in widths:
+            row = np.zeros(n)
+            for key, j in index.items():
+                if key[0] == 'y' and key[1] == idx: row[j] = key[2].count(w)
+                if key[0] == 'z' and key[1] == idx and key[2] == w: row[j] = -1
+            rows.append(row); lo.append(0); hi.append(0)
+    for (s, w), a in avail.items():
+        row = np.zeros(n)
+        for key, j in index.items():
+            if key[0] == 'z' and key[2] == w and key[3] == s: row[j] = 1
+        if group and w in group:
+            row[index[('g', w, s)]] = group[w]; rows.append(row); lo.append(a); hi.append(a)   # used + g*k = avail
+        else:
+            rows.append(row); lo.append(0); hi.append(a)
+    res = milp(c, constraints=LinearConstraint(np.array(rows), lo, hi), integrality=integ, bounds=Bounds(lb, ub),
+               options=dict(time_limit=600, disp=False))
+    assert res.x is not None, res.message
+    x = [int(round(t)) for t in res.x]
+    ys = {(k[1], k[2]): x[j] for k, j in index.items() if k[0] == 'y' and x[j]}
+    zs = {(k[1], k[2], k[3]): x[j] for k, j in index.items() if k[0] == 'z' and x[j]}
+    return ys, zs, -res.fun
+
+def expand(win, ys, zs, helpers, V2):
+    """helpers: {stage: [(helper, width), ...]} for ONE replica; returns list of
+    (idx, copy, offset, width, stage, helper) and the remainder rank of every (idx, copy).
+    Copies of a piece are the 2V (side, port) data families; residuals packed from offset 0 in decreasing width."""
+    pool = defaultdict(list)                    # (stage, width) -> helpers
+    for s, hs in helpers.items():
+        for h, w in hs: pool[s, w].append(h)
+    for k in pool: pool[k].sort()
+    need = defaultdict(list)                    # (idx, width) -> stages multiset in deterministic order
+    for (idx, w, s), cnt in sorted(zs.items()): need[idx, w] += [s] * cnt
+    out = []; rem = {}
+    for idx in sorted(win):
+        pats = sorted([(pat, cnt) for (i, pat), cnt in ys.items() if i == idx], key=lambda t: (-sum(t[0]), t[0]))
+        copy = 0; ptr = Counter()
+        r = win[idx][1]
+        for pat, cnt in pats:
+            for _ in range(cnt):
+                off = 0
+                for w in sorted(pat, reverse=True):
+                    s = need[idx, w][ptr[idx, w]]; ptr[idx, w] += 1
+                    h = pool[s, w].pop(0)
+                    out.append((idx, copy, off, w, s, h)); off += w
+                rem[idx, copy] = r - off; copy += 1
+        while copy < V2: rem[idx, copy] = r; copy += 1
+    return out, rem
+
+def save_selection(path, key, ys, zs, val):
+    """freeze the integer-programme choice (patterns per child, residual stages per child) for stdlib-only replay"""
+    import json
+    from pathlib import Path
+    p = Path(path); d = json.loads(p.read_text()) if p.exists() else {}
+    d[key] = dict(patterns=sorted([[i, list(pat), n] for (i, pat), n in ys.items()]),
+                  stages=sorted([[i, w, s, n] for (i, w, s), n in zs.items()]), proxy_saving=val)
+    p.write_text(json.dumps(d, indent=1, sort_keys=True) + '\n')
+
+def load_selection(path, key):
+    import json
+    from pathlib import Path
+    d = json.loads(Path(path).read_text())[key]
+    ys = {(i, tuple(pat)): n for i, pat, n in d['patterns']}
+    zs = {(i, w, s): n for i, w, s, n in d['stages']}
+    return ys, zs, d['proxy_saving']
diff --git a/research/e8-rank138-idle-hosting/code/residual_routes.py b/research/e8-rank138-idle-hosting/code/residual_routes.py
new file mode 100644
index 0000000000..04feccfe52
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/code/residual_routes.py
@@ -0,0 +1,26 @@
+"""Generate exact coordinate isometries for this kernel's residuals.
+OpenAI Codex. Route witness/check conventions follow chafreaky's PR439.
+"""
+import sys
+from pathlib import Path
+sys.path.insert(0,str(Path(__file__).resolve().parent.parent/'vendor/pr439'))
+from bank_routes import validate_isometries
+
+def generate(word,dimensions):
+    roots=word['lines'];index={tuple(r):i for i,r in enumerate(roots)};out=[]
+    for f in sorted(set(word['start'][240:])):
+        e=dimensions[f];rs=[roots[j] for j in word['frames'][f]]
+        axes=sorted({i for r in rs for i,x in enumerate(r) if x})
+        assert len(axes)==e, 'This finite selection must have coordinate entrances'
+        order=axes+[i for i in range(8) if i not in axes]
+        matrix=[[2*int(i==j) for j in range(8)] for i in order]
+        basis=[index[tuple(r)] for r in matrix]
+        assert set(basis[:e])<=set(word['frames'][f])
+        reduced=order[:];ops=[]
+        for i in range(8):
+            j=reduced.index(i)
+            if i!=j:reduced[i],reduced[j]=reduced[j],reduced[i];ops.append(['swap',i,j,None])
+        assert reduced==list(range(8)) and len(ops)<=7
+        out.append(dict(frame=f,entrance_rank=e,denominator=2,entrance_basis=basis[:e],residual_basis=basis[e:],orthogonal_rows_numerator=matrix,gaussian_reduction=ops))
+    assert validate_isometries(out,word['frames'],roots,dimensions)==set(word['start'][240:])
+    return out
diff --git a/research/e8-rank138-idle-hosting/local-evidence/TESTED-MANIFEST.json b/research/e8-rank138-idle-hosting/local-evidence/TESTED-MANIFEST.json
new file mode 100644
index 0000000000..b6be61282a
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/TESTED-MANIFEST.json
@@ -0,0 +1,167 @@
+{
+  "parent_manifest_sha256": "344d58298774e9e2bbfd0af6332507c3b3d2172bc70d88a79853e679bdaaa33f",
+  "files": {
+    "AUDIT.json": "c8f4f258773e3e03594318ddc35e34ac53917f0b73eca6eb47eab21062fd16ce",
+    "CERTIFICATE.json": "3e83186e02e98ddc85b6092924c5e37f95b023f5319b130a7285db7e83e26bde",
+    "EXPECTED.json": "ebbebef5de7bb36085bbb80f547d1c05096ebe2364f553e49567152dfcca1587",
+    "INHERITED-HOSTING-PROOF.md": "4f06d1dead63c62b076f0a6c1521c68c0b0544aa2c5df5e74a408fdfc34f91c4",
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE.md": "55c72da491d6d87643708ca7bc65f0193189a920ab43147c0941232db4742355",
+    "PROOF.md": "a1c23257c8bee1e47419a5a178ce7b3082e77c8e4036ee4ad7f4f0796bc84558",
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+    "vendor/pr439/tile_m.py": "d6ae4a556472d403773cd2117c992bfc10e1187112da1b3893f3fae628a131dd",
+    "verify.py": "3d7cdf274e54852d097cc23a9009856ce79b207bc81da4fcf9874dbeb9c80675"
+  }
+}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full311/AUDIT.json b/research/e8-rank138-idle-hosting/local-evidence/full311/AUDIT.json
new file mode 100644
index 0000000000..0519d52555
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full311/AUDIT.json
@@ -0,0 +1,41 @@
+{
+  "status": "PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT",
+  "bit_template_sha256": "50d9302688535aee7196ddba537c99620195b39ec096b3cfde8c2d6b2e691ef7",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f",
+  "bit_profile": {
+    "1": 728640,
+    "2": 305600,
+    "3": 80832,
+    "4": 111584,
+    "5": 33984,
+    "6": 8576,
+    "7": 16704,
+    "8": 2592
+  },
+  "complex_profile": {
+    "1": 138384,
+    "2": 56448,
+    "3": 15936,
+    "4": 16128,
+    "5": 32064,
+    "7": 3840,
+    "8": 7488
+  },
+  "bit_live": 37464,
+  "complex_live": 8400,
+  "bit_hosted_residuals": 159168,
+  "complex_hosted_residuals": 34560,
+  "bit_maxchild": 8,
+  "complex_maxchild": 8,
+  "mutations_rejected": [
+    "bit: hosted residual outside its window",
+    "bit: overlapping hosted coordinates",
+    "bit: understated live stock",
+    "bit: hosted owner on the active pair",
+    "bit: missing remainder child",
+    "complex: hosted residual outside its window",
+    "complex: remainder child understated",
+    "complex: dropped bank",
+    "complex: duplicated hosted residual"
+  ]
+}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full311/RECEIPT.json b/research/e8-rank138-idle-hosting/local-evidence/full311/RECEIPT.json
new file mode 100644
index 0000000000..098e9ba8f8
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full311/RECEIPT.json
@@ -0,0 +1,54 @@
+{
+  "status": "PASS_FULL_RANK138_IDLE_HOSTING",
+  "python": "3.11.15",
+  "kappa": "623036752743971/500000000000000000",
+  "kappa_decimal": "0.001246073505487942",
+  "manifest_sha256": "cf742207a00951e991a3ed667ee015449dedcd3fc41f3f857f36ed60a77fa7a8",
+  "checks": [
+    {
+      "name": "parent-full",
+      "seconds": 152.77,
+      "log_sha256": "b6b21746622747ea37b7423dd7600953185f3da7c5cca1019526ab4d9cfb06f1"
+    },
+    {
+      "name": "rank138-rebuild",
+      "seconds": 196.52,
+      "log_sha256": "023692adb1c2b7fea087b728940b3ae515f5a0bc3b6b633f0e7c803a83b9ef51"
+    },
+    {
+      "name": "export-records",
+      "seconds": 0.58,
+      "log_sha256": "9dce550911b0cf793ee3b9d1b02d438a4cf3e7de21854908d90c4c0a17398428"
+    },
+    {
+      "name": "bit-global-32",
+      "seconds": 10.41,
+      "log_sha256": "84a8b999a5ae5257692cea40cdb315ae9dc8b6e309b3f54cbf3c494033d95c9e"
+    },
+    {
+      "name": "bit-global-audit",
+      "seconds": 12.69,
+      "log_sha256": "0a7785ca29a6c66f234d7ff6016ee0aba1af7b484f78d6804035b1947300d5ce"
+    },
+    {
+      "name": "bit-hosting",
+      "seconds": 1.62,
+      "log_sha256": "fd8b27814b47ded2df679e78a8e9854334589992652cca0292ab6fc57a559535"
+    },
+    {
+      "name": "complex-hosting",
+      "seconds": 0.4,
+      "log_sha256": "3b42f65586cb5c37e06df560fae4dcde1c42526238697a73d103f9895df24fcd"
+    },
+    {
+      "name": "independent-hosting-audit",
+      "seconds": 7.93,
+      "log_sha256": "119d2232617c758984b3d5267343ec2841e640cfc2bc882a673b7bb8880ebeff"
+    },
+    {
+      "name": "exact-assembly",
+      "seconds": 0.24,
+      "log_sha256": "a7f1a4df38e65e43a3e8b3e8b0bf48f77b7b8e1c218ba590559dea28f5bf20bc"
+    }
+  ]
+}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full311/RESULT.json b/research/e8-rank138-idle-hosting/local-evidence/full311/RESULT.json
new file mode 100644
index 0000000000..79f353344d
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full311/RESULT.json
@@ -0,0 +1,116 @@
+{
+  "status": "PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY",
+  "kappa": "623036752743971/500000000000000000",
+  "kappa_decimal": "0.001246073505487942",
+  "bit_lower": "1247628141860215921989/1000000000000000000000000",
+  "complex_lower": "1267453159029119/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr434_percent": 9.97024959309606,
+  "bit": {
+    "live": 37464,
+    "physical": 37473,
+    "maxchild": 8,
+    "rank_mass": 2387712,
+    "hosted_residuals": 159168,
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 286,
+    "charged_two_level_coefficient_bits": 320,
+    "row_coefficient": 18355
+  },
+  "complex": {
+    "live": 8400,
+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
+  },
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+    "bulk_exposure_above_kappa": "94887473893671717996516814246485348104726063359519287252627776452954618443174044033128392250851780720284666136895050656759211998894561371080237426335078260687/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "Gaussian_arithmetic_above_kappa": "274051918678175416727146490513925253077022220380972006071168963223149938269066820315405846072782386955205777951310685216255296461012517172787321343582976940785881435881888112280392667/244445221714321341776106542638614302387960946769739466194364172702598935664175751673964508876621458014770616111526540765956864759518900417840230247253714183822074106100589319373914504000000000000000000",
+    "scalar_work_above_kappa": "396274529535336087615199761833232404271002693765841739168351049574449406101154696152388100511093115962591086007073955599233728840771967381707436467209834032696918488932182771967349919/244445221714321341776106542638614302387960946769739466194364172702598935664175751673964508876621458014770616111526540765956864759518900417840230247253714183822074106100589319373914504000000000000000000",
+    "dimension_above_kappa": "15239751767854916135152649350688247059328258305832482867195852463091264798654426218019360261409700443553940500571516090530034266343492048571131668028632234382211946375997436643797703012172277305568077/15277826357145083861006658914913393899247559173108716637147760793912433479010984479622781804788841125923163506970408797872304047469931276115014390453357136488879631631286832460869656500000000000000000"
+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "94287020424277834163680254991104056367009/62500000000000000000000000000000000000000000000",
+      "cutoff_log2": "15818260083840"
+    },
+    {
+      "gap": "29408785023369495427727557576784775208283541746515592160223473/15625000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "10162215197593843554"
+    },
+    {
+      "gap": "9172806953268257565007102287437866302700738375134023268194695915019528111703606081/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "6528569967547151436395053"
+    },
+    {
+      "gap": "2861063023687136162665647272462448282050413362534253607940694932308513294882957767367031894837944602257/976562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "4194186502884772884117694502077"
+    },
+    {
+      "gap": "892385685996938155756805007131692738674820820957983219861627580057577912447454106275234926512117420246977622028593300181729/244140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "2694495197022448340895066350774684894"
+    },
+    {
+      "gap": "278341373810753514651895273936640480712747372223547045381556825955966871607749148219279715333863104949343240788001105438628919762573664921739313/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1731039943451104430442680727076306832163430"
+    }
+  ],
+  "bit_template_sha256": "50d9302688535aee7196ddba537c99620195b39ec096b3cfde8c2d6b2e691ef7",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f"
+}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full311/bit-global-32.log b/research/e8-rank138-idle-hosting/local-evidence/full311/bit-global-32.log
new file mode 100644
index 0000000000..faa203d683
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full311/bit-global-32.log
@@ -0,0 +1,2 @@
+Fresh prefix bits 123 charged 128
+{"status": "PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE", "h": 8, "m": 64, "v": 120, "R": 740, "replicas": 32, "live": 56739, "physical": 56748, "word_sha256": "64d7d1e0c6ea7a3a8e91254c0dfd51b71637b49703ef4c1fce184fded5040bc9", "source_records_sha256": "93d36bac33afbe2a4b6a20064449766c72f91132d104071692c63c885e7c27d3", "independent_unbanked_scalar_columns": 7620, "all_scalar_columns_restored": true, "geometry_sha256": "51d0165bb89579eaea969630b48b290448dddb22e88a687f83a8c9760929846a", "template_sha256": "4d35d8f9c42d3823d3a40dc88e11dce08f1911131960b081073a13ac3a23fa22", "emitted_program_sha256": "4f83de501c4175bd9c4f3b107d7c24ff5980abfa551b8674a0c0149fdef74e46", "emitted_events": 5681952, "local_invocations": 288, "bank_assignments": 213120, "banks_per_stage": 2891, "entrance_rank_total": 138, "mixed_width_slots": true, "padding_calls": 0, "residual_isometries": 16, "extra_helper_route_factor_bound": 144, "profile": {"1": 728640, "2": 290304, "3": 80640, "4": 99936, "5": 33984, "7": 27072, "8": 2592, "14": 15360, "28": 15360, "42": 15360}, "paid_calls": 1309248, "rank_mass": 3621312, "deficit": 9984, "maxchild": 42, "halving_depth": 2, "halving_integer_inequality": [4096, 3528], "local_additions": 15414, "bridge_additions": 69120, "copy_erase_episodes": 2592, "global_prefix_bits": 123, "charged_prefix_bits": 128, "omitted_bridge_shears_rejected": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], "scope": "Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.", "seconds": 10.332607334014028}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full311/bit-global-audit.log b/research/e8-rank138-idle-hosting/local-evidence/full311/bit-global-audit.log
new file mode 100644
index 0000000000..b1ec560f88
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full311/bit-global-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT", "template_sha256": "4d35d8f9c42d3823d3a40dc88e11dce08f1911131960b081073a13ac3a23fa22", "source_frames": 944, "exact_nested_frame_pairs": 3364, "exact_reflected_pairs": 3364, "orthogonal_lift_argument": "Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.", "exact_bank_families": 26019, "mixed_width_slots": true, "entrance_rank_total": 138, "residual_isometries": 16, "mutations_rejected": ["omit an idle child", "omit a bridge", "omit terminal exchange", "remove a local invocation", "re-use a helper bank slot", "understate live stock", "omit a local paid move", "wrong reflected copy charge", "alter residual orthogonal basis", "wrong residual frame", "omit a residual route factor"], "profile": {"1": 728640, "2": 290304, "3": 80640, "4": 99936, "5": 33984, "7": 27072, "8": 2592, "14": 15360, "28": 15360, "42": 15360}, "seconds": 12.633058750070632}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full311/bit-hosting.log b/research/e8-rank138-idle-hosting/local-evidence/full311/bit-hosting.log
new file mode 100644
index 0000000000..7ce174fb44
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full311/bit-hosting.log
@@ -0,0 +1 @@
+{"live": 37464, "maxchild": 8, "hosted_residuals": 159168, "banks_per_stage_hosted": {"0": 0, "1": 0, "2": 2120, "3": 2504, "4": 0, "5": 0, "6": 0, "7": 2120, "8": 0}, "rank_mass": 2387712}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full311/complex-hosting.log b/research/e8-rank138-idle-hosting/local-evidence/full311/complex-hosting.log
new file mode 100644
index 0000000000..b8925ed69d
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full311/complex-hosting.log
@@ -0,0 +1 @@
+{"live": 8400, "maxchild": 8, "hosted_residuals": 34560, "banks_per_stage": [0, 0, 0, 160, 0, 120, 0, 0, 440], "deficit": 2496}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full311/exact-assembly.log b/research/e8-rank138-idle-hosting/local-evidence/full311/exact-assembly.log
new file mode 100644
index 0000000000..c761ef84f0
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full311/exact-assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY 0.001246073505487942 binding bit gain over #434 9.9702%
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full311/export-records.log b/research/e8-rank138-idle-hosting/local-evidence/full311/export-records.log
new file mode 100644
index 0000000000..43c21e206c
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full311/export-records.log
@@ -0,0 +1 @@
+exported 19729 records, 944 frames, n 980 ZERO 0
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full311/independent-hosting-audit.log b/research/e8-rank138-idle-hosting/local-evidence/full311/independent-hosting-audit.log
new file mode 100644
index 0000000000..e57495e0ef
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full311/independent-hosting-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT", "bit_template_sha256": "50d9302688535aee7196ddba537c99620195b39ec096b3cfde8c2d6b2e691ef7", "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f", "bit_live": 37464, "complex_live": 8400, "bit_hosted_residuals": 159168, "complex_hosted_residuals": 34560, "bit_maxchild": 8, "complex_maxchild": 8, "mutations_rejected": ["bit: hosted residual outside its window", "bit: overlapping hosted coordinates", "bit: understated live stock", "bit: hosted owner on the active pair", "bit: missing remainder child", "complex: hosted residual outside its window", "complex: remainder child understated", "complex: dropped bank", "complex: duplicated hosted residual"]}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full311/parent-full.log b/research/e8-rank138-idle-hosting/local-evidence/full311/parent-full.log
new file mode 100644
index 0000000000..ee23b611cb
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full311/parent-full.log
@@ -0,0 +1,16 @@
+PASS hamming_packets
+PASS complex_construct
+PASS complex_audit
+PASS complex_emit
+PASS complex_phases
+PASS bit_construct
+PASS bit_kernel
+PASS bit_export
+PASS bit_global
+PASS bit_audit
+PASS bit_price
+PASS complex_integrate
+PASS complex_replay
+PASS combined
+PASS independent_audit
+PASS conditional kappa 0.001138798055343319
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full311/parent/RESULT.json b/research/e8-rank138-idle-hosting/local-evidence/full311/parent/RESULT.json
new file mode 100644
index 0000000000..655468f65f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full311/parent/RESULT.json
@@ -0,0 +1,126 @@
+{
+  "status": "PASS_CONDITIONAL_SPLIT_CENTRE_ASSEMBLY",
+  "kappa": "1138798055343319/1000000000000000000",
+  "kappa_decimal": "0.001138798055343319",
+  "bit_lower": "17814006170324008149/15625000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr425_percent": 8.663365470849168,
+  "bit_invoice": {
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "extra_helper_route_factor_bound": 144,
+    "selector_charge": 2375347104,
+    "full_counted_coefficient": "8271410009661736653226855278395470361",
+    "two_level_coefficient": "7323242093316479963924177312150069573045566553609912891292783054664675728289084971684",
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 282,
+    "charged_two_level_coefficient_bits": 512,
+    "row_coefficient": 18355,
+    "live": 14187,
+    "physical": 14196
+  },
+  "strict_outer_constraints": {
+    "bit_positive": "14593233854729427444681100920656130015510389359413765203363540962808559686244019848566041670026752010920212879329346077390830883874588140959948475412165679011557/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "561793975111583755318899079343869984489610640586234796636459037191440313755980151433958329973247989079787120670653922609169116125411859040051524587834320988443/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "30066013450793671/1000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "561793975111583740163871249502858784489610640586234796636459037191440313755980151433958329973247989079787120670653922609169116125411859040051524587834320988443/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_positive": "7296616927364713707747316605598637563074093759050752586171381121990514639758468961474461148769356156894064769637921027775202562607947993089143353831494698545830024587834320988443/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_internal": "14593233854729427444681100920656130015510389359413765203363540962808559686244019848566041670026752010920212879329346077390830883874588140959948475412165679011557/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_leaf": "280896987555791884675169479480856836925906240949247413828618878009485360241531038525538851230643843105935230362078972224797437392052006910856646168505301454169975412165679011557/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_positive": "7296616927364715307747316605598637563074093759050752586171381121990514639758468961474461148769356156894064769637921027775202562607947993089143353831494698545830024587834320988443/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_below_one": "6392703383072635284692252683394401362436925906240949247413828618878009485360241531038525538851230643843105935230362078972224797437392052006910856646168505301454169975412165679011557/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_reservations": "1/4000000000000000000",
+    "lambda_above_tau": "14593233854729427444681100920656130015510389359413765203363540962808559686244019848566041670026752010920212879329346077390830883874588140959948475412165679011557/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_sigma": "561793975111583769912132934073297429170711561242364812146848396605205517119521114242518016217267837645828790697405933529381995454757936430882408462422461948391475412165679011557/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+    "lambda_prime_above_lambda": "14593233854729427444681100920656130015510389359413765203363540962808559686244019848566041670026752010920212879329346077390830883874588140959948475412165679011557/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_leaf": "280896987555791884675169479480856836925906240949247413828618878009485360241531038525538851230643843105935230362078972224797437392052006910856646168505301454169975412165679011557/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_reservations": "1/4000000000000000000",
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+    "epsilon_positive": "6399999999999999993600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/6407296616927364713707747316605598637563074093759050752586171381121990514639758468961474461148769356156894064769637921027775202562607947993089143353831494698545830024587834320988443",
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+    "gamma_sublinear": "1/2000000000000000000",
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+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "50238871853096532822362240972278860750249/40000000000000000000000000000000000000000000000",
+      "cutoff_log2": "22821423299056"
+    },
+    {
+      "gap": "11455431336719088296695724797447540819776987379259584929022443/8000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "17557374861114977035"
+    },
+    {
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+      "cutoff_log2": "13507545431071750093791293"
+    },
+    {
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+      "cutoff_log2": "10391860116659867549821478467986"
+    },
+    {
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+      "cutoff_log2": "7994846823599212441742710007613379908"
+    },
+    {
+      "gap": "30966899079343869984489610640586234796636459037191440313755980151433958329973247989079787120670653922609169116125411859040051524587834320988443/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "6150734807365621625035986466966332327804006"
+    }
+  ],
+  "bit_template_sha256": "b87ed8c20819237f2daacdd1383a2776419551a62a7014eb9720af146a9dd9ec",
+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f",
+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim.",
+  "verification_steps": [
+    "hamming_packets",
+    "complex_construct",
+    "complex_audit",
+    "complex_emit",
+    "complex_phases",
+    "bit_construct",
+    "bit_kernel",
+    "bit_export",
+    "bit_global",
+    "bit_audit",
+    "bit_price",
+    "complex_integrate",
+    "complex_replay",
+    "combined",
+    "independent_audit"
+  ],
+  "phase_mode": "full replay",
+  "manifest_sha256": "344d58298774e9e2bbfd0af6332507c3b3d2172bc70d88a79853e679bdaaa33f"
+}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full311/rank138-rebuild.log b/research/e8-rank138-idle-hosting/local-evidence/full311/rank138-rebuild.log
new file mode 100644
index 0000000000..376524fe7c
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full311/rank138-rebuild.log
@@ -0,0 +1 @@
+{"donor_slots": 103, "entrance_rank": 138, "entries": 114, "input_sha256": "d6ec8811541d6ab59a3bbbaaa15bccc8918b3b43b23d9f593198cfe90826fd20", "interface": {"R": 740, "helper_start_dims": {"0": 626, "1": 106, "4": 8}, "n": 980, "prefix_allow": 192, "prefix_bits": 123, "prefix_ok": true, "streams": {"forward": {"adds": 15414, "copies": 9, "hist": {"1": 2530, "2": 1008, "3": 280, "4": 347, "5": 118, "7": 14, "8": 9}, "row_l1": 780}, "reverse": {"adds": 15414, "copies": 9, "hist": {"1": 2530, "2": 1008, "3": 280, "4": 347, "5": 118, "7": 14, "8": 9}, "row_l1": 18182}}}, "mutations_rejected": ["retained row used as pivot", "duplicate pivot", "eight replicas do not fill integral banks", "omit a kernel dirty-response correction", "wrong primitive input frame"], "output_sha256": "64d7d1e0c6ea7a3a8e91254c0dfd51b71637b49703ef4c1fce184fded5040bc9", "post_kernel_frame_changes": [112, 42], "pre_kernel_frame_changes": 57, "replicas": 32, "retimed_sha256": "fec026cda755e5ef93f7ed56923d1452da925cbe0051585e913e0837d9a70ffb", "status": "PASS_FROZEN_RETIMING_KERNEL_REPLICA_REBUILD"}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full314/AUDIT.json b/research/e8-rank138-idle-hosting/local-evidence/full314/AUDIT.json
new file mode 100644
index 0000000000..0519d52555
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full314/AUDIT.json
@@ -0,0 +1,41 @@
+{
+  "status": "PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT",
+  "bit_template_sha256": "50d9302688535aee7196ddba537c99620195b39ec096b3cfde8c2d6b2e691ef7",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f",
+  "bit_profile": {
+    "1": 728640,
+    "2": 305600,
+    "3": 80832,
+    "4": 111584,
+    "5": 33984,
+    "6": 8576,
+    "7": 16704,
+    "8": 2592
+  },
+  "complex_profile": {
+    "1": 138384,
+    "2": 56448,
+    "3": 15936,
+    "4": 16128,
+    "5": 32064,
+    "7": 3840,
+    "8": 7488
+  },
+  "bit_live": 37464,
+  "complex_live": 8400,
+  "bit_hosted_residuals": 159168,
+  "complex_hosted_residuals": 34560,
+  "bit_maxchild": 8,
+  "complex_maxchild": 8,
+  "mutations_rejected": [
+    "bit: hosted residual outside its window",
+    "bit: overlapping hosted coordinates",
+    "bit: understated live stock",
+    "bit: hosted owner on the active pair",
+    "bit: missing remainder child",
+    "complex: hosted residual outside its window",
+    "complex: remainder child understated",
+    "complex: dropped bank",
+    "complex: duplicated hosted residual"
+  ]
+}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full314/RECEIPT.json b/research/e8-rank138-idle-hosting/local-evidence/full314/RECEIPT.json
new file mode 100644
index 0000000000..24e3926f9b
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full314/RECEIPT.json
@@ -0,0 +1,54 @@
+{
+  "status": "PASS_FULL_RANK138_IDLE_HOSTING",
+  "python": "3.14.8",
+  "kappa": "623036752743971/500000000000000000",
+  "kappa_decimal": "0.001246073505487942",
+  "manifest_sha256": "cf742207a00951e991a3ed667ee015449dedcd3fc41f3f857f36ed60a77fa7a8",
+  "checks": [
+    {
+      "name": "parent-full",
+      "seconds": 131.48,
+      "log_sha256": "b6b21746622747ea37b7423dd7600953185f3da7c5cca1019526ab4d9cfb06f1"
+    },
+    {
+      "name": "rank138-rebuild",
+      "seconds": 120.84,
+      "log_sha256": "023692adb1c2b7fea087b728940b3ae515f5a0bc3b6b633f0e7c803a83b9ef51"
+    },
+    {
+      "name": "export-records",
+      "seconds": 0.4,
+      "log_sha256": "9dce550911b0cf793ee3b9d1b02d438a4cf3e7de21854908d90c4c0a17398428"
+    },
+    {
+      "name": "bit-global-32",
+      "seconds": 10.97,
+      "log_sha256": "80b69cf534526a05dbec64e4c500972436b6b1e33ca139b9a860d337843bb796"
+    },
+    {
+      "name": "bit-global-audit",
+      "seconds": 6.97,
+      "log_sha256": "f6d16f9fa3a585590049dc39281fbd2f6a73e48e3a9f10f616ab8d8112099c9d"
+    },
+    {
+      "name": "bit-hosting",
+      "seconds": 1.11,
+      "log_sha256": "fd8b27814b47ded2df679e78a8e9854334589992652cca0292ab6fc57a559535"
+    },
+    {
+      "name": "complex-hosting",
+      "seconds": 0.38,
+      "log_sha256": "3b42f65586cb5c37e06df560fae4dcde1c42526238697a73d103f9895df24fcd"
+    },
+    {
+      "name": "independent-hosting-audit",
+      "seconds": 4.0,
+      "log_sha256": "119d2232617c758984b3d5267343ec2841e640cfc2bc882a673b7bb8880ebeff"
+    },
+    {
+      "name": "exact-assembly",
+      "seconds": 0.23,
+      "log_sha256": "a7f1a4df38e65e43a3e8b3e8b0bf48f77b7b8e1c218ba590559dea28f5bf20bc"
+    }
+  ]
+}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full314/RESULT.json b/research/e8-rank138-idle-hosting/local-evidence/full314/RESULT.json
new file mode 100644
index 0000000000..79f353344d
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full314/RESULT.json
@@ -0,0 +1,116 @@
+{
+  "status": "PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY",
+  "kappa": "623036752743971/500000000000000000",
+  "kappa_decimal": "0.001246073505487942",
+  "bit_lower": "1247628141860215921989/1000000000000000000000000",
+  "complex_lower": "1267453159029119/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr434_percent": 9.97024959309606,
+  "bit": {
+    "live": 37464,
+    "physical": 37473,
+    "maxchild": 8,
+    "rank_mass": 2387712,
+    "hosted_residuals": 159168,
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 286,
+    "charged_two_level_coefficient_bits": 320,
+    "row_coefficient": 18355
+  },
+  "complex": {
+    "live": 8400,
+    "physical": 8978,
+    "maxchild": 8,
+    "rank_mass": 610704,
+    "hosted_residuals": 34560,
+    "physical_stock_bits": 2641,
+    "router_bits": 7983,
+    "literal_bits": 35283,
+    "row_coefficient": 15443
+  },
+  "strict_outer_constraints": {
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+    "complex_below_one_over32": "29982546840970881/1000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "1210023020562932208550531584855138187051523936640480712747372223547045381556825955966871607749148219279715333863104949343240788001105438628919762573664921739313/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_positive": "38074589290167722013317829826787798495118346217433274295521587824866958021968959245563609577682251846327013940817595744608094939862552230028780906714272977759263262573664921739313/30517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+    "q_below_reservations": "1/4000000000000000000",
+    "lambda_above_tau": "76149178580335444178934016814246485348104726063359519287252627776452954618443174044033128392250851780720284666136895050656759211998894561371080237426335078260687/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+    "compact_reservations": "1/4000000000000000000",
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+    "dimension_above_kappa": "15239751767854916135152649350688247059328258305832482867195852463091264798654426218019360261409700443553940500571516090530034266343492048571131668028632234382211946375997436643797703012172277305568077/15277826357145083861006658914913393899247559173108716637147760793912433479010984479622781804788841125923163506970408797872304047469931276115014390453357136488879631631286832460869656500000000000000000"
+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "94287020424277834163680254991104056367009/62500000000000000000000000000000000000000000000",
+      "cutoff_log2": "15818260083840"
+    },
+    {
+      "gap": "29408785023369495427727557576784775208283541746515592160223473/15625000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "10162215197593843554"
+    },
+    {
+      "gap": "9172806953268257565007102287437866302700738375134023268194695915019528111703606081/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "6528569967547151436395053"
+    },
+    {
+      "gap": "2861063023687136162665647272462448282050413362534253607940694932308513294882957767367031894837944602257/976562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "4194186502884772884117694502077"
+    },
+    {
+      "gap": "892385685996938155756805007131692738674820820957983219861627580057577912447454106275234926512117420246977622028593300181729/244140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "2694495197022448340895066350774684894"
+    },
+    {
+      "gap": "278341373810753514651895273936640480712747372223547045381556825955966871607749148219279715333863104949343240788001105438628919762573664921739313/61035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1731039943451104430442680727076306832163430"
+    }
+  ],
+  "bit_template_sha256": "50d9302688535aee7196ddba537c99620195b39ec096b3cfde8c2d6b2e691ef7",
+  "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f"
+}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full314/bit-global-32.log b/research/e8-rank138-idle-hosting/local-evidence/full314/bit-global-32.log
new file mode 100644
index 0000000000..357fcf412c
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full314/bit-global-32.log
@@ -0,0 +1,2 @@
+Fresh prefix bits 123 charged 128
+{"status": "PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE", "h": 8, "m": 64, "v": 120, "R": 740, "replicas": 32, "live": 56739, "physical": 56748, "word_sha256": "64d7d1e0c6ea7a3a8e91254c0dfd51b71637b49703ef4c1fce184fded5040bc9", "source_records_sha256": "93d36bac33afbe2a4b6a20064449766c72f91132d104071692c63c885e7c27d3", "independent_unbanked_scalar_columns": 7620, "all_scalar_columns_restored": true, "geometry_sha256": "51d0165bb89579eaea969630b48b290448dddb22e88a687f83a8c9760929846a", "template_sha256": "4d35d8f9c42d3823d3a40dc88e11dce08f1911131960b081073a13ac3a23fa22", "emitted_program_sha256": "4f83de501c4175bd9c4f3b107d7c24ff5980abfa551b8674a0c0149fdef74e46", "emitted_events": 5681952, "local_invocations": 288, "bank_assignments": 213120, "banks_per_stage": 2891, "entrance_rank_total": 138, "mixed_width_slots": true, "padding_calls": 0, "residual_isometries": 16, "extra_helper_route_factor_bound": 144, "profile": {"1": 728640, "2": 290304, "3": 80640, "4": 99936, "5": 33984, "7": 27072, "8": 2592, "14": 15360, "28": 15360, "42": 15360}, "paid_calls": 1309248, "rank_mass": 3621312, "deficit": 9984, "maxchild": 42, "halving_depth": 2, "halving_integer_inequality": [4096, 3528], "local_additions": 15414, "bridge_additions": 69120, "copy_erase_episodes": 2592, "global_prefix_bits": 123, "charged_prefix_bits": 128, "omitted_bridge_shears_rejected": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], "scope": "Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.", "seconds": 10.859118791064247}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full314/bit-global-audit.log b/research/e8-rank138-idle-hosting/local-evidence/full314/bit-global-audit.log
new file mode 100644
index 0000000000..c7f2143a69
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full314/bit-global-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT", "template_sha256": "4d35d8f9c42d3823d3a40dc88e11dce08f1911131960b081073a13ac3a23fa22", "source_frames": 944, "exact_nested_frame_pairs": 3364, "exact_reflected_pairs": 3364, "orthogonal_lift_argument": "Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.", "exact_bank_families": 26019, "mixed_width_slots": true, "entrance_rank_total": 138, "residual_isometries": 16, "mutations_rejected": ["omit an idle child", "omit a bridge", "omit terminal exchange", "remove a local invocation", "re-use a helper bank slot", "understate live stock", "omit a local paid move", "wrong reflected copy charge", "alter residual orthogonal basis", "wrong residual frame", "omit a residual route factor"], "profile": {"1": 728640, "2": 290304, "3": 80640, "4": 99936, "5": 33984, "7": 27072, "8": 2592, "14": 15360, "28": 15360, "42": 15360}, "seconds": 6.887823792058043}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full314/bit-hosting.log b/research/e8-rank138-idle-hosting/local-evidence/full314/bit-hosting.log
new file mode 100644
index 0000000000..7ce174fb44
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full314/bit-hosting.log
@@ -0,0 +1 @@
+{"live": 37464, "maxchild": 8, "hosted_residuals": 159168, "banks_per_stage_hosted": {"0": 0, "1": 0, "2": 2120, "3": 2504, "4": 0, "5": 0, "6": 0, "7": 2120, "8": 0}, "rank_mass": 2387712}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full314/complex-hosting.log b/research/e8-rank138-idle-hosting/local-evidence/full314/complex-hosting.log
new file mode 100644
index 0000000000..b8925ed69d
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full314/complex-hosting.log
@@ -0,0 +1 @@
+{"live": 8400, "maxchild": 8, "hosted_residuals": 34560, "banks_per_stage": [0, 0, 0, 160, 0, 120, 0, 0, 440], "deficit": 2496}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full314/exact-assembly.log b/research/e8-rank138-idle-hosting/local-evidence/full314/exact-assembly.log
new file mode 100644
index 0000000000..c761ef84f0
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full314/exact-assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY 0.001246073505487942 binding bit gain over #434 9.9702%
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full314/export-records.log b/research/e8-rank138-idle-hosting/local-evidence/full314/export-records.log
new file mode 100644
index 0000000000..43c21e206c
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full314/export-records.log
@@ -0,0 +1 @@
+exported 19729 records, 944 frames, n 980 ZERO 0
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full314/independent-hosting-audit.log b/research/e8-rank138-idle-hosting/local-evidence/full314/independent-hosting-audit.log
new file mode 100644
index 0000000000..e57495e0ef
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full314/independent-hosting-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT", "bit_template_sha256": "50d9302688535aee7196ddba537c99620195b39ec096b3cfde8c2d6b2e691ef7", "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f", "bit_live": 37464, "complex_live": 8400, "bit_hosted_residuals": 159168, "complex_hosted_residuals": 34560, "bit_maxchild": 8, "complex_maxchild": 8, "mutations_rejected": ["bit: hosted residual outside its window", "bit: overlapping hosted coordinates", "bit: understated live stock", "bit: hosted owner on the active pair", "bit: missing remainder child", "complex: hosted residual outside its window", "complex: remainder child understated", "complex: dropped bank", "complex: duplicated hosted residual"]}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full314/parent-full.log b/research/e8-rank138-idle-hosting/local-evidence/full314/parent-full.log
new file mode 100644
index 0000000000..ee23b611cb
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full314/parent-full.log
@@ -0,0 +1,16 @@
+PASS hamming_packets
+PASS complex_construct
+PASS complex_audit
+PASS complex_emit
+PASS complex_phases
+PASS bit_construct
+PASS bit_kernel
+PASS bit_export
+PASS bit_global
+PASS bit_audit
+PASS bit_price
+PASS complex_integrate
+PASS complex_replay
+PASS combined
+PASS independent_audit
+PASS conditional kappa 0.001138798055343319
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full314/parent/RESULT.json b/research/e8-rank138-idle-hosting/local-evidence/full314/parent/RESULT.json
new file mode 100644
index 0000000000..655468f65f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full314/parent/RESULT.json
@@ -0,0 +1,126 @@
+{
+  "status": "PASS_CONDITIONAL_SPLIT_CENTRE_ASSEMBLY",
+  "kappa": "1138798055343319/1000000000000000000",
+  "kappa_decimal": "0.001138798055343319",
+  "bit_lower": "17814006170324008149/15625000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr425_percent": 8.663365470849168,
+  "bit_invoice": {
+    "prefix_bits": 123,
+    "charged_prefix_bits": 128,
+    "extra_helper_route_factor_bound": 144,
+    "selector_charge": 2375347104,
+    "full_counted_coefficient": "8271410009661736653226855278395470361",
+    "two_level_coefficient": "7323242093316479963924177312150069573045566553609912891292783054664675728289084971684",
+    "coefficient_bits": 123,
+    "two_level_coefficient_bits": 282,
+    "charged_two_level_coefficient_bits": 512,
+    "row_coefficient": 18355,
+    "live": 14187,
+    "physical": 14196
+  },
+  "strict_outer_constraints": {
+    "bit_positive": "14593233854729427444681100920656130015510389359413765203363540962808559686244019848566041670026752010920212879329346077390830883874588140959948475412165679011557/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "561793975111583755318899079343869984489610640586234796636459037191440313755980151433958329973247989079787120670653922609169116125411859040051524587834320988443/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "30066013450793671/1000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "561793975111583740163871249502858784489610640586234796636459037191440313755980151433958329973247989079787120670653922609169116125411859040051524587834320988443/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f",
+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim.",
+  "verification_steps": [
+    "hamming_packets",
+    "complex_construct",
+    "complex_audit",
+    "complex_emit",
+    "complex_phases",
+    "bit_construct",
+    "bit_kernel",
+    "bit_export",
+    "bit_global",
+    "bit_audit",
+    "bit_price",
+    "complex_integrate",
+    "complex_replay",
+    "combined",
+    "independent_audit"
+  ],
+  "phase_mode": "full replay",
+  "manifest_sha256": "344d58298774e9e2bbfd0af6332507c3b3d2172bc70d88a79853e679bdaaa33f"
+}
diff --git a/research/e8-rank138-idle-hosting/local-evidence/full314/rank138-rebuild.log b/research/e8-rank138-idle-hosting/local-evidence/full314/rank138-rebuild.log
new file mode 100644
index 0000000000..376524fe7c
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/local-evidence/full314/rank138-rebuild.log
@@ -0,0 +1 @@
+{"donor_slots": 103, "entrance_rank": 138, "entries": 114, "input_sha256": "d6ec8811541d6ab59a3bbbaaa15bccc8918b3b43b23d9f593198cfe90826fd20", "interface": {"R": 740, "helper_start_dims": {"0": 626, "1": 106, "4": 8}, "n": 980, "prefix_allow": 192, "prefix_bits": 123, "prefix_ok": true, "streams": {"forward": {"adds": 15414, "copies": 9, "hist": {"1": 2530, "2": 1008, "3": 280, "4": 347, "5": 118, "7": 14, "8": 9}, "row_l1": 780}, "reverse": {"adds": 15414, "copies": 9, "hist": {"1": 2530, "2": 1008, "3": 280, "4": 347, "5": 118, "7": 14, "8": 9}, "row_l1": 18182}}}, "mutations_rejected": ["retained row used as pivot", "duplicate pivot", "eight replicas do not fill integral banks", "omit a kernel dirty-response correction", "wrong primitive input frame"], "output_sha256": "64d7d1e0c6ea7a3a8e91254c0dfd51b71637b49703ef4c1fce184fded5040bc9", "post_kernel_frame_changes": [112, 42], "pre_kernel_frame_changes": 57, "replicas": 32, "retimed_sha256": "fec026cda755e5ef93f7ed56923d1452da925cbe0051585e913e0837d9a70ffb", "status": "PASS_FROZEN_RETIMING_KERNEL_REPLICA_REBUILD"}
diff --git a/research/e8-rank138-idle-hosting/research/ALL-COORDINATE-AUGMENTED138.json b/research/e8-rank138-idle-hosting/research/ALL-COORDINATE-AUGMENTED138.json
new file mode 100644
index 0000000000..05cbd3ba33
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/ALL-COORDINATE-AUGMENTED138.json
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+}
diff --git a/research/e8-rank138-idle-hosting/research/BASIS-EXCHANGES138.json b/research/e8-rank138-idle-hosting/research/BASIS-EXCHANGES138.json
new file mode 100644
index 0000000000..1a8a089c50
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/BASIS-EXCHANGES138.json
@@ -0,0 +1,7 @@
+{
+  "status": "BASIS_EXCHANGE_NOMINATIONS_REQUIRE_REPLAY",
+  "tested": 281,
+  "reference_score": 32.25815033883536,
+  "improving": 0,
+  "top": []
+}
diff --git a/research/e8-rank138-idle-hosting/research/KERNEL138-GROUP45-SEARCH.json b/research/e8-rank138-idle-hosting/research/KERNEL138-GROUP45-SEARCH.json
new file mode 100644
index 0000000000..268513c261
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/KERNEL138-GROUP45-SEARCH.json
@@ -0,0 +1,8 @@
+{
+  "status": "GROUP_NOMINATION_NEEDS_EXACT_REPLAY",
+  "source_sha256": "64d7d1e0c6ea7a3a8e91254c0dfd51b71637b49703ef4c1fce184fded5040bc9",
+  "output_sha256": "fb0d1109e54a9e8b2c88a08f0360515dd5273d3a177ba15383ce23c0a862c2d4",
+  "groups_tested": 49681,
+  "positive": 0,
+  "selected": []
+}
diff --git a/research/e8-rank138-idle-hosting/research/KERNEL138-MIXED-FRAMES.json b/research/e8-rank138-idle-hosting/research/KERNEL138-MIXED-FRAMES.json
new file mode 100644
index 0000000000..e572b02d53
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/KERNEL138-MIXED-FRAMES.json
@@ -0,0 +1,8 @@
+{
+  "status": "MIXED_FRAME_NOMINATION_NEEDS_EXACT_REPLAY",
+  "source_sha256": "64d7d1e0c6ea7a3a8e91254c0dfd51b71637b49703ef4c1fce184fded5040bc9",
+  "output_sha256": "fb0d1109e54a9e8b2c88a08f0360515dd5273d3a177ba15383ce23c0a862c2d4",
+  "groups_tested": 21420,
+  "positive": 0,
+  "selected": []
+}
diff --git a/research/e8-rank138-idle-hosting/research/KERNEL138-MIXED-FRAMES45.json b/research/e8-rank138-idle-hosting/research/KERNEL138-MIXED-FRAMES45.json
new file mode 100644
index 0000000000..bd4e38b889
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/KERNEL138-MIXED-FRAMES45.json
@@ -0,0 +1,8 @@
+{
+  "status": "MIXED_FRAME_NOMINATION_NEEDS_EXACT_REPLAY",
+  "source_sha256": "64d7d1e0c6ea7a3a8e91254c0dfd51b71637b49703ef4c1fce184fded5040bc9",
+  "output_sha256": "fb0d1109e54a9e8b2c88a08f0360515dd5273d3a177ba15383ce23c0a862c2d4",
+  "groups_tested": 223744,
+  "positive": 0,
+  "selected": []
+}
diff --git a/research/e8-rank138-idle-hosting/research/STORAGE-FAILURE.json b/research/e8-rank138-idle-hosting/research/STORAGE-FAILURE.json
new file mode 100644
index 0000000000..a343090f22
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/STORAGE-FAILURE.json
@@ -0,0 +1,6 @@
+{
+  "status": "FAILED_STORAGE",
+  "process": "32-replica global replay",
+  "exit_code": 120,
+  "error": "SSD filled while lossless archive was also being created; unfinished archive removed, original run retained. Global output must be rebuilt in a fresh directory."
+}
diff --git a/research/e8-rank138-idle-hosting/research/assembly.log b/research/e8-rank138-idle-hosting/research/assembly.log
new file mode 100644
index 0000000000..c761ef84f0
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/assembly.log
@@ -0,0 +1 @@
+PASS_CONDITIONAL_IDLE_AXIS_HOSTING_ASSEMBLY 0.001246073505487942 binding bit gain over #434 9.9702%
diff --git a/research/e8-rank138-idle-hosting/research/bit-hosting.log b/research/e8-rank138-idle-hosting/research/bit-hosting.log
new file mode 100644
index 0000000000..7ce174fb44
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/bit-hosting.log
@@ -0,0 +1 @@
+{"live": 37464, "maxchild": 8, "hosted_residuals": 159168, "banks_per_stage_hosted": {"0": 0, "1": 0, "2": 2120, "3": 2504, "4": 0, "5": 0, "6": 0, "7": 2120, "8": 0}, "rank_mass": 2387712}
diff --git a/research/e8-rank138-idle-hosting/research/complex-hosting.log b/research/e8-rank138-idle-hosting/research/complex-hosting.log
new file mode 100644
index 0000000000..b8925ed69d
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/complex-hosting.log
@@ -0,0 +1 @@
+{"live": 8400, "maxchild": 8, "hosted_residuals": 34560, "banks_per_stage": [0, 0, 0, 160, 0, 120, 0, 0, 440], "deficit": 2496}
diff --git a/research/e8-rank138-idle-hosting/research/export.log b/research/e8-rank138-idle-hosting/research/export.log
new file mode 100644
index 0000000000..43c21e206c
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/export.log
@@ -0,0 +1 @@
+exported 19729 records, 944 frames, n 980 ZERO 0
diff --git a/research/e8-rank138-idle-hosting/research/global-audit.log b/research/e8-rank138-idle-hosting/research/global-audit.log
new file mode 100644
index 0000000000..c097a95a7b
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/global-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT", "template_sha256": "4d35d8f9c42d3823d3a40dc88e11dce08f1911131960b081073a13ac3a23fa22", "source_frames": 944, "exact_nested_frame_pairs": 3364, "exact_reflected_pairs": 3364, "orthogonal_lift_argument": "Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.", "exact_bank_families": 26019, "mixed_width_slots": true, "entrance_rank_total": 138, "residual_isometries": 16, "mutations_rejected": ["omit an idle child", "omit a bridge", "omit terminal exchange", "remove a local invocation", "re-use a helper bank slot", "understate live stock", "omit a local paid move", "wrong reflected copy charge", "alter residual orthogonal basis", "wrong residual frame", "omit a residual route factor"], "profile": {"1": 728640, "2": 290304, "3": 80640, "4": 99936, "5": 33984, "7": 27072, "8": 2592, "14": 15360, "28": 15360, "42": 15360}, "seconds": 6.769209749996662}
diff --git a/research/e8-rank138-idle-hosting/research/global-retry.log b/research/e8-rank138-idle-hosting/research/global-retry.log
new file mode 100644
index 0000000000..2a5d6fe409
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/global-retry.log
@@ -0,0 +1,6 @@
+Traceback (most recent call last):
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/hosted138-screen/code/bit_global.py", line 10, in <module>
+    from residual_routes import generate
+  File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/hosted138-screen/code/residual_routes.py", line 7, in <module>
+    from bank_routes import validate_isometries
+ModuleNotFoundError: No module named 'bank_routes'
diff --git a/research/e8-rank138-idle-hosting/research/global-retry2.log b/research/e8-rank138-idle-hosting/research/global-retry2.log
new file mode 100644
index 0000000000..41a40b0917
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/global-retry2.log
@@ -0,0 +1,2 @@
+Fresh prefix bits 123 charged 128
+{"status": "PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE", "h": 8, "m": 64, "v": 120, "R": 740, "replicas": 32, "live": 56739, "physical": 56748, "word_sha256": "64d7d1e0c6ea7a3a8e91254c0dfd51b71637b49703ef4c1fce184fded5040bc9", "source_records_sha256": "93d36bac33afbe2a4b6a20064449766c72f91132d104071692c63c885e7c27d3", "independent_unbanked_scalar_columns": 7620, "all_scalar_columns_restored": true, "geometry_sha256": "51d0165bb89579eaea969630b48b290448dddb22e88a687f83a8c9760929846a", "template_sha256": "4d35d8f9c42d3823d3a40dc88e11dce08f1911131960b081073a13ac3a23fa22", "emitted_program_sha256": "4f83de501c4175bd9c4f3b107d7c24ff5980abfa551b8674a0c0149fdef74e46", "emitted_events": 5681952, "local_invocations": 288, "bank_assignments": 213120, "banks_per_stage": 2891, "entrance_rank_total": 138, "mixed_width_slots": true, "padding_calls": 0, "residual_isometries": 16, "extra_helper_route_factor_bound": 144, "profile": {"1": 728640, "2": 290304, "3": 80640, "4": 99936, "5": 33984, "7": 27072, "8": 2592, "14": 15360, "28": 15360, "42": 15360}, "paid_calls": 1309248, "rank_mass": 3621312, "deficit": 9984, "maxchild": 42, "halving_depth": 2, "halving_integer_inequality": [4096, 3528], "local_additions": 15414, "bridge_additions": 69120, "copy_erase_episodes": 2592, "global_prefix_bits": 123, "charged_prefix_bits": 128, "omitted_bridge_shears_rejected": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], "scope": "Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.", "seconds": 9.94310954096727}
diff --git a/research/e8-rank138-idle-hosting/research/group45-negative.json b/research/e8-rank138-idle-hosting/research/group45-negative.json
new file mode 100644
index 0000000000..82aeb6e166
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/group45-negative.json
@@ -0,0 +1,8 @@
+{
+  "status": "GROUP_NOMINATION_NEEDS_EXACT_REPLAY",
+  "source_sha256": "00d8aa8608e40b53fd8752399de06cb730cc55caaadc528f88379cb31b8460a6",
+  "output_sha256": "00d8aa8608e40b53fd8752399de06cb730cc55caaadc528f88379cb31b8460a6",
+  "groups_tested": 613,
+  "positive": 0,
+  "selected": []
+}
diff --git a/research/e8-rank138-idle-hosting/research/hosting-audit.log b/research/e8-rank138-idle-hosting/research/hosting-audit.log
new file mode 100644
index 0000000000..e57495e0ef
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/hosting-audit.log
@@ -0,0 +1 @@
+{"status": "PASS_INDEPENDENT_IDLE_AXIS_HOSTING_AUDIT", "bit_template_sha256": "50d9302688535aee7196ddba537c99620195b39ec096b3cfde8c2d6b2e691ef7", "complex_template_sha256": "6f48c811e981bbd76436dfe19f497ed627794987fd4347daf123d0d698a5fe3f", "bit_live": 37464, "complex_live": 8400, "bit_hosted_residuals": 159168, "complex_hosted_residuals": 34560, "bit_maxchild": 8, "complex_maxchild": 8, "mutations_rejected": ["bit: hosted residual outside its window", "bit: overlapping hosted coordinates", "bit: understated live stock", "bit: hosted owner on the active pair", "bit: missing remainder child", "complex: hosted residual outside its window", "complex: remainder child understated", "complex: dropped bank", "complex: duplicated hosted residual"]}
diff --git a/research/e8-rank138-idle-hosting/research/hosting138-64-replica-screen.json b/research/e8-rank138-idle-hosting/research/hosting138-64-replica-screen.json
new file mode 100644
index 0000000000..e64b48f227
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/hosting138-64-replica-screen.json
@@ -0,0 +1,48 @@
+{
+  "status": "PASS_TWO_EXACT_AGGREGATE_MOMENTS_EMITTED_TEMPLATE_AND_INVOICE_PENDING",
+  "reference_bit_lower": "249369163853537814231/200000000000000000000000",
+  "prior_score": 23476.37893908448,
+  "new_score": 23627.612271644153,
+  "same_patterns": false,
+  "same_stages": false,
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+  "live": 74928,
+  "profile": {
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+    "4": 223168,
+    "2": 611200,
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+  "banks": {
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diff --git a/research/e8-rank138-idle-hosting/research/hosting443-kernel138-eight-screen.json b/research/e8-rank138-idle-hosting/research/hosting443-kernel138-eight-screen.json
new file mode 100644
index 0000000000..0d82c7e4bd
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/hosting443-kernel138-eight-screen.json
@@ -0,0 +1,48 @@
+{
+  "status": "PASS_TWO_EXACT_AGGREGATE_MOMENTS_EMITTED_TEMPLATE_AND_INVOICE_PENDING",
+  "reference_bit_lower": "249369163853537814231/200000000000000000000000",
+  "prior_score": 23476.37893908448,
+  "new_score": 23627.612271644153,
+  "same_patterns": false,
+  "same_stages": false,
+  "widths": {
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+    "7": 106,
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+  },
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+  "live": 9366,
+  "profile": {
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+    "6": 2144
+  },
+  "rank_mass": 596928,
+  "banks": {
+    "0": 0,
+    "1": 0,
+    "2": 0,
+    "3": 532,
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+    "5": 0,
+    "6": 528,
+    "7": 0,
+    "8": 0
+  },
+  "bit_lower": "1247628141860215921989/1000000000000000000000000",
+  "bit_upper": "124762814186021592199/100000000000000000000000"
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diff --git a/research/e8-rank138-idle-hosting/research/hosting443-kernel138-screen.json b/research/e8-rank138-idle-hosting/research/hosting443-kernel138-screen.json
new file mode 100644
index 0000000000..55fc0ae0e8
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/hosting443-kernel138-screen.json
@@ -0,0 +1,48 @@
+{
+  "status": "PASS_TWO_EXACT_AGGREGATE_MOMENTS_EMITTED_TEMPLATE_AND_INVOICE_PENDING",
+  "reference_bit_lower": "249369163853537814231/200000000000000000000000",
+  "prior_score": 23476.37893908448,
+  "new_score": 23627.612271644153,
+  "same_patterns": false,
+  "same_stages": false,
+  "widths": {
+    "8": 626,
+    "7": 106,
+    "4": 8
+  },
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+    "3": 280,
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+  },
+  "replicas": 32,
+  "live": 37464,
+  "profile": {
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+    "5": 33984,
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+    "6": 8576
+  },
+  "rank_mass": 2387712,
+  "banks": {
+    "0": 0,
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+    "2": 2120,
+    "3": 2504,
+    "4": 0,
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+  "bit_lower": "1247628141860215921989/1000000000000000000000000",
+  "bit_upper": "124762814186021592199/100000000000000000000000"
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diff --git a/research/e8-rank138-idle-hosting/research/hosting443-replica32-screen.json b/research/e8-rank138-idle-hosting/research/hosting443-replica32-screen.json
new file mode 100644
index 0000000000..ef0d170aab
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/hosting443-replica32-screen.json
@@ -0,0 +1,8 @@
+{
+  "status": "MILP_NOMINATION_REQUIRES_EXACT_REPLAY",
+  "reference_bit_lower": "249369163853537814231/200000000000000000000000",
+  "prior_score": 23476.37893908448,
+  "new_score": 23476.37893908448,
+  "same_patterns": true,
+  "same_stages": false
+}
diff --git a/research/e8-rank138-idle-hosting/research/rebuild443.log b/research/e8-rank138-idle-hosting/research/rebuild443.log
new file mode 100644
index 0000000000..376524fe7c
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/rebuild443.log
@@ -0,0 +1 @@
+{"donor_slots": 103, "entrance_rank": 138, "entries": 114, "input_sha256": "d6ec8811541d6ab59a3bbbaaa15bccc8918b3b43b23d9f593198cfe90826fd20", "interface": {"R": 740, "helper_start_dims": {"0": 626, "1": 106, "4": 8}, "n": 980, "prefix_allow": 192, "prefix_bits": 123, "prefix_ok": true, "streams": {"forward": {"adds": 15414, "copies": 9, "hist": {"1": 2530, "2": 1008, "3": 280, "4": 347, "5": 118, "7": 14, "8": 9}, "row_l1": 780}, "reverse": {"adds": 15414, "copies": 9, "hist": {"1": 2530, "2": 1008, "3": 280, "4": 347, "5": 118, "7": 14, "8": 9}, "row_l1": 18182}}}, "mutations_rejected": ["retained row used as pivot", "duplicate pivot", "eight replicas do not fill integral banks", "omit a kernel dirty-response correction", "wrong primitive input frame"], "output_sha256": "64d7d1e0c6ea7a3a8e91254c0dfd51b71637b49703ef4c1fce184fded5040bc9", "post_kernel_frame_changes": [112, 42], "pre_kernel_frame_changes": 57, "replicas": 32, "retimed_sha256": "fec026cda755e5ef93f7ed56923d1452da925cbe0051585e913e0837d9a70ffb", "status": "PASS_FROZEN_RETIMING_KERNEL_REPLICA_REBUILD"}
diff --git a/research/e8-rank138-idle-hosting/research/upstream-shell-path-failure.log b/research/e8-rank138-idle-hosting/research/upstream-shell-path-failure.log
new file mode 100644
index 0000000000..215cfbf7c8
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/research/upstream-shell-path-failure.log
@@ -0,0 +1,4 @@
+== Frozen package and complete upstream provenance
+PASS package manifest, byte-identical PR436 parent, PR417 code and PR441 witnesses
+== Reproduce PR436 with its unchanged verification wrapper
+mkdir: /Volumes/SP: Permission denied
diff --git a/research/e8-rank138-idle-hosting/upstream443/EXPECTED.json b/research/e8-rank138-idle-hosting/upstream443/EXPECTED.json
new file mode 100644
index 0000000000..bab8013596
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/EXPECTED.json
@@ -0,0 +1,35 @@
+{
+  "global": {
+    "R": 740,
+    "replicas": 32,
+    "live": 56739,
+    "physical": 56748,
+    "banks_per_stage": 2891,
+    "entrance_rank_total": 138,
+    "bank_assignments": 213120,
+    "local_invocations": 288,
+    "independent_unbanked_scalar_columns": 7620,
+    "deficit": 9984,
+    "global_prefix_bits": 123,
+    "local_additions": 15414,
+    "copy_erase_episodes": 2592,
+    "profile": {
+      "1": 728640,
+      "4": 99936,
+      "2": 290304,
+      "3": 80640,
+      "5": 33984,
+      "8": 2592,
+      "7": 27072,
+      "14": 15360,
+      "28": 15360,
+      "42": 15360
+    }
+  },
+  "result": {
+    "kappa": "1138823042306561/1000000000000000000",
+    "bit_lower": "1140121438872176364117/1000000000000000000000000",
+    "complex_lower": "1183986549206329/1000000000000000000",
+    "binding_component": "bit"
+  }
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/LICENSE b/research/e8-rank138-idle-hosting/upstream443/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
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diff --git a/research/e8-rank138-idle-hosting/upstream443/MANIFEST.json b/research/e8-rank138-idle-hosting/upstream443/MANIFEST.json
new file mode 100644
index 0000000000..5b72d8bc17
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/MANIFEST.json
@@ -0,0 +1,119 @@
+{
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+  "parent436/verify.sh": "19bf483b109163b0ccc941f459e70c2e37d20c9c04e69e7c8eb98f329577b26c",
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+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/NOTICE.md b/research/e8-rank138-idle-hosting/upstream443/NOTICE.md
new file mode 100644
index 0000000000..c47f06f58c
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/NOTICE.md
@@ -0,0 +1,37 @@
+# Attribution and scope
+
+New primitive retiming, untrimmed kernel selection, 32-replica residual banking,
+integration and audits:
+chafreaky, with substantial OpenAI Codex assistance. Apache-2.0.
+
+- eumemic, PR #441 (`6160c13526f5f957902910b462164c93c1d8f39a`):
+  paired-gate and window B-frame retiming witnesses, transplanted and independently
+  rechecked on the new kernel, with substantial OpenAI Codex assistance.
+- eumemic, PR #440 (`bd03373b6d4d4e380d0b6ea7d55cd2ac8f163544`):
+  primitive-retiming composition and the 112-pivot kernel used as the search
+  warm start, with substantial OpenAI Codex assistance.
+- rohanarun, PR #434: primitive retiming composed with response kernels,
+  with OpenAI Codex assistance.
+- chafreaky, PR #439 (`fa3a588ec1e383083abb8de9c51904fb9d689ad4`): explicit
+  residual isometries, finite route charges and the starting release verifier.
+- eumemic, PR #436 (`da8ca2025472553ac9b36f4400138ed48a6a0e3b`): R740 bit word,
+  reconstruction, elimination/reuse, independent checkers and #433 composition.
+  The entire parent package is byte-identical, including its notices, licenses,
+  source pins and Anthropic Claude disclosure.
+- chafreaky, PR #417: shared-donor kernel, exact local replay and tiling code;
+  the earlier implementation had substantial Anthropic Claude assistance.
+- rohanarun, PR #435 (`2c9c833ac8709402c37fc88a6a23393fb0d397fb`): prior mixed-width
+  residual-bank composition on #433. The new implementation derives from the
+  pinned #436 global/audit code and adds explicit residual isometries and controls.
+- icekylinx, PR #433: split-centre complex supplier, bit finite invoice and tail,
+  with OpenAI Codex assistance; the complex result is cited, not rebuilt here.
+- jacklightChen, PRs #386 and #425: compressed nine-stage geometry and the
+  mutable-basis complex interface, with OpenAI Codex assistance.
+- utcorvusvolat-dotcom / Dylan Crow, PR #370: E8 bit format, producer and
+  independent checker lineage, with Anthropic Claude assistance.
+- applecrusher (#376), ai-nanachi (#389/#426), DaysSky (#363/#375/#381),
+  DreamingOfClouds (#315), Jacob Sussman, and all earlier credited contributors:
+  see the unchanged `parent436/NOTICE.md` and source-specific notices.
+
+Do not infer an unconditional theorem or a new Lean proof from the finite
+certificates. No inherited author or AI-assistance disclosure has been removed.
diff --git a/research/e8-rank138-idle-hosting/upstream443/PROOF.md b/research/e8-rank138-idle-hosting/upstream443/PROOF.md
new file mode 100644
index 0000000000..ae1ad94af0
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/PROOF.md
@@ -0,0 +1,119 @@
+# Replication removes the eight-replica rank restriction
+
+## Local word and frozen transformations
+
+Start with eumemic's byte-identical PR #436 R740 word. Expand each grouped ADD
+into its ordered primitive ADDs and apply 57 frozen frame changes. The ordered
+scalar operands are unchanged. For every changed gate, the PR #417 retimer
+checks its integer source-support lower bound and both neighboring register
+frames in the joint configuration. All frames remain nested.
+
+Apply a 114-pivot shared-donor response kernel with 103 donor slots and total
+entrance rank 138. Each pivot p has an entrance E contained in its first frame
+and every donor's first frame, and response(p) = XOR response(donors). Start p
+at E, remove its frame-zero target correction, and add it to those donors at E
+before A and again at FULL after C. Pivots and donors are disjoint; each donor
+uses one entrance. The exact local replay checks all 980 independent columns,
+including all helper dirt, and integer source-span legality. Frozen input,
+intermediate and output hashes bind both transformations.
+
+The PR #417 kernel code is retained unchanged. A separate adaptation keeps its
+local checks and replaces only its eight-replica rank congruence with
+
+```
+T * (8R - entrance_rank) = 0 mod 64.
+```
+
+After the kernel, transplant the two frozen PR #441 joint B-frame stages: 112
+paired-gate changes and 42 window changes, with 126 net changed B frames. The
+original witnesses remain byte-identical and pinned. Their frame choices are
+independently checked against the new word's joint feasible intervals, integer
+source supports and complete arbitrary-dirt replay; input/output hashes are
+recomputed for this composition. Every scalar ADD and its position is retained.
+
+The complete selected word has local paid profile
+`{1:2530, 2:1008, 3:280, 4:347, 5:118, 7:14, 8:9}`. The forward and reflected emitted
+streams have the same profile, restore arbitrary input columns and erase each
+private copy. The initial 57-frame retiming and PR #440 selection supplied a search
+starting point; this selection retains two additional rank-one pivots.
+
+## Why 32 replicas are admissible
+
+The compressed nine-stage identity is an identity for one data-replica index.
+Its four data pairs, alternating local calls, nine paired bridges and terminal
+exchange do not refer to any other replica's data. Repeating that schedule for
+four groups of eight replicas therefore gives a direct sum of the original
+identities. The local eight-dimensional frames, 64-dimensional ambient form,
+42-dimensional largest child, cover class and port maps are unchanged.
+
+Banking changes only the embeddings of helper residuals. The local theorem holds
+for arbitrary independent helper dirt. Assigning every helper residual an
+injective isometry into a disjoint bank interval preserves this theorem. The
+same proof applies when those intervals belong to different replica groups:
+no data owner is shared across groups, and each stage's helper intervals are a
+partition of its entire bank coordinate space. The emitter and independent
+audit enumerate all 288 calls and all 213,120 helper owner assignments, check
+every data owner formula, and reject cross-group data aliasing, omission of a
+replica group and an incorrect replica count. They also replay the one-replica
+nine-stage identity on 7,620 unbanked scalar columns, which is the repeated
+block identity, not a claim to replay 32 separate enlarged matrices.
+
+Here `8R - entrance_rank = 5782`. Eight replicas would require 722.75 banks;
+32 replicas require exactly 2,891 banks. Thus 32 is the least positive multiple
+of eight satisfying the exact bank equation. No incomplete bank is counted and
+no padding calls or unused bank coordinates are introduced. Merely repeating a
+fixed eight-replica word scales its profile and stock equally and gives no
+rate improvement; the gain comes from admitting the stronger untrimmed kernel.
+
+## Residual routes and accounting
+
+Every distinct entrance has a stored integer matrix N with N N^T = 4I. Its
+first dim(E) rows span exactly E, checked against every root of E. The remaining
+rows give an isometry of E-perp to a coordinate block. For these 16 entrances,
+N/2 is a coordinate permutation, reduced to identity with at most seven swaps.
+Extending it by identity on 56 exterior coordinates and permuting coordinates
+places the residual into its assigned interval. This is an explicit isometry
+for I_64/2 at every inherited odd address prime. Reversal has the same residual
+projector I-P_E; the common exterior window cancels from the endpoint difference.
+
+Per stage, the exact bank partition is:
+
+- 424 banks with widths `(7,7,7,7,7,7,7,7,8)`;
+- 16 banks with sixteen width-four blocks;
+- 2,451 banks with eight width-eight blocks.
+
+Each coordinate is used exactly once. The independent audit checks all intervals,
+frame IDs, orthogonal matrices and elementary route factors. It rejects reused
+slots, wrong frames, altered bases, missing route factors and omitted calls.
+The 32 replicas use `8*120*32 = 30,720` data families. Hence live stock is
+`30,720 + 9*2,891 = 56,739`, with nine sequential private-centre reserves giving
+physical stock 56,748. The paid profile is 288 times the local profile plus
+23,040 rank-seven idle children and 15,360 each of ranks 14, 28 and 42.
+Its rank deficit is `64*56,739 - paid_rank_mass = 9,984 = 32*312`.
+No rank mass, idle move, copied centre or bridge is omitted.
+
+## Finite and analytic gates
+
+The finite invoice is recomputed with T=32, the larger live/physical stock, all
+288 local calls, replicated bridges and copy episodes, and explicit residual
+routes. It charges 144 additional elementary route factors per helper routing,
+covering seven local swaps and 64 coordinate swaps. The prefix bound comes from
+the emitted forward and reflected programs. Independent replicas act on separate
+data and disjoint residual coordinates; sequential private copies are erased,
+so replication does not multiply the per-coordinate coefficient-growth bound.
+The invoice nevertheless charges every emitted operation and route.
+
+Both rational moment engines must certify the bit lower endpoint
+`0.001140121438872176364117`, including the inherited 10^-16 bad-branch allowance.
+The maximum child still satisfies `2*42^2 < 64^2`. The newly computed two-level
+coefficient must fit the retained 512-bit budget and row coefficient 18,355.
+With the cited PR #433 complex rate, six ordinary bootstrap levels and all 47
+strict outer inequalities give conditional
+`kappa = 1138823042306561 / 1000000000000000000 = 0.001138823042306561`.
+The adjacent 10^-18 grid point and invalid outer parameters must be rejected.
+These are release-verifier requirements, not substitutes for its receipts.
+
+The original all-size compiler, correlated dirty-bank, compressed-window,
+restored-work, tape/common-grid, precision and analytic assumptions remain.
+The complex supplier and its mutable-basis interface are cited from PR #433;
+this package does not rerun its Gaussian phases or prove an unconditional theorem.
diff --git a/research/e8-rank138-idle-hosting/upstream443/README.md b/research/e8-rank138-idle-hosting/upstream443/README.md
new file mode 100644
index 0000000000..c8e8d3042a
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/README.md
@@ -0,0 +1,62 @@
+# R740 kernel with 32 replicas and complete residual banks
+
+The conditional candidate is **κ = 0.001138823042306561**, with bit lower endpoint
+**0.001140121438872176364117**. Full verification is required before admission.
+It exceeds PR #441 at `6160c13526f5f957902910b462164c93c1d8f39a` by about 0.00219%.
+
+Eight replicas forced the previous search to drop kernel pivots so that residuals
+filled whole width-64 banks. Four independent groups of eight replicas allow a
+114-pivot kernel with entrance rank 138 to fill 2,891 banks per stage exactly.
+This preserves two rank-one pivots that the eight-replica packing discarded.
+All bank coordinates are occupied; there is no padding. The primitive ADD
+sequence retains PR #440's 57 A-frame choices and PR #441's two B-frame stages
+(112 and 42 changes, 126 net changed B gates). Both stages are rechecked on the
+new kernel word.
+
+| Quantity | Result |
+| --- | ---: |
+| Helpers / local arbitrary input columns | 740 / 980 |
+| Replicas / local invocations | 32 / 288 |
+| Kernel pivots / donor slots / entrance rank | 114 / 103 / 138 |
+| Banks per stage | 2,891 |
+| Live / physical families | 56,739 / 56,748 |
+| One-replica unbanked global columns | 7,620 |
+| Helper owner assignments | 213,120 |
+| Rank deficit | 9,984 |
+| Cited complex lower endpoint (#433) | 0.001183986549206329 |
+| Binding side | Bit |
+
+## Reproduction
+
+Python 3.11 or newer, numpy, mpmath, sympy, a C++17 compiler and Boost headers:
+
+```sh
+python3 -m pip install -r research/e8-r740-replica32/parent436/requirements.txt
+bash research/e8-r740-replica32/verify.sh /tmp/e8-r740-replica32-full
+```
+
+Set `PYTHON`, `CXX` or `BOOST_INCLUDE` when needed. `--quick` skips only the
+parent's historical regressions. Every mode checks the frozen manifest and
+parent source blobs, reconstructs PR #436 and both new transformations, verifies
+local arbitrary-dirt columns, reflected copy chronology, exact frame projectors,
+all replica owners and residual bank coordinates, 16 explicit orthogonal routes,
+mutation controls, two rational moments, a fresh finite invoice, six bootstrap
+levels and 47 strict outer inequalities. The next grid point is rejected.
+
+## Scope
+
+PR #442 reports a larger bound using an additional idle-data hosting extension.
+This package isolates the gain from exact replica banking within the prior
+helper-bank interface.
+
+This is a finite conditional construction for the retained
+`T(n) = O(n (log n)^(1-κ))` assembly. The complex supplier is cited from #433,
+including its #425 mutable-basis interface; its construction and Gaussian-phase
+audits are not rerun here. Astronomical cover enumeration, all-size compiler,
+correlated dirty-bank, restored-work, precision, tape/common-grid and analytic
+interfaces remain assumptions. This is not a Lean proof or an unconditional
+integer-multiplication theorem. κ = 1 remains open.
+
+Search scores only nominated candidates. The admitted witnesses, costs, maps and
+strict comparisons use integers or exact rationals. See `PROOF.md`, `NOTICE.md`,
+`SOURCE.json` and the unchanged parent package for dependencies and proof scope.
diff --git a/research/e8-rank138-idle-hosting/upstream443/SOURCE.json b/research/e8-rank138-idle-hosting/upstream443/SOURCE.json
new file mode 100644
index 0000000000..405be7ad31
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/SOURCE.json
@@ -0,0 +1,125 @@
+{
+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "parent436_commit": "da8ca2025472553ac9b36f4400138ed48a6a0e3b",
+  "parent436_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/436",
+  "parent436_blobs": {
+    "EXPECTED.json": "7f5f7f3f9da9864220d4c6ee6bac23010f590d47",
+    "LICENSE": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64",
+    "MANIFEST.sha256": "399beb5da45c2e226ee7320b513f622938c0fdc1",
+    "NOTICE.md": "2c01026b8b300ccc16c313f652f9e46e61617304",
+    "README.md": "5ddb576f02f1e3ef8cfee443bd654ad8cf26b837",
+    "SOURCE-pr370.json": "db86b22e15681b5d120bdc7acd0a1e9cd5e6e363",
+    "SOURCE-pr376.json": "818f17fb6a01e198956b7faffc5d6ce87a0a4bbf",
+    "SOURCE-pr381.json": "042a26c7c2ec22de93dd2aa509a6087e71302f28",
+    "SOURCE-pr386.json": "ac24e5d262d38909a13ecc35fbf7bccb75f977aa",
+    "SOURCE-pr417.json": "33f0ae053c284e12097aaf810c56f7b235c160bc",
+    "SOURCE-pr425.json": "8d9c976b02a418eb2877375f1d83fcac17cc3df7",
+    "SOURCE-pr426.json": "7c72390e09ead086207b74e7d8029e9d14499545",
+    "SOURCE-pr431.json": "00f1075773f5db3d95075d524f412bd79d160c70",
+    "SOURCE-pr433.json": "910a7c34903b855e219a7ff47e48de018db2490d",
+    "code/b4/kappa_b4.py": "402a510e15fc8a3541ddd84d2044e79e288fef89",
+    "code/bit/checkers/certify_bit_k.py": "37ce2ee2b412b3b97a397159f48b912ef893b014",
+    "code/bit/checkers/columns_h.cpp": "00c5a3a5d81d083582f60f33dd2e7bea5049c37f",
+    "code/bit/checkers/columns_k.cpp": "42bb232fbec4de703e70cc13dc2f39a3b43a3a01",
+    "code/bit/checkers/cost.py": "677584c1c6b0e959c19f58521b68d4b3e847f97e",
+    "code/bit/checkers/finite_k.py": "8781815ee6ee663edc0e0afdf1380186594ec913",
+    "code/bit/checkers/geometry_k.py": "2a052980816d9b56b33c5e41132bb7f86286462b",
+    "code/bit/checkers/gram_frames.py": "b740d47295c02692260d7cc01874a49fe48f78ab",
+    "code/bit/checkers/json.hpp": "82d69f7c5d044c9887c96b90c97f5639083ecd14",
+    "code/bit/checkers/legality_h.cpp": "cb1233c7e96b1aa8bbf4d2e4165d75ab0dca64b9",
+    "code/bit/checkers/tile_k.py": "a4635e6681c2f1521b44f24364cc457d304cb077",
+    "code/bit/export_records.py": "3632d370486a02f5456f7643ced03f8c925b2350",
+    "code/bit/independent/checkword.py": "da4e0fe05067184d4dab1e130ae1384c1fa983f5",
+    "code/bit/independent/mutate.py": "eba592fd468e0d7e7e5100fe99da6eb548c5906b",
+    "code/bit/mutate_records.py": "6794516f665d36eac189894e350a5ad01113cb4c",
+    "code/bit/producer/compile.py": "86b12507ef86308336833a208a989d56072096d1",
+    "code/bit/producer/compile2.py": "a7bdfdfbe417c793b2a8c515f5432bdd10472259",
+    "code/bit/producer/e8lib.py": "8464b956f6a5aa5061695990a14b7a385d370c2e",
+    "code/bit/producer/frames.py": "b28c3b2413b9767e7ffe0a8b2db93836f3455494",
+    "code/bit/producer/fullword.py": "104f01b7803481b623809bc8a57682d28f09b5c3",
+    "code/bit/producer/ham1.py": "8086649a5f71c16698db7059bbada7187d781b56",
+    "code/bit/producer/ham2.py": "842f76b245a1bfb4150c53a853f6f472511f5a2f",
+    "code/bit/producer/params-r865.json": "110b4d94d884f03d4d37be22672ab27d836f1275",
+    "code/bit/producer/price.py": "9014d97d519eea1f8c96e4bfc75afa0febd5903f",
+    "code/bit/receipts_k.py": "428261488b4af028fd04df4f84eead1dad79a389",
+    "code/bit/regression/stage_cohort.py": "f6d7afe3e623208c4207b6a683a1e3e49249e31c",
+    "code/complex/code/bridged.py": "626a28614b07066528fd5f189d87cffa5015ac60",
+    "code/nine/audit_g.py": "719b378a0e20e99a79a3da6462be0e430fe7ee60",
+    "code/nine/certify_g.py": "9f4ae1600ae2f2cedd17ea37338f5d54ec7e83b9",
+    "code/nine/cited.py": "3aedb7a5c5bb06e04dae1f135ca5d5a4a5fdd2fe",
+    "code/nine/compose433.py": "b2f3fb6ba1a35b6dfcc6da12f0425c16be832cde",
+    "code/nine/geometry.py": "91594e0223e8fac49162b5aef834ffaa8e94a254",
+    "code/nine/global_word_g.py": "10eab502ded5374cf05bf89864044007e37458ed",
+    "code/nine/regress386.py": "8cbca55668a445502b3a0f07f27687474d0d764f",
+    "code/pricing/base_two_moment.py": "14a90fa0e788217856f070382c9e61bd7c603c61",
+    "code/pricing/moment.py": "7d697cb45203fe72d97037403d6da41f71f3b7fd",
+    "code/pricing/outer.py": "43007488ad2c43187c77cc6798beff8b1cd76ad2",
+    "code/pricing/prime_witnesses.py": "7f16d930302ae879c562dd58e085d9747fcac077",
+    "code/provenance.py": "9bfcb106230e454d9405ce5eb42dd2218d905ea6",
+    "code/reuse/controls.py": "ceb15852b726423f8b6978ba80817ba2b4ac5b39",
+    "code/reuse/ecost.py": "4ec2a959b1cd599e3297de17563446d623e2867c",
+    "code/reuse/regen.py": "529de1b8b37f28e877a57ab3e22a506002860370",
+    "code/reuse/retime.py": "9c3e94b800b70cfe1383ea6478d85bf859903006",
+    "code/reuse/reuse.py": "df455a0b37cca6ebd1a214661b540e8665467208",
+    "code/tail/apply376.py": "c401a84d8f549e0752464ab8313ce648bb4d14fa",
+    "code/tail/bootstrap.py": "1bc17e768259c342fb8b94b919bfeaea10304153",
+    "code/tail/e8core.py": "78983b368715e89fe8524a6dd2c13585d2b5394e",
+    "code/tail/engines/base_two_moment.py": "14a90fa0e788217856f070382c9e61bd7c603c61",
+    "code/tail/engines/moment.py": "7d697cb45203fe72d97037403d6da41f71f3b7fd",
+    "code/tail/engines/outer.py": "43007488ad2c43187c77cc6798beff8b1cd76ad2",
+    "data/bit/bitE8-r740.json.gz": "8a8ce996b890c7d11b2f8c7fbbd8148747627f46",
+    "data/bit/bitE8-r865.json.gz": "8bec1751f7e33c3a1e4673ef5dbc34d6f205321e",
+    "data/bit/reuse-ledger.json": "51eb63c7d8b3b4a0640412a215df042e878f1034",
+    "data/complex-b-433.json": "2d1db891592346fa225924d8d1666743c2144e11",
+    "data/complex-b-b4.json": "4fd117cd047ebbe86db44c732e72f1b75e9e45d4",
+    "data/complex-b-nine.json": "a215ba618871f09cdea2ede90240b980f62228e5",
+    "data/controls/LICENSE-pr426": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64",
+    "data/controls/pr376/LICENSE-pr376": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64",
+    "data/controls/pr376/frame-selection.json": "647b34368f3f0c7d228c70fa335af872e7946beb",
+    "data/controls/pr376/reuse-selection.json": "a6954dc65f28137ad16d015b42c40dbbde0bd66f",
+    "data/controls/pr386/AUDIT.json": "698e827ae87ae9db47fd30cf69537176276cff4e",
+    "data/controls/pr386/COMBINED.json": "8d6e3f22667fa0f6fa1a5495223e87f90a4cd103",
+    "data/controls/pr386/GLOBAL.json": "21bc6dcc7bbefedcd3064485d0e82c95e585044c",
+    "data/controls/pr417-bitE8-nine-kernel.json.gz": "572172b8148538d1937b9f7fa7f3939755008a8c",
+    "data/controls/pr425/FINAL.json": "1e9c8784c3cb719acb5274126141fe360af253fa",
+    "data/controls/pr426-bit-candidate.json.gz": "807cea53ebe1322721463ee2319bcd52b9714f24",
+    "data/controls/pr431/VALIDATION-LOCAL.json": "0f0a80418d7f3e521c980ef0354fc3945eae1795",
+    "data/controls/pr433/CERTIFICATE.json": "7e807079c1ec4907306035c84be1ba2fb1d69d79",
+    "data/params/params-r740.json": "d9bc74d95b4bd1acde79ada315508f24b4fc06e3",
+    "discovery/README.md": "025c3ac932a976b3ad5ff31ba08a39c0d3c9d4ff",
+    "discovery/search_params.py": "6e57d290f31e748753a4aa77472278c92407edf9",
+    "portable-include/bits/stdc++.h": "fc5664e929d9a81d9b4926bee049a93330be86ec",
+    "requirements.txt": "1cc9b96f593a9ce8a70b6b951c633452cb97e778",
+    "verify.sh": "1f03e028799147b03ecd6339cc951f1debbd9dbe"
+  },
+  "kernel_origin": "https://github.com/CrocSwap/integer-mult-bounds/pull/417",
+  "kernel_origin_commit": "3f681fb571036ca4a267570318260b0d083f7b9d",
+  "bank_integration_reference": "https://github.com/CrocSwap/integer-mult-bounds/pull/435",
+  "bank_reference_commit": "2c9c833ac8709402c37fc88a6a23393fb0d397fb",
+  "note": "PR439 exact bank routes generalized to 32 replicas. PR440 inspired primitive retiming and supplied the search warm start. The new 114-pivot rank138 selection is re-derived on a frozen primitive-retimed PR436 word. Retained PR417 sources and the complete PR436 package remain byte-identical.",
+  "kernel_identical_blobs": {
+    "code/e8core.py": "78983b368715e89fe8524a6dd2c13585d2b5394e",
+    "code/stages.py": "9ef95d52f4b2ba0389bb2edb15228da698dd75f4",
+    "code/export249.py": "462a0f121f5363265b02d812cb12bed39e33dc74",
+    "code/tile_m.py": "cd5fd9b5399f5e7afe5d2a95bd3504bd543c0d60"
+  },
+  "replica_origin": {
+    "pr": 439,
+    "commit": "fa3a588ec1e383083abb8de9c51904fb9d689ad4",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/439"
+  },
+  "warm_start": {
+    "pr": 440,
+    "commit": "bd03373b6d4d4e380d0b6ea7d55cd2ac8f163544",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/440"
+  },
+  "joint_retiming": {
+    "pr": 441,
+    "commit": "6160c13526f5f957902910b462164c93c1d8f39a",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/441"
+  },
+  "witness_identical_blobs": {
+    "data/upstream441/pair-retime-selection.json": "1b7b7f33ff071d9f474ee6623c8a3fbfd7659646",
+    "data/upstream441/window-retime-selection.json": "d816fc0da675ead91188a8e9565c1275c31a18fc"
+  }
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/audit_kernel.py b/research/e8-rank138-idle-hosting/upstream443/code/audit_kernel.py
new file mode 100644
index 0000000000..5bfcd07320
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/audit_kernel.py
@@ -0,0 +1,150 @@
+# Explicit residual-bank audit added by chafreaky with OpenAI Codex assistance.
+"""Independent projector, 32-replica ownership and emitted-template audit.
+PR386 audit by Zhihao Chen with OpenAI Codex assistance; PR436 generalization by
+eumemic with Anthropic Claude assistance; PR439 routes and this replication
+extension by chafreaky with OpenAI Codex assistance. Apache-2.0.
+Historical regression is performed by the unchanged parent wrapper.
+"""
+import argparse, copy, gzip, hashlib, json, struct, time
+from collections import Counter, defaultdict
+from pathlib import Path
+import sympy as S
+from bank_routes import validate_isometries
+from config import REPLICAS
+
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    ap.add_argument('--word',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out
+    blob=gzip.decompress((out/'GLOBAL-TEMPLATE.json.gz').read_bytes()); t=json.loads(blob)
+    g=json.loads((out/'GLOBAL.json').read_text()); geo=json.loads((out/'GEOMETRY.json').read_text())
+    assert hashlib.sha256(blob).hexdigest()==g['template_sha256']
+    assert t['geometry_sha256']==sha(out/'GEOMETRY.json') and t['source_record_sha256']==sha(a.local_check/'records/249-records.bin')
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    records=list(struct.iter_unpack('<6i',(a.local_check/'records/249-records.bin').read_bytes()))
+    T=REPLICAS
+    assert T==32 and T%8==0 and g['replicas']==T
+    V,R=g['v'],g['R']; LOCAL=2*V+R; DATA=2*4*V*T; LIVE=g['live']
+    assert V==120 and DATA==30720 and g['live']==LIVE
+    I=S.eye(8); proj={}; dimensions={}
+    for key,f in fs.items():
+        k=int(key); B=S.Matrix(f['B']) if f['B'] else S.zeros(0,8)
+        P=B.T*(B*B.T).inv()*B if B.rows else S.zeros(8)
+        assert P.T==P and P*P==P and P.trace()==f['dim']
+        proj[k]=P; dimensions[k]=f['dim']
+    pairs={}
+    for op,x,y,c,r,z in records:
+        if op==0:
+            key=(y,c)
+            if key not in pairs:
+                D=proj[c]-proj[y]
+                assert proj[c]*proj[y]==proj[y] and proj[y]*proj[c]==proj[y]
+                assert D*D==D and D.trace()==r
+                # Reflected reverse has exactly the same positive projector.
+                assert (I-proj[y])-(I-proj[c])==D
+                pairs[key]=r
+    assert len(proj)==len(fs)
+    print('exact frame projectors',len(proj),'nested pairs',len(pairs),flush=True)
+    expected={}
+    for rev in (False,True):
+        es=[]
+        for op,x,y,c,f,z in (reversed(records) if rev else records):
+            if op==0: es.append([0,x,c if rev else y,y if rev else c,f,int(rev)])
+            elif op==1: es.append([1,x,y,-c if rev else c,f,int(rev)])
+            elif op==(3 if rev else 2): es.append([2,x,y,c,f,abs(dimensions[c]-dimensions[f]),int(rev)])
+            else: es.append([3,x,y,c,f,z,int(rev)])
+        expected['reverse' if rev else 'forward']=es
+    assert t['local_programs']==expected
+
+    word=json.loads(gzip.decompress(a.word.read_bytes()))
+    assert sha(a.word)==g['word_sha256']
+    state=json.loads((a.local_check/'records/249-states.json').read_text())
+    initial=[state['initial'][str(i)] for i in range(LOCAL)]
+    assert initial==word['start']
+    widths=[8-dimensions[f] for f in initial[2*V:]]
+    ENT=sum(8-x for x in widths)
+    assert T*(8*R-ENT)%64==0
+    NB=T*(8*R-ENT)//64
+    assert LIVE==DATA+9*NB and g['banks_per_stage']==NB
+
+    def validate(q,check_profile=True):
+        assert validate_isometries(q['residual_isometries'],word['frames'],word['lines'],dimensions)==set(initial[2*V:])
+        assert (q['m'],q['live'],q['replicas'],q['stages'])==(64,LIVE,T,9)
+        assert q['bank_padding'] is None and q['local_programs']==expected
+        hist=Counter(); occupation=defaultdict(set); calls=set()
+        for c in q['calls']:
+            st,rep,p=c['stage'],c['replica'],c['pair']; rev=c['orientation']=='reverse'
+            assert 0<=st<9 and 0<=rep<T and p==max(0,(st-1)//2)
+            assert rev==(st in (1,3,5,7)) and (st,rep) not in calls; calls.add((st,rep))
+            own=c['owners']; assert len(own)==LOCAL
+            assert len({(f,tuple(r)) for f,r in own})==LOCAL
+            for i,(family,route) in enumerate(own):
+                assert 0<=family<LIVE
+                if i<2*V:
+                    side=i//V; side=1-side if rev else side
+                    assert family==rep*960+(2*p+side)*120+i%120 and route==['data',st,i%120]
+                else:
+                    j=i-2*V
+                    assert len(route)==4 and route[0]=='bank' and route[2]==widths[j] and route[3]==initial[i]
+                    assert DATA+st*NB<=family<DATA+(st+1)*NB
+                    cells=set(range(route[1],route[1]+route[2]))
+                    assert cells<=set(range(64)) and not cells & occupation[family]
+                    occupation[family]|=cells
+            for e in q['local_programs'][c['orientation']]:
+                if e[0]==0 and e[4]: hist[e[4]]+=1
+                if e[0]==2: hist[e[5]]+=1
+        assert calls=={(s,r) for s in range(9) for r in range(T)}
+        assert set(occupation)==set(range(DATA,LIVE)) and all(s==set(range(64)) for s in occupation.values())
+        levels=[-1]*4; scalar=[1<<i for i in range(8)]; seen=[]; br=0; exchanged=False
+        for e in q['schedule']:
+            if e['kind']=='local_cover_sweep':
+                s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1 and not exchanged
+                src,dst=(2*p+1,2*p) if rev else (2*p,2*p+1)
+                scalar[dst]^=scalar[src]; levels[p]=s; seen.append(s)
+            elif e['kind']=='idle':
+                p,src,dst,r=e['pair'],e['source_level'],e['target_level'],e['rank']
+                assert levels[p]==src and src<=dst<=8
+                assert r==7*(dst-src); levels[p]=dst
+                if r: hist[r]+=2*V*T
+            elif e['kind']=='bridge':
+                d,s=e['dst'],e['src']; assert levels[d]==levels[s] and e['coefficient'] in (-1,1)
+                scalar[2*d]^=scalar[2*s]; scalar[2*s+1]^=scalar[2*d+1]; br+=1
+            else:
+                assert e['kind']=='exchange' and levels==[8]*4 and not exchanged
+                for p in range(4): scalar[2*p],scalar[2*p+1]=scalar[2*p+1],scalar[2*p]
+                exchanged=True
+        assert exchanged and scalar==[1<<i for i in range(8)] and seen==list(range(9)) and br==9
+        assert 64*LIVE-sum(r*n for r,n in hist.items())==312*T
+        if check_profile: assert hist==Counter({int(k):v for k,v in g['profile'].items()})
+        return hist
+    hist=validate(t)
+    controls=[]
+    def rejects(name,mutator):
+        q=copy.deepcopy(t); mutator(q)
+        try: validate(q)
+        except (AssertionError,KeyError,IndexError): controls.append(name)
+        else: raise AssertionError('mutation accepted: '+name)
+    rejects('omit an idle child',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='idle')))
+    rejects('omit a bridge',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='bridge')))
+    rejects('omit terminal exchange',lambda q:q['schedule'].pop())
+    rejects('remove a local invocation',lambda q:q['calls'].pop())
+    rejects('re-use a helper bank slot',lambda q:q['calls'][0]['owners'].__setitem__(241,q['calls'][0]['owners'][240]))
+    rejects('understate live stock',lambda q:q.__setitem__('live',LIVE-1))
+    rejects('omit a local paid move',lambda q:q['local_programs']['forward'].pop(next(i for i,e in enumerate(q['local_programs']['forward']) if e[0]==0)))
+    rejects('wrong reflected copy charge',lambda q:q['local_programs']['reverse'][next(i for i,e in enumerate(q['local_programs']['reverse']) if e[0]==2)].__setitem__(5,0))
+    rejects('alter residual orthogonal basis',lambda q:q['residual_isometries'][0]['orthogonal_rows_numerator'][0].__setitem__(0,99))
+    rejects('wrong residual frame',lambda q:q['calls'][0]['owners'][240][1].__setitem__(3,-1))
+    rejects('omit a residual route factor',lambda q:next(r for r in q['residual_isometries'] if r['gaussian_reduction'])['gaussian_reduction'].pop())
+    rejects('alias data across replica groups',lambda q:q['calls'][8]['owners'].__setitem__(0,q['calls'][0]['owners'][0]))
+    rejects('omit the fourth replica group',lambda q:q.__setitem__('calls',[c for c in q['calls'] if c['replica']<24]))
+    rejects('misstate replication count',lambda q:q.__setitem__('replicas',8))
+    result=dict(status='PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT',template_sha256=g['template_sha256'],
+                source_frames=len(proj),exact_nested_frame_pairs=len(pairs),exact_reflected_pairs=len(pairs),
+                orthogonal_lift_argument='Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.',
+                exact_bank_families=9*NB,residual_isometries=len(t['residual_isometries']),entrance_rank_total=ENT,mutations_rejected=controls,
+                profile=dict(sorted(hist.items())),seconds=time.monotonic()-start)
+    (out/'AUDIT.json').write_text(json.dumps(result,indent=2)+'\n'); print(json.dumps(result),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/bank_routes.py b/research/e8-rank138-idle-hosting/upstream443/code/bank_routes.py
new file mode 100644
index 0000000000..9e43a87666
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/bank_routes.py
@@ -0,0 +1,65 @@
+"""Exact residual bank routes for the kernel word; chafreaky with OpenAI Codex.
+
+The stored integer rows divided by two are an orthonormal basis. Entrance
+rows span E; the remaining rows span E-perp. A coordinate permutation sends
+the latter to the assigned contiguous block in a width-64 bank. This gives
+an explicit rational isometry, with only powers of two in denominators.
+"""
+from collections import Counter, deque
+from tile_m import tile
+
+
+def placement(widths, replicas=32):
+    assert replicas > 0 and replicas % 8 == 0
+    by_width = {}
+    for rep in range(replicas):
+        for helper, width in enumerate(widths):
+            assert 0 < width <= 8
+            by_width.setdefault(width, deque()).append((rep, helper))
+    patterns = tile({w: len(q) for w, q in by_width.items()}, 64)
+    result = {}
+    bank = 0
+    for widths_in_bank, count in patterns:
+        for _ in range(count):
+            offset = 0
+            for width in widths_in_bank:
+                key = by_width[width].popleft()
+                result[key] = (bank, offset, width)
+                offset += width
+            assert offset == 64
+            bank += 1
+    assert all(not q for q in by_width.values())
+    assert len(result) == replicas * len(widths)
+    return result, bank
+
+
+def validate_isometries(rows, frames, roots, dimensions):
+    seen = set()
+    dot = lambda a, b: sum(x*y for x, y in zip(a, b))
+    for record in rows:
+        f = record['frame']
+        assert f not in seen
+        seen.add(f)
+        e = record['entrance_rank']
+        assert e == dimensions[f] and record['denominator'] == 2
+        basis = record['entrance_basis'] + record['residual_basis']
+        matrix = record['orthogonal_rows_numerator']
+        assert len(basis) == len(matrix) == 8
+        assert matrix == [roots[i] for i in basis]
+        assert all(len(r) == 8 and all(type(x) is int for x in r) for r in matrix)
+        assert all(dot(a,b) == 4*(i==j) for i,a in enumerate(matrix) for j,b in enumerate(matrix))
+        # The first e rows span precisely the frame, not only its dimension.
+        for i in frames[f]:
+            assert sum(dot(roots[i], q)**2 for q in matrix[:e]) == 4*dot(roots[i], roots[i])
+        assert len(record['entrance_basis']) == e
+        # This selected family needs coordinate permutations only. Checking the
+        # elementary reduction also bounds the literal route cost and primes.
+        reduced = [[x // 2 for x in row] for row in matrix]
+        assert all(x % 2 == 0 for row in matrix for x in row)
+        operations = record['gaussian_reduction']
+        assert len(operations) <= 7
+        for kind, i, j, scalar in operations:
+            assert kind == 'swap' and scalar is None and 0 <= i < 8 and 0 <= j < 8
+            reduced[i], reduced[j] = reduced[j], reduced[i]
+        assert reduced == [[int(i == j) for j in range(8)] for i in range(8)]
+    return seen
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/compose_kernel.py b/research/e8-rank138-idle-hosting/upstream443/code/compose_kernel.py
new file mode 100644
index 0000000000..0d92ae7c41
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/compose_kernel.py
@@ -0,0 +1,179 @@
+# Kernel finite invoice by chafreaky with OpenAI Codex assistance.
+"""This word's bit side composed with PR #433's complex supplier, with PR #433's own bit pricing, finite invoice and
+outer tail (icekylinx's code/bit_price.py and code/combined.py, ported line by line onto this package's receipts).
+
+Bit price (#433 bit_price.py): PR #315's moment.certify with the inherited 10^-16 bad-branch allowance; c is its
+  10^-24-grid lower endpoint; the second engine (base_two_moment, same allowance) must put the lower endpoint below 1
+  and the upper endpoint above 1.
+Finite invoice (#433 combined.py): #386's coefficient with the fresh prefix bound charged at the next multiple of 64
+  bits (at most 256), two-level coefficient below 2^512, row coefficient 18,355 < 20,161.
+Tail (#433 combined.py): eta = beta = 10^-18, seed s = min(c, (1 - beta) b) - 10^-24, six bootstrap levels with the
+  512-bit cutoff, kappa = the last 10^-18 grid point below (1 - eta) q / (1 + q), q = a_6 (1 - 2 eta); PR #315's outer
+  assembly with its 47 strict inequalities; next grid point, zero eta, zero beta and unit beta rejected.
+Controls: PR #433's stated R758 profile must price to PR #433's bit c, and (that c, PR #433's b) must give PR #433's
+  kappa, before this word is composed.
+usage: compose433.py --pricing DIR --out DIR --cited FILE --receipt CERTIFICATE.json
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import argparse
+import hashlib
+import importlib.util
+import json
+from fractions import Fraction as Q
+from pathlib import Path
+from config import REPLICAS
+
+
+def load(path, name):
+    s = importlib.util.spec_from_file_location(name, path)
+    m = importlib.util.module_from_spec(s)
+    s.loader.exec_module(m)
+    return m
+
+
+def sha(p):
+    return hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+ap = argparse.ArgumentParser()
+ap.add_argument("--pricing", type=Path, required=True)
+ap.add_argument("--out", type=Path, required=True)
+ap.add_argument("--cited", type=Path, required=True)
+ap.add_argument("--receipt", type=Path, required=True)
+a = ap.parse_args()
+M = load(a.pricing / "moment.py", "c433_moment")
+Other = load(a.pricing / "base_two_moment.py", "c433_other")
+Outer = load(a.pricing / "outer.py", "c433_outer")
+cited = json.loads(a.cited.read_text())
+cert = json.loads(a.receipt.read_text())
+assert cert["status"] == "PASS_CONDITIONAL_SPLIT_CENTRE_ASSEMBLY" and cert["binding_component"] == "bit"
+assert (cert["complex_lower"], cert["bit_lower"], cert["kappa"]) == (cited["b"], cited["bit_c"], cited["kappa"])
+grid = Q(1, 10 ** 18)
+
+
+def price(P, m, W):
+    """#433 bit_price.py: 10^-24 lower endpoint of PR #315's certify (bad-branch allowance), second engine check"""
+    root = M.certify(P, m, W, True)
+    lo, hi = Q(root["lower"]), Q(root["upper"])
+    fb = 32 * m * m * sum(P.values())
+
+    def other(x):
+        l, u = Other.moment(m, W, list(P.items()), x)
+        p, q = Other.moment(m, W, [(1, fb)], x)
+        return l + p / 10 ** 16, u + q / 10 ** 16
+    assert other(lo)[1] < 1 < other(hi)[0]
+    lo2, hi2 = Other.moment(m, W, list(P.items()), lo)
+    bl, bh = Other.moment(m, W, [(1, fb)], lo)
+    assert hi2 + bh / 10 ** 16 < 1                      # #433 combined.py's check at c
+    return lo, hi
+
+
+def tail(c, b):
+    """#433 combined.py: six fixed bootstrap levels and the 47-inequality outer assembly"""
+    eta = beta = Q(1, 10 ** 18)
+    s = min(c, (1 - beta) * b) - Q(1, 10 ** 24)
+    assert 0 < s < c and s < (1 - beta) * b
+    chain = [Q(384599, 10 ** 10)]
+    cutoffs = []
+
+    def ceil(x):
+        return -((-x.numerator) // x.denominator)
+    for _ in range(6):
+        old = chain[-1]
+        z = (1 - s) * s + s * old
+        gap = min(s - z, 1 - z - s, 1 - z - s * (1 - old), 1 - s)
+        assert old < z < s < 1 - z and gap > 0
+        cutoff = max(ceil(36 / gap ** 2), ceil(2 * (4 + 512) / gap))
+        assert cutoff * gap ** 2 >= 36 and cutoff * gap >= 2 * (4 + 512)
+        cutoffs.append(dict(gap=str(gap), cutoff_log2=str(cutoff)))
+        chain.append(z)
+    q = chain[-1] * (1 - 2 * eta)
+    ticks = (1 - eta) * q / (1 + q) / grid
+    k = grid * ((ticks.numerator - 1) // ticks.denominator)
+    bridge = {"semantic": {"C0": {"base": 2, "exponent": 210000}, "strict_literal_gap": 1},
+              "rows": {"degree_gap": Q(10 ** 6) - Q(51 * 20161, 25)}}
+    asm = Outer.assembly(chain[-1], b, bridge, k, eta=eta, beta=beta)
+    assert len(asm["strict_constraints"]) == 47 and all(x > 0 for x in asm["strict_constraints"].values())
+    rejected = []
+    for name, kk, ee, bb in [("next_grid", k + grid, eta, beta), ("zero_eta", k, Q(0), beta),
+                             ("zero_beta", k, eta, Q(0)), ("unit_beta", k, eta, Q(1))]:
+        try:
+            Outer.assembly(chain[-1], b, bridge, kk, eta=ee, beta=bb)
+        except AssertionError:
+            rejected.append(name)
+        else:
+            raise AssertionError(name)
+    binding = "bit" if c < (1 - beta) * b else "complex"
+    return k, binding, rejected, cutoffs, asm
+
+
+b = Q(cited["b"])
+# control 1: PR #433's stated R758 profile, priced by the same code, gives PR #433's bit c
+L433 = {int(r): n for r, n in cited["bit_local_profile"].items()}
+R433 = cited["bit_R"]
+P433 = {r: 72 * n for r, n in L433.items()}
+for r, n in ((7, 48 * 120), (14, 32 * 120), (28, 32 * 120), (42, 32 * 120)):
+    P433[r] = P433.get(r, 0) + n
+W433 = 64 * 120 + 9 * R433
+assert sum(r * n for r, n in L433.items()) == 8 * R433 + 72 + 2 * 120 * 7
+assert 64 * W433 - sum(r * n for r, n in P433.items()) == 2496
+c433, _ = price(P433, 64, W433)
+assert c433 == Q(cited["bit_c"]), (str(c433), cited["bit_c"])
+# control 2: PR #433's (c, b) through the tail gives PR #433's kappa
+k433, bind433, _, _, _ = tail(c433, b)
+assert k433 == Q(cited["kappa"]) and bind433 == "bit", str(k433)
+print("   control: PR #433's R758 profile prices to c = %s (= PR #433 bit_lower); with b = %s the tail gives kappa = %s"
+      " (= PR #433, bit-bound)" % (c433, b, k433), flush=True)
+# this word: the compressed nine-stage receipts of global_word_g.py / audit_g.py, #433's invoice and tail
+out = a.out
+g = json.loads((out / "GLOBAL.json").read_text())
+geo = json.loads((out / "GEOMETRY.json").read_text())
+audit = json.loads((out / "AUDIT.json").read_text())
+assert audit["template_sha256"] == g["template_sha256"] and len(audit["mutations_rejected"]) == 14
+P = {int(r): z for r, z in audit["profile"].items()}
+m, W = 64, g["live"]
+E = sum(P.values())
+T, L, R, V, K = REPLICAS, 9, g["R"], 120, 4
+assert T==32 and g["replicas"]==T
+mass = sum(r * z for r, z in P.items())
+assert m * W - mass == 312*T and W == 8*T*V + 9 * g["banks_per_stage"]
+physical = g["physical"]
+d = m * m
+N = 2 * m
+unit = L * T * g["local_additions"] + g["bridge_additions"]
+J = 8 * T * L * (2 * V + R) + 8 * (2 * K * V * T) + 2 * g["bank_assignments"] + 2 * g["copy_erase_episodes"]
+high = 16 * (d + 1) ** 2
+good = 8 * m * m + 8
+compiler = 128 * N ** 3
+# Each new bank route is an 8-by-8 rational orthogonal matrix followed by
+# a coordinate permutation. A conservative 8^2+16 elementary factors plus
+# 64 transpositions is covered by an extra 144 factors per helper route.
+selectors = 2 * L * T * ((W - 1) + R * m * (geo["max_route_factors"] + 144 + (m - 1) + m))
+prefix = int(g["global_prefix_bound"])
+charged_prefix = 64 * ((prefix.bit_length() + 63) // 64)
+assert prefix < 1 << charged_prefix <= 1 << 256
+coefficient = unit + J * high + J * physical + E * (good + compiler) + 16 * m ** 3 + g["copy_erase_episodes"] + selectors + prefix + 1
+two = (coefficient + 1) ** 2 * (E + 1) ** 2
+assert two < 1 << 512 and 2 * max(P) ** 2 < m * m
+row = 2 * (m * m + 1) + 9909 + 252
+assert row == 18355 < 20161
+assert geo["bad_prime_factors"] == [2] and geo["route_denominators"] == [1, 2, 4]
+c, chi = price(P, m, W)
+k, binding, rejected, cutoffs, asm = tail(c, b)
+result = dict(status="PASS_KERNEL_BIT_SIDE_COMPOSED_WITH_CITED_PR433_COMPLEX", bit_lower=str(c), bit_upper=str(chi),
+              bit_lower_decimal=format(float(c), ".24f"), complex_lower=str(b), kappa=str(k),
+              kappa_decimal=format(float(k), ".18f"), binding_component=binding,
+              gain_over_pr433_percent=float(100 * (k / Q(cited["kappa"]) - 1)),
+              bit_gain_over_pr433_percent=float(100 * (c / Q(cited["bit_c"]) - 1)),
+              bit_invoice=dict(prefix_bits=prefix.bit_length(), charged_prefix_bits=charged_prefix,
+                               coefficient_bits=coefficient.bit_length(), two_level_coefficient_bits=two.bit_length(),
+                               charged_two_level_coefficient_bits=512, row_coefficient=row, live=W, physical=physical),
+              strict_outer_constraints={n: str(x) for n, x in asm["strict_constraints"].items()},
+              minimum_strict_constraint=str(min(asm["strict_constraints"].values())), outer_controls=rejected,
+              bootstrap=cutoffs, bit_global_sha256=sha(out / "GLOBAL.json"), bit_audit_sha256=sha(out / "AUDIT.json"),
+              controls=dict(pr433_bit_c=str(c433), pr433_kappa=str(k433)), source=cited["source"])
+(out / "COMPOSED-433.json").write_text(json.dumps(result, indent=2) + "\n")
+print("PASS this word with PR #433's bit engine and invoice: c = %s = %.24f (prefix %d bits, charged %d; two-level %d"
+      " bits < 512)" % (c, float(c), prefix.bit_length(), charged_prefix, two.bit_length()), flush=True)
+print("PASS composed with PR #433's complex b = %s: kappa = %s = %.18f (%s-bound; PR #433: %s, %+.6f%%; 47 strict"
+      " inequalities, next grid point, zero eta, zero beta and unit beta rejected)"
+      % (b, k, float(k), binding, cited["kappa"], result["gain_over_pr433_percent"]), flush=True)
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/config.py b/research/e8-rank138-idle-hosting/upstream443/code/config.py
new file mode 100644
index 0000000000..c6824d9c4e
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/config.py
@@ -0,0 +1,2 @@
+"""Four independent groups of eight replicas; no bank padding."""
+REPLICAS = 32
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/e8core.py b/research/e8-rank138-idle-hosting/upstream443/code/e8core.py
new file mode 100644
index 0000000000..78983b3687
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/e8core.py
@@ -0,0 +1,203 @@
+"""Our own engine for bitE8/1 words (E8 root-line labels, h = 8): frame algebra over Q via root-line masks,
+legality/F2 replay, five-stage histogram, exact bit coarse saving and PR #315 outer assembly (our engine copies).
+Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0."""
+import gzip, json, os, importlib.util
+from fractions import Fraction as Q
+from collections import Counter
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+def _load(n):
+    s = importlib.util.spec_from_file_location('e8_' + n, os.path.join(HERE, "engines", n + ".py"))
+    m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+moment = _load('moment'); other = _load('base_two_moment'); outer = _load('outer')
+
+B2 = Q(876248285600677, 10**18)   # Sussman E8 five-stage (PR #352)
+B3 = Q(932783231884153, 10**18)   # DaysSky seven-stage B_3 (PR #363; no Lean proof)
+
+
+def load_word(p):
+    with (gzip.open(p, 'rt') if p.endswith('.gz') else open(p)) as f:
+        return json.load(f)
+
+
+def save_word(c, p):
+    with gzip.open(p, 'wt') as f:
+        json.dump(c, f, separators=(',', ':'))
+
+
+def rank(vecs):
+    rows = [[Q(x) for x in r] for r in vecs]; rk = 0
+    n = len(rows[0]) if rows else 0
+    for col in range(n):
+        p = next((i for i in range(rk, len(rows)) if rows[i][col] != 0), None)
+        if p is None: continue
+        rows[rk], rows[p] = rows[p], rows[rk]
+        for i in range(len(rows)):
+            if i != rk and rows[i][col] != 0:
+                f = rows[i][col] / rows[rk][col]; rows[i] = [a - f * b for a, b in zip(rows[i], rows[rk])]
+        rk += 1
+    return rk
+
+
+class Lat:
+    """Root-spanned subspaces of Q^8 represented by the mask of root lines they contain."""
+    def __init__(self, lines):
+        self.lines = [tuple(x) for x in lines]; self.v = len(lines)
+        self._dim = {0: 0}; self._close = {}
+        # Gram (form <x,y>/2) for orthogonality
+        self.ip = [[sum(a * b for a, b in zip(x, y)) // 2 for y in self.lines] for x in self.lines]
+
+    def close(self, mask):
+        """mask of all root lines in span(roots of mask)"""
+        if mask in self._close: return self._close[mask]
+        idx = [i for i in range(self.v) if mask >> i & 1]
+        basis = []
+        for i in idx:
+            if rank([self.lines[j] for j in basis] + [self.lines[i]]) > len(basis): basis.append(i)
+        d = len(basis); out = 0
+        if d == 8: out = (1 << self.v) - 1
+        elif d:
+            B = [self.lines[j] for j in basis]
+            for i in range(self.v):
+                if rank(B + [self.lines[i]]) == d: out |= 1 << i
+        self._close[mask] = out; self._close[out] = out; self._dim[out] = d
+        return out
+
+    def dim(self, mask):
+        if mask not in self._dim: self.close(mask)
+        return self._dim[mask]
+
+    def basis(self, mask):
+        b = []
+        for i in range(self.v):
+            if mask >> i & 1 and rank([self.lines[j] for j in b] + [self.lines[i]]) > len(b): b.append(i)
+        return b
+
+    def perp(self, t):
+        return self.close(sum(1 << j for j in range(self.v) if self.ip[t][j] == 0))
+
+
+def to_masks(c, L):
+    return [L.close(sum(1 << i for i in fr)) for fr in c['frames']]
+
+
+PHASES = ('D', 'A', 'B', 'C')
+
+
+def replay(c, L=None, masks=None, check_f2=True, span=True, span_mode='z'):
+    """Exact legality + F2 replay + histogram of a bitE8/1 word. Returns dict(H_local, steps, ...).
+    Legality: each register's frames nested (mask inclusion = exact Q-subspace inclusion for root-spanned frames) and
+    strictly increasing at each move; every gate at one common frame; D compensation at frame 0; y at frame 0 at the
+    scatter; COPY of retained totals; final frames (x, helpers FULL; y_t at its cap t-perp).
+    Source-span: every non-target operand's x-support lies in the gate frame."""
+    L = L or Lat(c['lines']); masks = masks or to_masks(c, L)
+    v, R, h = c['v'], c['R'], c['h']; n = 2 * v + R; FULL = (1 << v) - 1
+    cur = [masks[f] for f in c['start']]
+    for r in range(v): assert cur[r] == L.close(1 << r), 'x start'
+    for r in range(v, 2 * v): assert cur[r] == 0, 'y start at 0'
+    sig = [L.dim(cur[r]) for r in range(n)]
+    H = Counter(); steps = 0; viol = []
+    val = [1 << i for i in range(n)]
+    zsupp = [{i: 1} if i < v else {} for i in range(n)]  # integer support of each register over the x columns (all ADDs are +1)
+    def climb(r, m):
+        nonlocal steps
+        if cur[r] == m: return
+        assert cur[r] & ~m == 0 and cur[r] != m, ('not nested', r)
+        H[L.dim(m) - L.dim(cur[r])] += 1; steps += 1; cur[r] = m
+    def run(gates, ph):
+        for k, (f, d, srcs) in enumerate(gates):
+            m = masks[f]
+            assert d >= v and d not in srcs and len(set(srcs)) == len(srcs), (ph, k)
+            for x in [d] + srcs: climb(x, m)
+            for s in srcs:
+                val[d] ^= val[s]
+                if span:
+                    if s < v or s >= 2 * v:
+                        ms = sum(1 << i for i in zsupp[s])
+                        if ms & ~m: viol.append((ph, k, s))
+                    zd = zsupp[d]
+                    for i, a in zsupp[s].items():
+                        w = zd.get(i, 0) + a
+                        if w: zd[i] = w
+                        else: zd.pop(i, None)
+                    if span_mode == 'f2':
+                        zsupp[d] = {i: 1 for i in range(v) if val[d] >> i & 1}
+            if span and d >= 2 * v:
+                md = sum(1 << i for i in zsupp[d])
+                if md & ~m: viol.append((ph, k, d))
+    run(c['D'], 'D')
+    for r in range(v, n): assert cur[r] == masks[c['start'][r]], 'D compensation at frame 0 (helpers untouched otherwise)'
+    run(c['A'], 'A')
+    for t in range(v): assert cur[v + t] == 0, 'y at frame 0 at the scatter'
+    copies = [val[q] for q in c['ret']]
+    for q in c['ret']:
+        assert q >= 2 * v; H[L.dim(cur[q])] += 1
+    for t, row in enumerate(c['scatter']):
+        for k in row: val[v + t] ^= copies[k]
+    run(c['B'], 'B'); run(c['C'], 'C')
+    for r in range(n): climb(r, masks[c['final'][r]])
+    for r in range(v): assert cur[r] == FULL
+    for r in range(2 * v, n): assert cur[r] == FULL
+    for t in range(v): assert cur[v + t] == L.perp(t), 'y final at cap'
+    if check_f2:
+        for s in range(v): assert val[s] == 1 << s
+        for t in range(v): assert val[v + t] == (1 << (v + t)) | (1 << t), ('target', t)
+        for r in range(2 * v, n): assert val[r] == 1 << r, ('helper', r)
+    return dict(sig=sig, viol=viol, H=H, steps=steps, n=n, v=v, R=R, h=h, L=L, masks=masks, ncopy=len(c['ret']))
+
+
+def profile(H_local, v, h=8):
+    prof = Counter({j: 5 * c for j, c in H_local.items()})
+    for j in (2 * h - 2, h - 1, 2 * h + 2, 4): prof[j] += 2 * v
+    return prof
+
+
+def coarse(H, m, W):
+    grid = Q(1, 10**18)
+    root = moment.certify(dict(H), m, W, True); c = Q(int(Q(root['lower']) * 10**18), 10**18)
+    assert moment.moment(H, m, W, c, True)[1] < 1 < moment.moment(H, m, W, c + grid, True)[0]
+    fb = 32 * m * m * sum(H.values())
+    _, up = other.moment(m, W, list(H.items()), c); _, bad = other.moment(m, W, [(1, fb)], c)
+    lo, _ = other.moment(m, W, list(H.items()), c + grid); blo, _ = other.moment(m, W, [(1, fb)], c + grid)
+    assert up + Q(1, 10**16) * bad < 1 < lo + Q(1, 10**16) * blo
+    return c
+
+
+def kappa(c, b):
+    grid = Q(1, 10**18); eta = Q(1, 10**12); beta = Q(1, 10**9); cap = (1 - beta) * b
+    sv = min(c, Q(((cap - grid) * 10**18).__floor__(), 10**18)); binding = 'bit' if sv == c else 'complex'
+    chain = [Q(384599, 10**10)]
+    for _ in range(3):
+        a = (1 - sv) * sv + sv * chain[-1]; assert chain[-1] < a < sv < 1 - a; chain.append(a)
+    bit = chain[-1]
+    bridge = dict(proof='PROOF.md', representation='Exact powers with source-bound finite overcharges',
+                  semantic=dict(G=dict(base=2, exponent=30000), E=dict(base=2, exponent=100000), B_upper=dict(base=2, exponent=100001),
+                                C0=dict(base=2, exponent=210000), C1=1, strict_literal_gap=1, induction_gap_lower=1),
+                  rows=dict(coefficient=20161, degree=10**6, suffix_slope=4 * 10**6, degree_gap=Q(10**6) - Q(51 * 20161, 25)))
+    q = bit * (1 - 2 * eta); mn = (1 - eta) * q / (1 + q); t = mn * 10**18; k = Q((t.numerator - 1) // t.denominator, 10**18)
+    asm = outer.assembly(bit, b, bridge, k, eta=eta, beta=beta)
+    assert len(asm['strict_constraints']) == 47 and min(asm['strict_constraints'].values()) > 0
+    try:
+        outer.assembly(bit, b, bridge, k + grid, eta=eta, beta=beta); raise SystemExit('ADJACENT ADMITTED')
+    except AssertionError: pass
+    return k, binding
+
+
+def price_word(c, **kw):
+    r = replay(c, **kw)
+    v, h, R = r['v'], r['h'], r['R']; m = 5 * h
+    resid = sum(h - r['sig'][x] for x in range(2 * v, 2 * v + R))
+    T = 1 if resid % h == 0 else h
+    W = (4 * v * h + resid) * T // h; assert (4 * v * h + resid) * T % h == 0
+    prof = Counter({j: T * k for j, k in profile(r['H'], v, h).items()}); mass = sum(a * b for a, b in prof.items())
+    L_copy = h * r['ncopy']
+    assert m * W - mass == T * (4 * v - 5 * L_copy), ('deficit', m * W - mass)
+    assert 2 * max(prof) < m
+    cc = coarse(prof, m, W)
+    return dict(c=cc, H=r['H'], prof=prof, W=W, T=T, resid=resid, m=m, deficit=m * W - mass, replay=r)
+
+
+def phi_fn(m, W, a):
+    """linearized moment term per child of rank r (float), for search scoring"""
+    import math
+    return lambda r: r / (m * W) * math.exp(a * math.log(m / r))
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/engines/base_two_moment.py b/research/e8-rank138-idle-hosting/upstream443/code/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/engines/moment.py b/research/e8-rank138-idle-hosting/upstream443/code/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/engines/outer.py b/research/e8-rank138-idle-hosting/upstream443/code/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/export249.py b/research/e8-rank138-idle-hosting/upstream443/code/export249.py
new file mode 100644
index 0000000000..462a0f121f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/export249.py
@@ -0,0 +1,86 @@
+"""Export a bitE8/1 word to PR249 snapshot format (249-records.bin, 249-states.json, frames.json) and stage it for
+PR #266's official cohort checkers. Our own exporter (helpers may start at a kernel entrance E, sigma = dim E).
+Records (int32 x 6): MOVE(0,role,old,new,rank,0), ADD(1,dst,src,1,frame,phase), COPY(2,centre,temp,frame,ZERO,rank),
+ERASE(3,centre,temp,frame,ZERO,0). A gate with several sources: MOVE every participant to the gate frame, then one ADD
+per source. Frames: B = integer label vectors of a basis among the frame's root lines; A = primitive integer
+annihilator rows under the standard dot product (exact over Q).
+usage: export249.py WORD.json.gz SNAPDIR COHORT_IN COHORT_OUT
+Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0."""
+import sys, os, json, struct, math, shutil
+from fractions import Fraction as Q
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+from e8core import load_word, Lat, to_masks
+
+
+def nullspace(B, h):
+    M = [[Q(x) for x in r] for r in B]; piv = []; rk = 0
+    for col in range(h):
+        p = next((i for i in range(rk, len(M)) if M[i][col] != 0), None)
+        if p is None: continue
+        M[rk], M[p] = M[p], M[rk]; pv = M[rk][col]; M[rk] = [x / pv for x in M[rk]]
+        for i in range(len(M)):
+            if i != rk and M[i][col] != 0:
+                f = M[i][col]; M[i] = [a - f * b for a, b in zip(M[i], M[rk])]
+        piv.append(col); rk += 1
+    A = []
+    for fc in [x for x in range(h) if x not in piv]:
+        a = [Q(0)] * h; a[fc] = Q(1)
+        for i, pc in enumerate(piv): a[pc] = -M[i][fc]
+        den = 1
+        for x in a: den = den * x.denominator // math.gcd(den, x.denominator)
+        ai = [int(x * den) for x in a]; g = 0
+        for x in ai: g = math.gcd(g, abs(x))
+        A.append([x // g for x in ai])
+    return A
+
+
+def export(c, out):
+    os.makedirs(out, exist_ok=True)
+    L = Lat(c['lines']); masks = to_masks(c, L); v, R, h = c['v'], c['R'], c['h']; n = 2 * v + R
+    fid = {}; frames = {}
+    for k, m in enumerate(masks):
+        if m in fid: continue
+        fid[m] = k; B = [list(L.lines[i]) for i in L.basis(m)]
+        A = nullspace(B, h) if B else [[int(i == j) for j in range(h)] for i in range(h)]
+        assert len(A) + len(B) == h and all(sum(x * y for x, y in zip(a, b)) == 0 for a in A for b in B)
+        frames[str(k)] = dict(dim=len(B), B=B, A=A)
+    F = lambda f: fid[masks[f]]
+    ZERO = fid[0]; FULL = fid[(1 << v) - 1]
+    dim = {int(a): b['dim'] for a, b in frames.items()}
+    cur = [F(f) for f in c['start']]; rec = []
+    def move(r, f):
+        if cur[r] != f: rec.append((0, r, cur[r], f, dim[f] - dim[cur[r]], 0)); cur[r] = f
+    def run(gates, ph):
+        for f, d, srcs in gates:
+            f = F(f)
+            for r in [d] + srcs: move(r, f)
+            for s in srcs: rec.append((1, d, s, 1, f, ph))
+    run(c['D'], 1); run(c['A'], 2)
+    temp = n
+    for k, q in enumerate(c['ret']):
+        fq = cur[q]; rec.append((2, q, temp, fq, ZERO, dim[fq]))
+        for t, row in enumerate(c['scatter']):
+            if k in row: rec.append((1, v + t, temp, 1, ZERO, 3))
+        rec.append((3, q, temp, fq, ZERO, 0))
+    run(c['B'], 4); run(c['C'], 5)
+    for r in range(n): move(r, F(c['final'][r]))
+    with open(out + '/249-records.bin', 'wb') as fh:
+        for e in rec: fh.write(struct.pack('<6i', *e))
+    st = dict(n=n, v=v, h=h, R=R, ZERO=ZERO, FULL=FULL, initial={str(r): F(c['start'][r]) for r in range(n)},
+              final={str(r): F(c['final'][r]) for r in range(n)}, retained_totals=c['ret'], source_owned_roles=[], regs=[])
+    json.dump(st, open(out + '/249-states.json', 'w'), sort_keys=True, separators=(',', ':'))
+    json.dump(dict(frames=frames), open(out + '/frames.json', 'w'), sort_keys=True, separators=(',', ':'))
+    return st, frames, rec
+
+
+if __name__ == '__main__':
+    c = load_word(sys.argv[1]); snap, cin, cout = sys.argv[2:5]
+    st, frames, rec = export(c, snap)
+    os.makedirs(cin, exist_ok=True); os.makedirs(cout, exist_ok=True)
+    json.dump(st, open(cin + '/249-states.json', 'w')); json.dump(dict(frames=frames), open(cin + '/frames.json', 'w'))
+    json.dump({'donor_keys': []}, open(cin + '/249-DONOR-OWNERSHIP.json', 'w'))
+    json.dump({}, open(cout + '/COHORT249-FRAMES.json', 'w'))
+    json.dump({k: int(x) for k, x in st['initial'].items()}, open(cout + '/COHORT249-INITIAL.json', 'w'))
+    json.dump([], open(cout + '/COHORT249-SELECTION.json', 'w'))
+    shutil.copy(snap + '/249-records.bin', cout + '/COHORT249-RECORDS.bin')
+    print('   exported %d records, %d distinct frames, n %d, ZERO %d, FULL %d' % (len(rec), len(frames), st['n'], st['ZERO'], st['FULL']))
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/global_kernel.py b/research/e8-rank138-idle-hosting/upstream443/code/global_kernel.py
new file mode 100644
index 0000000000..72856bf507
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/global_kernel.py
@@ -0,0 +1,243 @@
+# Kernel integration of PR436/PR386 by chafreaky, with OpenAI Codex assistance.
+# Original copyright and attribution retained below. This variant uses explicit
+# residual isometries and mixed-width banks; the original all-zero-start
+# requirement is replaced by the verified kernel entrance contract.
+"""Source-bound nine-stage bit template with 32 independent replicas.
+PR386 global identity and PR436 generalization by Zhihao Chen and eumemic,
+with their disclosed OpenAI Codex and Anthropic Claude assistance, Apache-2.0.
+PR439 explicit residual routes and this replication extension by chafreaky,
+with OpenAI Codex assistance. All owner assignments and emitted calls are checked.
+Historical PR386 regression is performed by the unchanged parent wrapper.
+"""
+import argparse, gzip, hashlib, json, struct, time
+from collections import Counter
+from pathlib import Path
+from bank_routes import placement, validate_isometries
+from config import REPLICAS
+
+H,L,K,T,M=8,9,4,REPLICAS,64
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+def write(p,x): p.write_text(json.dumps(x,indent=2)+'\n')
+
+def recipe():
+    out=[dict(kind='local',stage=0,pair=0,reverse=False)]; stage=1
+    for j in range(K):
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=True)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=1))
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=False)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=-1))
+    for j in reversed(range(K-1)): out.append(dict(kind='bridge',dst=j+1,src=j,coefficient=1))
+    out.append(dict(kind='exchange'))
+    return out
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--word',type=Path,required=True)
+    ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    ap.add_argument('--isometries',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out; out.mkdir(parents=True,exist_ok=True)
+    wp=a.word; w=json.loads(gzip.decompress(wp.read_bytes()))
+    V,R=w['v'],w['R']; LOCAL=2*V+R; DATA=2*K*V*T; LIVE=DATA+L*R
+    assert (w['h'],V,w['form'])==(8,120,'<x,y>/2')
+    geo=json.loads((out/'GEOMETRY.json').read_text())
+    assert geo['status']=='PASS_COMPRESSED_NINE_BIT_GEOMETRY_AND_BANK_BLOCKS'
+    # the port routes depend only on the labels: same 120 label vectors, in the same order
+    assert len(geo['ports'])==V and all(p['port']==t and p['q']==w['lines'][t] for t,p in enumerate(geo['ports']))
+    rp=a.local_check/'records/249-records.bin'; raw=rp.read_bytes(); rec=list(struct.iter_unpack('<6i',raw))
+    state=json.loads((a.local_check/'records/249-states.json').read_text())
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    dims={int(f):z['dim'] for f,z in fs.items()}
+    lg=json.loads((a.local_check/'cout/legality.json').read_text())
+    cc=json.loads((a.local_check/'cout/columns.json').read_text())
+    assert lg['status'].startswith('PASS') and cc['status'].startswith('PASS')
+    assert (state['v'],state['n'])==(V,LOCAL) and lg['copies']==lg['erasures']==9
+    ADDS=lg['common_frame_ADDs']
+    assert cc['formal_columns_checked']==4*V+R and cc['local_scalar_additions']==ADDS
+    initial=[state['initial'][str(i)] for i in range(LOCAL)]
+    final=[state['final'][str(i)] for i in range(LOCAL)]
+    assert all(dims[final[i]]==H for i in range(2*V,LOCAL))
+    widths=[H-dims[initial[i]] for i in range(2*V,LOCAL)]
+    ENT=sum(H-z for z in widths)
+    place,NB=placement(widths,T)
+    assert T%8==0 and T*(H*R-ENT)%M==0 and NB==T*(H*R-ENT)//M
+    LIVE=DATA+L*NB
+    isometries=json.loads(a.isometries.read_text())
+    assert validate_isometries(isometries,w['frames'],w['lines'],dims)==set(initial[2*V:])
+    streams={}; checks={}; localH=None
+    for reverse in (False,True):
+        cur=(final if reverse else initial)[:]+[-1]; val=[1<<i for i in range(LOCAL)]+[0]
+        norm=[1]*LOCAL+[0]; maxnorm=1; center=None; hist=Counter(); events=[]; copies=0; adds=0
+        dim=lambda f:H-dims[f] if reverse else dims[f]
+        for op,x,y,c,f,z in (reversed(rec) if reverse else rec):
+            if op==0:
+                oldf,newf=(c,y) if reverse else (y,c)
+                assert cur[x]==oldf and dim(newf)-dim(oldf)==f>=0
+                cur[x]=newf
+                if f: hist[f]+=1
+                events.append([0,x,oldf,newf,f,int(reverse)])
+            elif op==1:
+                assert cur[x]==cur[y]==f and x!=y and x<LOCAL
+                if center is not None: assert x!=center
+                if y==LOCAL: assert center is not None
+                if c&1: val[x]^=val[y]
+                norm[x]+=abs(c)*norm[y]; maxnorm=max(maxnorm,norm[x]); adds+=1
+                events.append([1,x,y,-c if reverse else c,f,int(reverse)])
+            elif op==(3 if reverse else 2):
+                assert center is None and y==LOCAL and cur[x]==c and val[LOCAL]==0
+                copy_rank=abs(dim(c)-dim(f)); assert copy_rank==8
+                assert z==(0 if reverse else copy_rank)
+                center=x; cur[LOCAL]=f; val[LOCAL]=val[x]; norm[LOCAL]=norm[x]
+                hist[copy_rank]+=1; copies+=1; events.append([2,x,LOCAL,c,f,copy_rank,int(reverse)])
+            else:
+                assert op==(2 if reverse else 3)
+                assert center==x and y==LOCAL and cur[x]==c and cur[LOCAL]==f
+                assert val[LOCAL]==val[x]
+                val[LOCAL]=0; norm[LOCAL]=0; cur[LOCAL]=-1; center=None
+                events.append([3,x,LOCAL,c,f,z,int(reverse)])
+        assert center is None and copies==9 and adds==ADDS
+        assert cur[:LOCAL]==(initial if reverse else final)
+        for i in range(LOCAL):
+            want=(1<<i) ^ ((1<<(i-V)) if V<=i<2*V else 0)
+            assert val[i]==want
+        assert val[LOCAL]==0
+        if localH is None: localH=hist
+        else: assert localH==hist
+        key='reverse' if reverse else 'forward'; streams[key]=events
+        checks[key]=dict(copies=copies,adds=adds,records=len(events),all_columns=LOCAL,
+                         cancellation_free_row_l1=maxnorm,profile=dict(sorted(hist.items())),
+                         sha256=hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest())
+    assert sum(r*n for r,n in localH.items())==H*R-ENT+72+2*V*(H-1)
+    assert localH==Counter({int(r):n for r,n in cc['local_raw_H']})
+
+    events=recipe(); levels=[-1]*K; schedule=[]; bridge_controls=[]
+    # Full scalar replay on separate dirty helpers for all nine stages.
+    # Physical banking then uses the separately checked injective cover owners.
+    n=2*K*V+L*R; vals=[1<<i for i in range(n)]+[0]; temp=n
+    stages=[]
+    for e in events:
+        if e['kind']=='local':
+            s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1
+            def mapper(i):
+                if i==LOCAL: return temp
+                if i<2*V:
+                    side=i//V; side=1-side if rev else side
+                    return (2*p+side)*V+i%V
+                return 2*K*V+s*R+i-2*V
+            before=vals[:]; opened=False
+            for z in streams['reverse' if rev else 'forward']:
+                if z[0]==0: continue
+                x,y=mapper(z[1]),mapper(z[2])
+                if z[0]==1:
+                    if z[3]&1: vals[x]^=vals[y]
+                elif z[0]==2:
+                    assert not opened; vals[temp]=vals[x]; opened=True
+                else:
+                    assert opened and vals[temp]==vals[x]; vals[temp]=0; opened=False
+            assert not opened
+            d=(2*p+(0 if rev else 1))*V; src=(2*p+(1 if rev else 0))*V
+            for t in range(V): before[d+t]^=before[src+t]
+            assert vals==before
+            levels[p]=s; schedule.append(dict(kind='local_cover_sweep',**{k:v for k,v in e.items() if k!='kind'}))
+            if s in (1,3,5):
+                j=(s+1)//2; assert levels[j]==-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7*(s+1),source_level=-1,target_level=s))
+            elif s in (2,4,6):
+                j=s//2; assert levels[j]==s-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7,source_level=s-1,target_level=s))
+            elif s==8:
+                for j in range(4):
+                    oldlevel=levels[j]; assert oldlevel==2*j+2
+                    schedule.append(dict(kind='idle',pair=j,rank=7*(8-oldlevel),source_level=oldlevel,target_level=8))
+                    levels[j]=8
+            stages.append(dict(stage=s,all_columns=n,helper_columns=L*R,reverse=rev))
+        elif e['kind']=='bridge':
+            d,s=e['dst'],e['src']; assert levels[d]==levels[s]
+            for t in range(V): vals[2*d*V+t]^=vals[2*s*V+t]; vals[(2*s+1)*V+t]^=vals[(2*d+1)*V+t]
+            schedule.append(e)
+        else:
+            assert levels==[8]*4
+            for j in range(K):
+                for t in range(V):
+                    x=2*j*V+t; y=(2*j+1)*V+t; vals[x],vals[y]=vals[y],vals[x]
+            schedule.append(e)
+    assert vals==[1<<i for i in range(n)]+[0]
+    # Integer scalar eight-bank matrix, with each individual bridge shear omitted.
+    def small(skip=-1):
+        z=[[int(i==j) for j in range(8)] for i in range(8)]; count=0
+        def add(d,s,c): z[d]=[x+c*y for x,y in zip(z[d],z[s])]
+        for e in events:
+            if e['kind']=='local':
+                p=e['pair']; add(2*p,2*p+1,-1) if e['reverse'] else add(2*p+1,2*p,1)
+            elif e['kind']=='bridge':
+                d,s,c=e['dst'],e['src'],e['coefficient']
+                for x,y,sgn in [(2*d,2*s,c),(2*s+1,2*d+1,-c)]:
+                    if count!=skip: add(x,y,sgn)
+                    count+=1
+            else:
+                for j in range(4): z[2*j],z[2*j+1]=z[2*j+1],[-x for x in z[2*j]]
+        return z,count
+    ident=[[int(i==j) for j in range(8)] for i in range(8)]
+    z,nb=small(); assert z==ident and nb==18
+    for skip in range(nb): assert small(skip)[0]!=ident; bridge_controls.append(skip)
+
+    paid=Counter(); calls=[]; assignment=set(); expanded=hashlib.sha256(); full_event_count=0
+    for e in events:
+        if e['kind']!='local': continue
+        s,p,rev=e['stage'],e['pair'],e['reverse']; ori='reverse' if rev else 'forward'
+        for rep in range(T):
+            owners=[]
+            for i in range(2*V):
+                side=i//V; side=1-side if rev else side
+                owners.append([rep*(2*K*V)+(2*p+side)*V+i%V, ['data',s,i%V]])
+            for r in range(R):
+                bank,offset,width=place[rep,r]
+                owners.append([DATA+s*NB+bank,['bank',offset,width,initial[2*V+r]]])
+                assignment.add((s,rep,r,bank,offset))
+            assert len({(f,tuple(route)) for f,route in owners})==LOCAL
+            assert all(0<=f<LIVE for f,route in owners)
+            # Stream one full renamed instruction program into a source-bound
+            # digest, including exact owner route descriptors and reflection.
+            for z in streams[ori]:
+                op=z[0]
+                if op==0: paid[z[4]]+=bool(z[4]); mapped=[op,owners[z[1]],*z[2:]]
+                else:
+                    ox=owners[z[1]]; oy=owners[z[2]] if z[2]<LOCAL else [LIVE,['private',0]]
+                    mapped=[op,ox,oy,*z[3:]]
+                    if op==2: paid[z[5]]+=1
+                expanded.update((json.dumps(mapped,separators=(',',':'))+'\n').encode()); full_event_count+=1
+            calls.append(dict(stage=s,replica=rep,pair=p,orientation=ori,owners=owners,local_hash=checks[ori]['sha256']))
+    paid.pop(0,None)
+    assert len(assignment)==L*T*R and len(calls)==L*T
+    for e in schedule:
+        if e['kind']=='idle' and e['rank']: paid[e['rank']]+=2*V*T
+    mass=sum(r*c for r,c in paid.items()); assert M*LIVE-mass==312*T
+    want=Counter({r:L*T*c for r,c in localH.items()})
+    for r,c in ((7,6*T*V),(14,4*T*V),(28,4*T*V),(42,4*T*V)): want[r]+=c
+    assert dict(sorted(paid.items()))==dict(sorted(want.items()))
+    cf=checks['forward']['cancellation_free_row_l1']; cb=checks['reverse']['cancellation_free_row_l1']
+    prefix=(1<<nb)*cf**5*cb**4; assert prefix<1<<192
+    template=dict(version='compressed-nine-e8-bit-v1',m=M,h=H,stages=L,replicas=T,live=LIVE,private_centre_reserve=9,
+                  cover='O(I_64/2,F_q) for admitted odd address primes q',loop_order='Each recipe phase: replicas then all cover classes; finish every local invocation before the next.',
+                  schedule=schedule,local_programs=streams,calls=calls,bank_padding=None,
+                  helper_route='Exact residual isometry from the listed root basis, extended by identity on exterior coordinates and permuted to the assigned bank interval.',
+                  residual_isometries=isometries,banks_per_stage=NB,entrance_rank_total=ENT,
+                  data_route='owner (replica*960 + (2*pair+side)*120+port, d*rho_stage,port)',
+                  bit_operator='D_U exchanges the two address halves on projector U; D_I D_P = D_(I-P) exactly.',
+                  geometry_sha256=sha(out/'GEOMETRY.json'),source_record_sha256=sha(rp))
+    blob=json.dumps(template,separators=(',',':'),sort_keys=True).encode(); (out/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+    result=dict(status='PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE',h=H,m=M,v=V,R=R,replicas=T,live=LIVE,physical=LIVE+9,
+                word_sha256=sha(wp),source_records_sha256=sha(rp),local_checks=checks,scalar_stages=stages,
+                independent_unbanked_scalar_columns=n,all_scalar_columns_restored=True,
+                geometry_sha256=sha(out/'GEOMETRY.json'),template_sha256=hashlib.sha256(blob).hexdigest(),
+                emitted_program_sha256=expanded.hexdigest(),emitted_events=full_event_count,local_invocations=len(calls),
+                bank_assignments=len(assignment),banks_per_stage=NB,entrance_rank_total=ENT,residual_bank_slots=True,padding_calls=0,
+                profile=dict(sorted(paid.items())),paid_calls=sum(paid.values()),rank_mass=mass,deficit=312*T,
+                maxchild=max(paid),halving_depth=2,halving_integer_inequality=[64**2,2*42**2],
+                local_additions=ADDS,bridge_additions=18*V*T,copy_erase_episodes=9*L*T,
+                global_prefix_bound=str(prefix),global_prefix_bits=prefix.bit_length(),charged_prefix_bits=192,
+                omitted_bridge_shears_rejected=bridge_controls,
+                scope='Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.',
+                seconds=time.monotonic()-start)
+    write(out/'GLOBAL.json',result)
+    print(json.dumps({k:v for k,v in result.items() if k not in ('local_checks','scalar_stages','global_prefix_bound')}),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/iface386.py b/research/e8-rank138-idle-hosting/upstream443/code/iface386.py
new file mode 100644
index 0000000000..05d9bab0b4
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/iface386.py
@@ -0,0 +1,47 @@
+"""Interface check of a bitE8/1 word against PR #386's local-stream conditions (our own reimplementation, data semantics
+from #386's PROOF.txt; no #386 code run): export to PR249 records (our export249), replay forward and reflected streams
+(reverse order, U -> U-perp, ERASE -> fresh COPY), F2 on all local columns + private centre, 9 copies of rank 8,
+equal forward/reverse paid histograms, cancellation-free row l1 bounds and the nine-stage prefix 2^18 cf^5 cb^4 < 2^192,
+helper initial/final frames (0 / FULL in #386; kernel pivots start at their entrance).  usage: iface386.py WORD.json.gz"""
+import sys, os, json, tempfile
+from collections import Counter
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+from e8core import load_word
+from export249 import export
+H = 8
+def check(c, allow=int(os.environ.get("PREFIX_ALLOW", "192"))):
+    st, frames, rec = export(c, tempfile.mkdtemp())
+    v, n = st['v'], st['n']; dims = {int(k): z['dim'] for k, z in frames.items()}
+    initial = [st['initial'][str(i)] for i in range(n)]; final = [st['final'][str(i)] for i in range(n)]
+    nz_start = Counter(dims[initial[i]] for i in range(2 * v, n)); assert all(dims[final[i]] == H for i in range(2 * v, n))
+    out = {}
+    for reverse in (False, True):
+        cur = (final if reverse else initial)[:] + [-1]; val = [1 << i for i in range(n)] + [0]
+        norm = [1] * n + [0]; mx = 1; centre = None; hist = Counter(); copies = adds = 0
+        dim = (lambda f: H - dims[f]) if reverse else (lambda f: dims[f])
+        for op, x, y, cc, f, z in (reversed(rec) if reverse else rec):
+            if op == 0:
+                old, new = (cc, y) if reverse else (y, cc)
+                assert cur[x] == old and dim(new) - dim(old) == f >= 0; cur[x] = new
+                if f: hist[f] += 1
+            elif op == 1:
+                assert cur[x] == cur[y] == f and x != y and x < n
+                if centre is not None: assert x != centre
+                if y == n: assert centre is not None
+                if cc & 1: val[x] ^= val[y]
+                norm[x] += abs(cc) * norm[y]; mx = max(mx, norm[x]); adds += 1
+            elif op == (3 if reverse else 2):
+                assert centre is None and y == n and cur[x] == cc and val[n] == 0
+                r = abs(dim(cc) - dim(f)); assert r == 8
+                centre = x; cur[n] = f; val[n] = val[x]; norm[n] = norm[x]; hist[r] += 1; copies += 1
+            else:
+                assert centre == x and y == n and cur[x] == cc and cur[n] == f and val[n] == val[x]
+                val[n] = 0; norm[n] = 0; cur[n] = -1; centre = None
+        assert centre is None and copies == 9 and cur[:n] == (initial if reverse else final)
+        for i in range(n): assert val[i] == (1 << i) ^ ((1 << (i - v)) if v <= i < 2 * v else 0)
+        out['reverse' if reverse else 'forward'] = dict(adds=adds, copies=copies, row_l1=mx, hist=dict(sorted(hist.items())))
+    assert out['forward']['hist'] == out['reverse']['hist']
+    cf, cb = out['forward']['row_l1'], out['reverse']['row_l1']; pre = (1 << 18) * cf ** 5 * cb ** 4
+    return dict(n=n, R=st['R'], helper_start_dims=dict(sorted(nz_start.items())), streams=out, prefix_bits=pre.bit_length(), prefix_ok=pre < 1 << allow, prefix_allow=allow)
+if __name__ == '__main__':
+    print(json.dumps(check(load_word(sys.argv[1]))))
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/rebuild.py b/research/e8-rank138-idle-hosting/upstream443/code/rebuild.py
new file mode 100644
index 0000000000..f7239ea69f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/rebuild.py
@@ -0,0 +1,65 @@
+"""Reconstruct primitive retiming and the kernel with 32 exact bank replicas.
+Prepared by chafreaky with OpenAI Codex assistance; Apache-2.0.
+"""
+import copy
+import json
+from pathlib import Path
+from e8core import load_word, replay
+from iface386 import check
+from stages import content_sha, retime
+from replica_kernel import kernel
+from config import REPLICAS
+
+ROOT=Path(__file__).resolve().parents[1]
+parent=load_word(str(ROOT/'parent436/data/bit/bitE8-r740.json.gz'))
+timing=json.loads((ROOT/'data/retiming.json').read_text())
+assert content_sha(parent)==timing['input_sha256']
+primitive=copy.deepcopy(parent)
+for phase in ('D','A','B','C'):
+    primitive[phase]=[[f,d,[s]] for f,d,ss in parent[phase] for s in ss]
+retimed=retime(primitive,timing['changes'])
+assert len(timing['changes'])==57 and content_sha(retimed)==timing['output_sha256']
+for phase in ('D','A','B','C'):
+    assert [(d,s) for f,d,ss in parent[phase] for s in ss]==[(d,s) for f,d,ss in retimed[phase] for s in ss]
+selected=json.loads((ROOT/'data/selection.json').read_text())
+assert content_sha(retimed)==selected['input_sha256']
+word,entries,rank,donors=kernel(retimed,selected['entries'],REPLICAS)
+assert (entries,rank,donors,REPLICAS)==(114,138,103,32)
+assert content_sha(word)==selected['output_sha256']
+post=json.loads((ROOT/'data/post-retiming.json').read_text())
+assert [len(s['gates']) for s in post]==[112,42]
+for stage in post:
+    original=json.loads((ROOT/'data/upstream441'/stage['source']).read_text())
+    assert stage['gates']==original['gates'] and all(g[0]=='B' for g in stage['gates'])
+    assert content_sha(word)==stage['input_sha256']
+    word=retime(word,stage['gates'])
+    assert content_sha(word)==stage['output_sha256']
+assert word==load_word(str(ROOT/'data/word.json.gz'))
+audit=replay(word,span_mode='z');assert not audit['viol'],audit['viol'][:5]
+interface=check(word,192);assert interface['prefix_ok']
+
+rejected=[]
+for name,mutate in [
+    ('retained row used as pivot',lambda s:s[0].__setitem__(1,parent['ret'][0])),
+    ('duplicate pivot',lambda s:s.append(copy.deepcopy(s[0]))),
+]:
+    bad=copy.deepcopy(selected['entries']);mutate(bad)
+    try:kernel(retimed,bad,REPLICAS)
+    except AssertionError:rejected.append(name)
+    else:raise AssertionError('accepted invalid kernel selection: '+name)
+try:kernel(retimed,selected['entries'],8)
+except AssertionError:rejected.append('eight replicas do not fill integral banks')
+else:raise AssertionError('accepted nonintegral bank stock')
+bad=copy.deepcopy(word);bad['A'][0][2].pop()
+try:bad_audit=replay(bad,span_mode='z')
+except AssertionError:pass
+else:assert bad_audit['viol'],'missing dirty-response correction accepted'
+rejected.append('omit a kernel dirty-response correction')
+bad=copy.deepcopy(timing['changes']);bad[0][2]=[]
+try:retime(primitive,bad)
+except AssertionError:rejected.append('wrong primitive input frame')
+else:raise AssertionError('accepted incorrect frame binding')
+print(json.dumps(dict(status='PASS_FROZEN_RETIMING_KERNEL_REPLICA_REBUILD',
+    input_sha256=content_sha(parent),retimed_sha256=content_sha(retimed),output_sha256=content_sha(word),
+    pre_kernel_frame_changes=57,post_kernel_frame_changes=[112,42],entries=entries,entrance_rank=rank,donor_slots=donors,replicas=REPLICAS,
+    interface=interface,mutations_rejected=rejected),sort_keys=True))
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/replica_kernel.py b/research/e8-rank138-idle-hosting/upstream443/code/replica_kernel.py
new file mode 100644
index 0000000000..b61f1d98f2
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/replica_kernel.py
@@ -0,0 +1,42 @@
+"""PR417 kernel with a checked replication count instead of the eight-replica
+rank congruence. All local response and frame checks are retained verbatim.
+Generalization by chafreaky with OpenAI Codex assistance; Apache-2.0.
+"""
+from stages import Lat, to_masks, occurrences, Framer, mask_of, json
+
+def kernel(c, sel, replicas=32):
+    L = Lat(c['lines']); masks = to_masks(c, L); v = c['v']; n = 2 * v + c['R']; FULL = (1 << v) - 1
+    occ = occurrences(c, masks)
+    gm = {(ph, k): masks[g[0]] for ph in ('D', 'A', 'B', 'C') for k, g in enumerate(c[ph])}
+    first = {}
+    for h in range(2 * v, n):
+        assert masks[c['start'][h]] == 0
+        first[h] = next(x if kind == 'p' else gm[x] for kind, x in occ[h][1:] if (x if kind == 'p' else gm[x]) != 0)
+    resp = {}
+    for f, t, srcs in c['D']:
+        assert masks[f] == 0
+        for s in srcs: resp[s] = resp.get(s, 0) ^ (1 << (t - v))
+    ret = set(c['ret']); pivots = {}; donor_at = {}; tot = 0
+    for E_lines, p, D in sel:
+        E = L.close(mask_of(E_lines)); assert E == mask_of(E_lines) and E != 0
+        assert p not in ret and p not in pivots and p not in donor_at and 2 * v <= p < n
+        x = resp.get(p, 0)
+        for d in D:
+            assert d not in ret and d not in pivots and 2 * v <= d < n
+            assert donor_at.setdefault(d, E) == E, 'donor serves one entrance'
+            x ^= resp.get(d, 0)
+        assert x == 0, ('response relation fails', p)
+        for h in [p] + D: assert E & ~first[h] == 0, ('entrance not inside first frame', h)
+        pivots[p] = E; tot += L.dim(E)
+    assert not set(pivots) & set(donor_at)
+    assert replicas > 0 and replicas % 8 == 0
+    assert replicas * (8*c['R']-tot) % 64 == 0, 'residual coordinates must fill whole banks'
+    out = json.loads(json.dumps(c)); fm = Framer(out)
+    for p, E in pivots.items(): out['start'][p] = fm.fid(E)
+    out['D'] = [[f, t, [s for s in srcs if s not in pivots]] for f, t, srcs in c['D']]
+    byd = {}
+    for E_lines, p, D in sel:
+        for d in D: byd.setdefault((d, mask_of(E_lines)), []).append(p)
+    out['A'] = [[fm.fid(E), d, sorted(ps)] for (d, E), ps in sorted(byd.items())] + out['A']
+    out['C'] = out['C'] + [[fm.fid(FULL), d, sorted(ps)] for (d, E), ps in sorted(byd.items())]
+    return out, len(sel), tot, len(byd)
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/stages.py b/research/e8-rank138-idle-hosting/upstream443/code/stages.py
new file mode 100644
index 0000000000..9ef95d52f4
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/stages.py
@@ -0,0 +1,143 @@
+"""Transcript stages on the E8 bit word (bitE8/1), applied from frozen selections, each bound to the exact input word.
+
+retime  (our #329 descent2 / #287 concave retiming, ported to E8 frames): every selected gate g gets a new frame F with
+        close(LB_g + prev frames of its participants) <= F <= rootspan(AND of their next frames), where LB_g is the
+        x-support of the non-target operands (source-span rule); pinned: D gates (frame 0), y at frame 0 at the scatter,
+        retained totals at FULL at COPY, start and final frames. Checked on the joint retimed configuration.
+kernel  (our #320/#329 shared-donor response kernel; #272/#299/#319 lineage): entry = pivot p, entrance E, donors D with
+        resp(p) = XOR resp(D) over F2, where resp(h) = the targets whose frame-0 completion (D) gates read h; E inside the
+        first frame of p and of every donor. p starts at E and leaves the D gates; each donor climbs to E at the start of
+        A and pays d += (its pivots) at E; after C it pays d += (its pivots) again at FULL (F2: d -= p).
+        Exclusivity: pivots are never donors, a donor serves one entrance. Total entrance rank = 0 mod 8 (integral
+        B_4 width W; the residuals then tile width-72 banks with 9 replicas, checked separately).
+
+usage: stages.py retime|kernel IN.json.gz OUT.json.gz SELECTION.json
+After applying, the full exact replay of e8core (legality, F2 on all columns, source spans) must pass and the output
+must equal the frozen output content hash. (This package uses the kernel stage only: on PR #376's word our retiming
+descent finds no move, before or after the kernel.)
+Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0."""
+import sys, os, json, hashlib
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+from e8core import *
+
+
+def content_sha(c):
+    return hashlib.sha256(json.dumps(c, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+
+
+class Framer:
+    def __init__(self, c):
+        self.fl = c['frames']; self.key = {}; self.v = c['v']
+        for k, fr in enumerate(self.fl): self.key.setdefault(sum(1 << i for i in fr), k)
+    def fid(self, m):
+        if m not in self.key: self.key[m] = len(self.fl); self.fl.append([i for i in range(self.v) if m >> i & 1])
+        return self.key[m]
+
+
+def mask_of(lines): return sum(1 << i for i in lines)
+
+
+def occurrences(c, masks):
+    """per register: list of (kind, ref) with pins ('p', mask) and gates ('g', (phase, k)) in time order"""
+    v = c['v']; n = 2 * v + c['R']; FULL = (1 << v) - 1
+    occ = [[('p', masks[c['start'][r]])] for r in range(n)]
+    for ph in ('D', 'A'):
+        for k, (f, d, s) in enumerate(c[ph]):
+            for x in [d] + s: occ[x].append(('g', (ph, k)))
+    for t in range(v): occ[v + t].append(('p', 0))
+    for q in c['ret']: occ[q].append(('p', FULL))
+    for ph in ('B', 'C'):
+        for k, (f, d, s) in enumerate(c[ph]):
+            for x in [d] + s: occ[x].append(('g', (ph, k)))
+    for r in range(n): occ[r].append(('p', masks[c['final'][r]]))
+    return occ
+
+
+def lower_bounds(c, L):
+    v = c['v']; n = 2 * v + c['R']; sup = [1 << i if i < v else 0 for i in range(n)]; lb = {}
+    for ph in ('D', 'A', 'B', 'C'):
+        for k, (f, d, srcs) in enumerate(c[ph]):
+            need = 0
+            for s in srcs:
+                sup[d] |= sup[s]
+                if s < v or s >= 2 * v: need |= sup[s]
+            if d >= 2 * v: need |= sup[d]
+            lb[(ph, k)] = L.close(need) if need else 0
+    return lb
+
+
+def retime(c, sel):
+    L = Lat(c['lines']); masks = to_masks(c, L); occ = occurrences(c, masks); lb = lower_bounds(c, L)
+    gm = {(ph, k): masks[g[0]] for ph in ('D', 'A', 'B', 'C') for k, g in enumerate(c[ph])}
+    pos = {}
+    for r, o in enumerate(occ):
+        for i, (kind, x) in enumerate(o):
+            if kind == 'g': pos.setdefault(x, []).append((r, i))
+    def fr(r, i):
+        kind, x = occ[r][i]; return x if kind == 'p' else gm[x]
+    seen = set()
+    for ph, k, old_lines, new_lines in sel:
+        g = (ph, k); assert ph != 'D' and g not in seen; seen.add(g)
+        assert gm[g] == L.close(mask_of(old_lines)), ('selection not bound to this word', g)
+        F = L.close(mask_of(new_lines)); assert F == mask_of(new_lines), 'frame given as all its root lines'
+        gm[g] = F
+    for g in seen:  # the joint retimed configuration: every moved gate inside its feasible interval
+        F = gm[g]; lo = lb[g]; hi = (1 << c['v']) - 1
+        for r, i in pos[g]: lo |= fr(r, i - 1); hi &= fr(r, i + 1)
+        assert lo & ~F == 0 and F & ~hi == 0, ('outside the feasible interval', g)
+    out = json.loads(json.dumps(c)); fm = Framer(out)
+    for ph in ('D', 'A', 'B', 'C'):
+        out[ph] = [[fm.fid(gm[(ph, k)]), d, list(s)] for k, (f, d, s) in enumerate(c[ph])]
+    return out
+
+
+def kernel(c, sel):
+    L = Lat(c['lines']); masks = to_masks(c, L); v = c['v']; n = 2 * v + c['R']; FULL = (1 << v) - 1
+    occ = occurrences(c, masks)
+    gm = {(ph, k): masks[g[0]] for ph in ('D', 'A', 'B', 'C') for k, g in enumerate(c[ph])}
+    first = {}
+    for h in range(2 * v, n):
+        assert masks[c['start'][h]] == 0
+        first[h] = next(x if kind == 'p' else gm[x] for kind, x in occ[h][1:] if (x if kind == 'p' else gm[x]) != 0)
+    resp = {}
+    for f, t, srcs in c['D']:
+        assert masks[f] == 0
+        for s in srcs: resp[s] = resp.get(s, 0) ^ (1 << (t - v))
+    ret = set(c['ret']); pivots = {}; donor_at = {}; tot = 0
+    for E_lines, p, D in sel:
+        E = L.close(mask_of(E_lines)); assert E == mask_of(E_lines) and E != 0
+        assert p not in ret and p not in pivots and p not in donor_at and 2 * v <= p < n
+        x = resp.get(p, 0)
+        for d in D:
+            assert d not in ret and d not in pivots and 2 * v <= d < n
+            assert donor_at.setdefault(d, E) == E, 'donor serves one entrance'
+            x ^= resp.get(d, 0)
+        assert x == 0, ('response relation fails', p)
+        for h in [p] + D: assert E & ~first[h] == 0, ('entrance not inside first frame', h)
+        pivots[p] = E; tot += L.dim(E)
+    assert not set(pivots) & set(donor_at)
+    assert tot % 8 == 0, 'total entrance rank 0 mod 8'
+    out = json.loads(json.dumps(c)); fm = Framer(out)
+    for p, E in pivots.items(): out['start'][p] = fm.fid(E)
+    out['D'] = [[f, t, [s for s in srcs if s not in pivots]] for f, t, srcs in c['D']]
+    byd = {}
+    for E_lines, p, D in sel:
+        for d in D: byd.setdefault((d, mask_of(E_lines)), []).append(p)
+    out['A'] = [[fm.fid(E), d, sorted(ps)] for (d, E), ps in sorted(byd.items())] + out['A']
+    out['C'] = out['C'] + [[fm.fid(FULL), d, sorted(ps)] for (d, E), ps in sorted(byd.items())]
+    return out, len(sel), tot, len(byd)
+
+
+if __name__ == '__main__':
+    st, inp, outp, selp = sys.argv[1:5]
+    c = load_word(inp); sel = json.load(open(selp))
+    assert sel['input_sha256'] == content_sha(c), 'selection bound to a different input word'
+    if st == 'retime':
+        w = retime(c, sel['gates']); info = '%d gates retimed' % len(sel['gates'])
+    else:
+        w, ne, tot, nd = kernel(c, sel['entries']); info = '%d entries, total entrance rank %d, %d donor slots' % (ne, tot, nd)
+    r = replay(w, span_mode='z'); assert not r['viol'], r['viol'][:5]
+    assert content_sha(w) == sel['output_sha256'], 'output differs from the frozen stage output'
+    save_word(w, outp)
+    print('   stage %s: %s | exact replay PASS (legality, F2 on %d columns, source spans) | local histogram %s | output sha %s'
+          % (st, info, r['n'], dict(sorted(r['H'].items())), sel['output_sha256'][:16]))
diff --git a/research/e8-rank138-idle-hosting/upstream443/code/tile_m.py b/research/e8-rank138-idle-hosting/upstream443/code/tile_m.py
new file mode 100644
index 0000000000..cd5fd9b539
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/code/tile_m.py
@@ -0,0 +1,93 @@
+"""Residual census (8 - sigma per helper) and an exact zero-padding bank tiling of width m = (2K+1)h with T replicas:
+tile() and economy_tile() verbatim from our PR #329 bank_template.py (via code/tile.py of our dtst3 package).
+usage: tile_m.py WORD.json.gz M [replicas]  (replicas default: the least T with T x residual sum = 0 mod M that tiles)"""
+import sys,os,collections
+from collections import Counter
+sys.path.insert(0,os.path.dirname(os.path.abspath(__file__)))
+from e8core import *
+def economy_tile(blocks, m):
+    """Exact zero-padding tiling used when the filler search of tile() runs out of filler blocks (the kernel pivots
+    and early restorations of the stage stack add many residual widths that do not divide m; the PR #299 analogue at
+    p = 12 was the (r^4, 24, 4^(24-r)) re-tiling). The fillers are the two most numerous widths dividing m (here the
+    full helper width h and the rank-4 entrance residual). Each other width w, in decreasing order, gets the bank
+    w^a F^c f^b (w*a + F*c + f*b = m) that spends the fewest narrow fillers f per w block (then the largest a), plus
+    at most one bank w^r F^c' f^b' for the remainder r = n mod a. The leftover fillers fill pure banks F^(m/F),
+    f^(m/f) and y residue banks F^j f^k. Every bank sums to m and every block is used exactly once (no padding)."""
+    from fractions import Fraction
+    blocks = {w: n for w, n in blocks.items() if n}
+    div = sorted((w for w in blocks if m % w == 0), key=lambda w: (-blocks[w], w))
+    assert len(div) >= 2, ('economy tiling needs two filler widths', blocks)
+    F, f = sorted(div[:2], reverse=True)
+
+    def fill(rest):
+        """(c, b) with F*c + f*b = rest, c maximal (fewest narrow fillers); None if impossible."""
+        return next(((c, (rest - F*c)//f) for c in range(rest//F, -1, -1) if (rest - F*c) % f == 0), None)
+
+    left = {F: blocks[F], f: blocks[f]}; out = []
+    for w in sorted((x for x in blocks if x not in (F, f)), reverse=True):
+        n = blocks[w]
+        opts = [(Fraction(cb[1], a), -a, a, cb) for a in range(m//w, 0, -1) for cb in [fill(m - w*a)] if cb]
+        assert opts, ('no bank for width', w)
+        _, _, a, (c, b) = min(opts); q, r = divmod(n, a)
+        if q: out.append(((w,)*a + (F,)*c + (f,)*b, q)); left[F] -= q*c; left[f] -= q*b
+        if r:
+            cb = fill(m - w*r); assert cb, ('no remainder bank', w, r)
+            out.append(((w,)*r + (F,)*cb[0] + (f,)*cb[1], 1)); left[F] -= cb[0]; left[f] -= cb[1]
+    assert left[F] >= 0 and left[f] >= 0, ('fillers exhausted', left)
+    pF, pf = m//F, m//f
+    for y in range((pF*pf) + 1):
+        for j in range(1 if y else 0, pF if y else 1):
+            if (m - F*j) % f: continue
+            k = (m - F*j)//f; aF, af = left[F] - y*j, left[f] - y*k
+            if aF >= 0 and af >= 0 and aF % pF == 0 and af % pf == 0:
+                out += ([((F,)*j + (f,)*k, y)] if y else []) + ([((F,)*pF, aF//pF)] if aF else []) + ([((f,)*pf, af//pf)] if af else [])
+                return out
+    raise AssertionError(('no exact zero-padding tiling', blocks, m))
+
+
+def tile(blocks, m):
+    """Exact tiling of {width: number of blocks} into banks of total width m, as ((widths, banks), ...).
+
+    A width dividing m fills pure banks. A width w not dividing m is mixed with a filler width f dividing m:
+    banks w^a f^b with a maximal (w*a + f*b = m), then at most one bank w^r f^t for the remainder r. Fillers
+    are tried in a fixed order (most blocks first) with backtracking until every pure width also divides out.
+    Fails (AssertionError) unless every block is used and every bank is full; there is no padding."""
+    blocks = {w: n for w, n in blocks.items() if n}
+    assert all(0 < w <= m for w in blocks)
+    mixed = sorted(x for x in blocks if m % x)
+
+    def search(i, left, out):
+        if i == len(mixed):
+            if any(left[w] % (m // w) for w in left): return None
+            return out + [(tuple([w]*(m // w)), left[w]//(m // w)) for w in sorted(left) if left[w]]
+        w = mixed[i]; n = blocks[w]
+        for f in sorted(left, key=lambda x: (-left[x], x)):
+            a = next((a for a in range(m // w, 0, -1) if (m - w*a) % f == 0), None)
+            if a is None: continue
+            b = (m - w*a)//f; q, r = divmod(n, a)
+            if r and (m - w*r) % f: continue
+            t = (m - w*r)//f if r else 0
+            if q*b + t > left[f]: continue
+            rest = dict(left); rest[f] -= q*b + t
+            found = search(i + 1, rest, out + ([(tuple([w]*a + [f]*b), q)] if q else []) + ([(tuple([w]*r + [f]*t), 1)] if r else []))
+            if found is not None: return found
+        return None
+    out = search(0, {w: n for w, n in blocks.items() if not m % w}, [])
+    if out is None: out = economy_tile(blocks, m)
+    assert all(sum(widths) == m and count > 0 for widths, count in out)
+    used = Counter()
+    for widths, count in out:
+        for x in widths: used[x] += count
+    assert used == Counter(blocks), 'every block used exactly once'
+    return tuple(out)
+if __name__ == '__main__':
+    c = load_word(sys.argv[1]); m = int(sys.argv[2])
+    L = Lat(c['lines']); M = to_masks(c, L); v = c['v']; n = 2 * v + c['R']
+    res = Counter(8 - L.dim(M[c['start'][r]]) for r in range(2 * v, n)); tot = sum(k * x for k, x in res.items())
+    reps = [int(sys.argv[3])] if len(sys.argv) > 3 else [t for t in range(1, 200) if t * tot % m == 0]
+    for T in reps:
+        try: pat = tile({r: T * k for r, k in res.items() if r > 0}, m); break
+        except AssertionError: pat = None
+    assert pat, 'no tiling'
+    print('   residual census', dict(sorted(res.items())), 'sum', tot)
+    print('   PASS exact width-%d tiling with %d replicas: %d banks' % (m, T, sum(k for _, k in pat)), pat)
diff --git a/research/e8-rank138-idle-hosting/upstream443/data/post-retiming.json b/research/e8-rank138-idle-hosting/upstream443/data/post-retiming.json
new file mode 100644
index 0000000000..f3306fa80d
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/data/post-retiming.json
@@ -0,0 +1,9998 @@
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diff --git a/research/e8-rank138-idle-hosting/upstream443/data/selection.json b/research/e8-rank138-idle-hosting/upstream443/data/selection.json
new file mode 100644
index 0000000000..ef068005b1
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/data/selection.json
@@ -0,0 +1,1291 @@
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diff --git a/research/e8-rank138-idle-hosting/upstream443/data/upstream441/pair-retime-selection.json b/research/e8-rank138-idle-hosting/upstream443/data/upstream441/pair-retime-selection.json
new file mode 100644
index 0000000000..1b7b7f33ff
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/data/upstream441/pair-retime-selection.json
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diff --git a/research/e8-rank138-idle-hosting/upstream443/data/upstream441/window-retime-selection.json b/research/e8-rank138-idle-hosting/upstream443/data/upstream441/window-retime-selection.json
new file mode 100644
index 0000000000..d816fc0da6
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/data/upstream441/window-retime-selection.json
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diff --git a/research/e8-rank138-idle-hosting/upstream443/data/word.json.gz b/research/e8-rank138-idle-hosting/upstream443/data/word.json.gz
new file mode 100644
index 0000000000..85390b07e4
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diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/EXPECTED.json b/research/e8-rank138-idle-hosting/upstream443/parent436/EXPECTED.json
new file mode 100644
index 0000000000..7f5f7f3f9d
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/EXPECTED.json
@@ -0,0 +1,45 @@
+{
+ "note": "Exact values that verify.sh must reproduce. Rationals are on the 10^-18 grid of the hub's pricing; each c is the largest grid point admitted by both PR #315 moment engines (with the 1e-16 fallback), and the next grid point is rejected.",
+ "word": {
+  "R": 740,
+  "content_sha256": "d6ec8811541d6ab59a3bbbaaa15bccc8918b3b43b23d9f593198cfe90826fd20",
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+  }
+ },
+ "b4": {
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+  "controls": {
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+   "pr376": "255384852701747/250000000000000000",
+   "pr417": "1044063934627389/1000000000000000000"
+  },
+  "kappa": {
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+   "pr410": "508781072593909/500000000000000000",
+   "pr409": "508625250464133/500000000000000000",
+   "pr407": "7941615395831/7812500000000000"
+  }
+ },
+ "b3": {
+  "c": "1058066102700151/1000000000000000000",
+  "controls": {
+   "pr376": "8128527708459/8000000000000000",
+   "pr426": "104575879789097/100000000000000000"
+  }
+ }
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/LICENSE b/research/e8-rank138-idle-hosting/upstream443/parent436/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
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+      direction or management of such entity, whether by contract or
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+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
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+
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+      (c) You must retain, in the Source form of any Derivative Works
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+          of the NOTICE file are for informational purposes only and
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+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
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+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
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+   7. Disclaimer of Warranty. Unless required by applicable law or
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+      risks associated with Your exercise of permissions under this License.
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+      whether in tort (including negligence), contract, or otherwise,
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diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/MANIFEST.sha256 b/research/e8-rank138-idle-hosting/upstream443/parent436/MANIFEST.sha256
new file mode 100644
index 0000000000..399beb5da4
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/MANIFEST.sha256
@@ -0,0 +1,87 @@
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+d737a3b77de97bdf67d2a140465be5b8886af6aa57516f78ad8f2839f3dae8cc  README.md
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+c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c  code/tail/engines/outer.py
+f8daa4982d865748fa9a3095b2cf4290f34e2c085d6d35673fd7171cab95623c  data/bit/bitE8-r740.json.gz
+1fb726ea3818fe0837cceb0dd22a71a0814f064e5e781628104610d6468e0e55  data/bit/bitE8-r865.json.gz
+e7bb324150a5342076c9a268f69b83c65f817a7cfc1d14fda9558a9f7e486f0b  data/bit/reuse-ledger.json
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+2815ca568c88edde758c31e756d0d07aa08233243f365bc111383d7f0c1c757a  data/complex-b-nine.json
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+a83d4880579fb1f8cffb701d1d685c157b7fa14ef9d6642e42ff1e4f5a1b8c5c  data/controls/pr376/frame-selection.json
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+6043a7486790ac8ca04dc67ddf5b57076e7c880b66eb456127c6cd933c77764a  data/controls/pr386/COMBINED.json
+55af2a11552c04f5a87268bc2d1798246297874e9e87b50e49773e91cc495c2d  data/controls/pr386/GLOBAL.json
+acc2b138ce16be1ff12570d3ec1634fe28cccaf259de797be0f62628fb37cccb  data/controls/pr417-bitE8-nine-kernel.json.gz
+46ea33ad1979cd14a2b686e8742792739312a07ab72945517c3809b647b31c42  data/controls/pr425/FINAL.json
+bd3b84244528767b85d8d7fe423b155630b5c659e21e51563674b1dcb6305ad7  data/controls/pr426-bit-candidate.json.gz
+2b77c882ac524adbbacc9775ee172c854ecd4027e36db59ed15a7d1b6b9e1ce5  data/controls/pr431/VALIDATION-LOCAL.json
+f71580f22193726fb582eae604807ff70a7302265e001d9484a718e63bbe14c4  data/controls/pr433/CERTIFICATE.json
+871fc75ce6fea2638f68553bcfe771d09297e987d59c123338227e29415851d1  data/params/params-r740.json
+d840952ed60b4b460da83b04c4c8be3622b9bef04b62961c0d496c445f8b84d1  discovery/README.md
+57de04a8ea7e2df8b783e02c454bb102edab48206db0a41a1f28d50e7f164441  discovery/search_params.py
+420094be2af295eed03a983dd66debbbe9cfb78d8252859f4498a615a0074b99  portable-include/bits/stdc++.h
+b9f87c1ec529679c19b8421a7a69b377b54b89949cfc5e1b1ed8c134bfab8917  requirements.txt
+19bf483b109163b0ccc941f459e70c2e37d20c9c04e69e7c8eb98f329577b26c  verify.sh
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/NOTICE.md b/research/e8-rank138-idle-hosting/upstream443/parent436/NOTICE.md
new file mode 100644
index 0000000000..2c01026b8b
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/NOTICE.md
@@ -0,0 +1,51 @@
+# Notice
+
+Apache-2.0 (`LICENSE`). Prepared by eumemic with substantial Anthropic Claude assistance.
+
+## New in this package
+
+- `code/reuse/`: the elimination-reuse stage (`reuse.py`), the frame retiming (`retime.py`), their integer cost tables (`ecost.py`), the regeneration driver (`regen.py`) and the elimination-reuse negative controls (`controls.py`).
+- `data/params/params-r740.json`: our parameters for PR #370's producer. `discovery/` holds the search that nominated them.
+- `data/bit/bitE8-r740.json.gz` (the word) and `data/bit/reuse-ledger.json` (its inserted elimination gates).
+- `code/nine/global_word_g.py`, `audit_g.py`, `certify_g.py`: generalisations of PR #386's `global_word.py`, `audit.py` and `certify.py` to any bitE8/1 word whose helpers start at frame 0 and end at the full frame. `regress386.py` checks them against PR #386's own receipts. `cited.py` binds the cited complex savings to the PRs' receipts. `compose433.py` ports PR #433's bit pricing, finite invoice and tail.
+- `code/b4/kappa_b4.py`, `code/provenance.py`, `verify.sh`, `EXPECTED.json`, `data/complex-b-*.json`, `.github/workflows/e8-bit-elimination-reuse.yml`.
+
+## Vendored, byte-identical (git blob ids in `SOURCE-pr*.json`, checked by `code/provenance.py`)
+
+- **PR #370 (Dylan Crow / utcorvusvolat-dotcom, with Anthropic Claude assistance), commit b7fe9cd:**
+  - the producer `code/bit/producer/`;
+  - the independent checker and its controls `code/bit/independent/`;
+  - the record exporter and the record-level controls;
+  - PR #266's official cohort checkers as generalised there (`legality_h.cpp`, `columns_h.cpp`, NCOPY);
+  - `gram_frames.py`, `stage_cohort.py`;
+  - PR #315's engines (`code/pricing/`, DreamingOfClouds);
+  - nlohmann/json (`json.hpp`, MIT licence in its header);
+  - the E8 bit word `data/bit/bitE8-r865.json.gz`;
+  - `LICENSE`.
+- **PR #381 (DaysSky, assisted with Claude), commit 00765b2:** the B_K checkers `columns_k.cpp`, `geometry_k.py`, `tile_k.py`, `certify_bit_k.py`, `finite_k.py`, `cost.py`, `receipts_k.py`, and PR #363's `bridged.py` (DaysSky).
+- **PR #386 (Zhihao Chen / jacklightChen, with OpenAI Codex assistance), commit dd11cf8:**
+  - `geometry.py` (compressed nine-stage bit geometry, unchanged);
+  - the portable `bits/stdc++.h`;
+  - the validation receipts `GLOBAL.json`, `AUDIT.json` and `COMBINED.json`, used only as regression references.
+- **PR #417 (Chafik Boukhalfa / chafreaky, with Anthropic Claude assistance), commit 3f681fb:**
+  - `bootstrap.py` (their reimplementation of rohanarun's PR #392 refined pricing tail), `e8core.py` and its copies of PR #315's engines;
+  - `apply376.py`;
+  - the final kernel word, used as a B_4 control.
+- **PR #376 (applecrusher, with OpenAI Codex assistance), commit 92328da:** `frame-selection.json`, `reuse-selection.json` and `LICENSE-pr376`, as vendored in PR #417.
+- **PR #426 (ai-nanachi, with OpenAI Codex assistance), commit 88d5525:** the R767 bit word, used only as a priced comparison and B_3 control, and `LICENSE-pr426`.
+- **PR #425 (Zhihao Chen / jacklightChen, with OpenAI Codex assistance), commit e11ccea:** the validation receipt `FINAL.json`, which states the cited b and κ.
+- **PR #431 (Rohan Arun / rohanarun, with OpenAI Codex assistance; draft), commit db4f465:** the validation receipt `VALIDATION-LOCAL.json`, which states the cited b and κ.
+- **PR #433 (icekylinx, with OpenAI Codex assistance), commit 6d92445:** `CERTIFICATE.json`, which states the cited complex b, the R758 bit c and κ. `code/nine/compose433.py` is our port of #433's `code/bit_price.py` and `code/combined.py` arithmetic. No #433 code is vendored or run.
+
+## Cited, not rebuilt
+
+Complex coarse savings in `data/complex-b-nine.json` and `data/complex-b-b4.json`, each with its PR, commit and receipt (git blob):
+
+- compressed nine-stage layout:
+  - PR #433 (icekylinx; `data/complex-b-433.json`, bound to its certificate by `compose433.py`);
+  - PR #386 (#377's component), PR #425 (jacklightChen) and PR #431 (rohanarun, draft), bound to their receipts by `code/nine/cited.py`.
+- B_4: PR #424, #407 (chafreaky), #410 (eumemic) and #409 (rohanarun).
+
+No complex construction is rebuilt here.
+
+The E8 label family follows Jacob Sussman's introduction of E8 for the complex supplier.
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/README.md b/research/e8-rank138-idle-hosting/upstream443/parent436/README.md
new file mode 100644
index 0000000000..5ddb576f02
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/README.md
@@ -0,0 +1,182 @@
+κ = 1128983115440183/10¹⁸ (conditional; bit-bound) with PR #433's complex supplier
+
+# An E8 bit word with 740 helpers: dead helper slots reused through F₂ relations
+
+This package is a bit-side supplier: an E8 bit word in PR #370's format (h = 8, v = 120, 9 retained totals) with **R = 740 helpers**. For comparison, #370 has 865, #376 has 822, #426 has 767 and #433 has 758. In the compressed nine-stage layout of PR #386 (m = 64), which #425, #431 and #433 use, its coarse saving is
+
+**c = 282564789736676592463/(2.5·10²³) ≈ 1.130259158946706·10⁻³**
+
+on PR #433's 10⁻²⁴ grid. On #386's 10⁻¹⁸ grid it is 565129579473353/(5·10¹⁷).
+
+PR #433 (icekylinx) pairs its split-centre complex supplier, b = 1183986549206329/10¹⁸ ≈ 1.183987·10⁻³, with a 758-helper bit word, c = 1.122122700265139·10⁻³. #433's bit side binds, at κ = 1.120864952258278·10⁻³. With this word in place of R758, through #433's own bit engine, finite invoice and six-level tail:
+
+**κ = 1128983115440183/10¹⁸ ≈ 1.128983115440183·10⁻³**, bit-bound, **+0.7243 % over #433**.
+
+The bit c is +0.7251 % over #433's R758. As controls, the same code reproduces #433's bit c from #433's stated R758 profile, and #433's κ from #433's (c, b), exactly. The complex side still has 4.75 % of headroom over this c.
+
+## Bit coarse savings
+
+| bit word | R | compressed nine-stage (#386 layout, m = 64) | B₄ unsplit (#381 layout, m = 72) | B₃ unsplit (m = 56) |
+| --- | ---: | ---: | ---: | ---: |
+| PR #370 (`bitE8-r865`) | 865 | **1057833103534317/10¹⁸** (= #386, #425, #431) | **249162322049641/(2.5·10¹⁷)** (= #381) | 9.912261·10⁻⁴ |
+| PR #376 (R822) | 822 | 1084538480613107/10¹⁸ | **255384852701747/(2.5·10¹⁷)** (= #390 … #424) | **8128527708459/(8·10¹⁵)** (= #376, #389 baseline) |
+| PR #417 (R822 + shared-donor kernel) | 822 | — (entrance residuals do not fill #386's rank-8 slots) | **1044063934627389/10¹⁸** (= #417) | 1.037508·10⁻³ |
+| PR #426 (R767, clean-reset reuse) | 767 | 1116714040089377/10¹⁸ | 1.051689·10⁻³ | **104575879789097/10¹⁷** (= #426) |
+| PR #433 (R758: #426 + source-basis totals) | 758 | **561061350132569610283/(5·10²³)** (= #433, 10⁻²⁴ grid) | — | — |
+| **this word** | **740** | **282564789736676592463/(2.5·10²³) ≈ 1.130259·10⁻³** | **1064525457834209/10¹⁸ ≈ 1.064525·10⁻³** | **1058066102700151/10¹⁸ ≈ 1.058066·10⁻³** |
+
+Compressed nine-stage values are on #386's 10⁻¹⁸ grid, except #433's and this word's, which are on #433's 10⁻²⁴ grid. On the 10⁻¹⁸ grid this word is 565129579473353/(5·10¹⁷).
+
+Bold entries in the control rows are the values the cited PRs publish. `verify.sh` reproduces each exactly with the same code that prices this word. Most come from the PR's own word. #433's R758 value comes from the R758 profile stated in #433, because the package does not ship that word. The other entries are computed here and are not published by those PRs.
+
+This word compared with the best published bit c in each layout:
+
+| layout | best published bit c | this word |
+| --- | --- | ---: |
+| compressed nine-stage | #433's R758 | +0.725 % |
+| B₄ | #417 | +1.960 % |
+| B₃ | #426 | +1.177 % |
+
+Against #426's R767 word priced in the same layouts, this word is +1.213 % (compressed nine-stage) and +1.221 % (B₄). The five-stage saving (PR #370's independent checker) is 9.63227·10⁻⁴.
+
+## κ with cited complex suppliers
+
+| complex supplier (cited, not rebuilt) | layout and tail | b | κ with this word | κ as published |
+| --- | --- | ---: | ---: | ---: |
+| **PR #433 (icekylinx)** | compressed nine-stage; #433's tail | 1183986549206329/10¹⁸ | **1128983115440183/10¹⁸** (bit-bound) | 560432476129139/(5·10¹⁷) (bit-bound, R758) |
+| PR #431 (rohanarun, draft) | compressed nine-stage; #386's tail | 529046848168159/(5·10¹⁷) | 1056975315151441/10¹⁸ (complex-bound) | 1056715272872389/10¹⁸ at db4f465 (bit-bound, #370 word); 1056975315151441/10¹⁸ at 71c5988 (with #376's retimed bit word) |
+| PR #425 (jacklightChen) | compressed nine-stage; #386's tail | 52455248902029/(5·10¹⁶) | 524002754014103/(5·10¹⁷) | same |
+| PR #386 (#377's component) | compressed nine-stage; #386's tail | 999240641319551/10¹⁸ | 998243154231047/10¹⁸ | same |
+| PR #424 (chafreaky) | B₄; #392's refined tail | 254887067002137341481/(2.5·10²³) | 1018509848057013/10¹⁸ | same |
+| PR #410, #409, #407 | B₄; #392's refined tail | as cited by #417 | as published | same |
+
+All κ values are on the 10⁻¹⁸ grid and satisfy PR #315's 47 strict outer inequalities. The next grid point is rejected. The three tails:
+
+- **#433's tail** (`compose433.py`, ported from #433's `bit_price.py` and `combined.py`):
+  - c is the 10⁻²⁴-grid lower endpoint of PR #315's `certify`, with the 10⁻¹⁶ bad-branch allowance, and is checked by the second engine;
+  - η = β = 10⁻¹⁸, seed min(c, (1 − β)b) − 10⁻²⁴, six bootstrap levels;
+  - zero η, zero β and unit β are rejected as well;
+  - the finite invoice charges the prefix at the next multiple of 64 bits: here 123 bits, charged 128.
+- **#386's tail** (#386, #425, #431): three bootstrap steps, η = 10⁻¹², β = 10⁻⁹. The seed is strictly below (1 − β) times both suppliers (#431's policy).
+- **B₄:** #392's refined tail, as reimplemented in PR #417's `bootstrap.refine`.
+
+With #431's complex supplier the complex side binds. Every bit word above #431's b gives that κ, including #376's and #426's words in this layout. #431's later head uses #376's retimed word. The PR #370 word reproduces #431's κ at db4f465, and #425's and #386's κ, exactly.
+
+## The word
+
+1. **PR #370's producer, unchanged, with new parameters.** `data/params/params-r740.json` differs from #370's `params-r865.json` in 67 of 520 entries. It was found by a local search with the reuse pass in the objective (`discovery/`). The producer gives a word with R = 863.
+2. **Elimination reuse** (`code/reuse/reuse.py`).
+   - A helper is dead after its last gate in phases A and B. It still holds a leftover x-content: an F₂ sum of source lines, at its last frame.
+   - Before a later helper is born at frame F, the pass looks for an F₂ relation content(r₀) = Σ_{q∈S} content(q) among dead slots whose frames lie inside F. It emits r₀ += S at the join G of their frames (G ⊆ F). r₀ then holds no x-content and hosts the new helper.
+   - The relation is found by Gaussian elimination over F₂. The cheapest relation with |S| ≤ 3 replaces it when one exists, scored by the extra climbing of r₀ and of the eliminators.
+   - The 9 retained totals take dead slots too. The slot's leftover x-lines are read from the sources at the full frame.
+   - The dirt compensation D and the cleanup C are rebuilt as in #370's `fullword.py`.
+   - **114 helper slots and 9 totals are reused: R 863 → 740.**
+   - **Prior and concurrent work.**
+     - #376 reused helper lifetimes by aliasing: 43 reuses.
+     - #426 (ai-nanachi, posted first) uses the same mechanism as this pass. It zeroes a retired helper's x-content with exact two- or three-parent "clean resets" before reusing the slot, rebuilds D and C, and keeps the totals protected. It makes 55 resets on #376's R822 word (R767).
+     - This pass was developed independently. It differs in four ways: it searches every dead slot inside the birth frame by elimination, uses cost-scored relations with up to three eliminators, puts the totals on dead slots as well, and starts from a re-parameterised #370 producer word (R863).
+   - **#433's source-basis trick does not apply here.** The trick computes the nine retained sums in source rows, which removes #426's nine dedicated total helpers (R767 → 758). In this word the totals already sit on slots of earlier helpers, and no helper is born after them, so the trick would remove no register.
+3. **Retiming** (`code/reuse/retime.py`, the idea of #389). Each gate moves to its lowest or highest legal frame when that lowers Σ r ln(64/r) over its registers' adjacent steps: 37 gate moves.
+
+All search choices use integer costs computed with Python's correctly rounded `decimal` logarithm, so the word is the same on every platform. One invocation's local histogram is {1: 2355, 2: 884, 3: 489, 4: 425, 5: 62, 8: 9}: 4,224 blocks, of which 9 are copies. Gates D/A/B/C: 120/1873/472/1873; 944 frames.
+
+## Verify
+
+    BOOST_INCLUDE=/usr/include bash research/e8-bit-elimination-reuse/verify.sh /fresh/output/dir
+    bash research/e8-bit-elimination-reuse/verify.sh --quick /fresh/output/dir
+
+Requirements: Python 3.11+ with numpy, mpmath and sympy (`requirements.txt`); a C++17 compiler (`CXX`); Boost headers (`BOOST_INCLUDE`). `--quick` skips the regressions on #370's word, the comparison words in the compressed nine-stage layout, and the B₃ rows. The workflow `.github/workflows/e8-bit-elimination-reuse.yml` runs both modes on Python 3.12 and 3.14.
+
+0. **Manifest and provenance.** `MANIFEST.sha256`. The git blob id of all 52 vendored files is checked against `SOURCE-pr*.json`: #370, #376, #381, #386, #417, #425, #426, #431 and #433.
+1. **The word from pinned inputs.**
+   - Control: #370's producer regenerates #370's word from its own parameters.
+   - `regen.py` rebuilds this word from our parameters (producer → reuse → retiming). It must equal the shipped word, and the reuse ledger must match.
+   - #376's R822 word is rebuilt from #370's word and #376's two witnesses with #417's `apply376.py`, as a control word.
+2. **One invocation, exact.**
+   - #370's independent checker: the 120 E8 root lines; nested frames; common gate frames; F₂ on all 980 columns, dirty helpers included; Gram determinants on 935 used frames (prime 2 only); the five-stage root.
+   - #370's 6 word-level controls, rejected.
+   - 6 elimination-reuse controls, rejected by the same checker: drop an elimination gate, drop one eliminator, drop one x-line read of a total's undo, lower an elimination below an eliminator's frame, remove all 123 elimination gates, move a total's undo gate to frame 0.
+3. **Official checkers.**
+   - PR #266's cohort legality, as generalised in #370 (NCOPY = 9): 19,527 records, 15,294 common-frame ADDs.
+   - Five-stage formal columns: 1,220 columns, prefix payload 64 bits < 104.
+   - #381's B₄ formal columns: all 1,700 physical columns over F₂ through 9 invocations, 18 twin bridges and the terminal exchange. All 18 omitted-bridge controls are rejected.
+   - #370's 6 record-level controls are rejected, including the unmodified copy count NCOPY = 8.
+4. **Nondegeneracy.** `gram_frames.py`: all 944 frames positive definite under the E8 form. Prime witnesses are valid; the only prime is 2.
+5. **Retained totals.** 9 COPY/ERASE episodes at the full frame (rank 8).
+6. **Compressed nine-stage layout (#386).**
+   - #386's `geometry.py`, unchanged: 120 port routes, 1,080 route checks, at most 77 route factors with denominators {1, 2, 4}, and the bank slots. It is bound to this word by the equality of the 120 label vectors.
+   - `global_word_g.py`, our generalisation of #386's `global_word.py`:
+     - both reflected local streams replay all 980 columns;
+     - the scalar replay over 9 stages covers 7,620 independent columns;
+     - 72 local invocations, 1,405,944 emitted events and 53,280 bank assignments (6,660 banks of 8 whole rank-8 slots, no padding);
+     - live stock 64v + 9R = 14,340;
+     - deficit 2,496 = 8(8v − 9·72);
+     - max child 42 of 64, so two-level halving;
+     - prefix bound 2¹⁸·776⁵·17,724⁴ of 123 bits, under #386's 192-bit allowance.
+   - `audit_g.py`: 944 exact rational projectors and 3,263 nested pairs. #386's 8 template mutations are rejected.
+   - `cited.py`: each cited complex b, and that PR's own κ, must equal the fields of the PR's receipt. The receipts are #386's `COMBINED.json`, #425's `FINAL.json` and #431's `VALIDATION-LOCAL.json`, vendored and pinned by blob id.
+   - `certify_g.py`: both PR #315 engines with the 10⁻¹⁶ fallback admit c and reject c + 10⁻¹⁸. The finite coefficient has 123 bits; the two-level coefficient has 282 bits, below 2⁵¹²; the row coefficient is 18,355 < 20,161. κ is then computed with each cited complex b.
+   - `compose433.py`: PR #433's bit engine, finite invoice and six-level tail, ported from #433's `bit_price.py` and `combined.py`.
+     - Controls: #433's stated R758 profile prices to #433's bit c, and #433's (c, b) gives #433's κ. Both are bound to #433's `CERTIFICATE.json`, which is vendored and pinned.
+     - Then this word's c, invoice and κ with #433's complex b: next grid point, zero η, zero β and unit β are rejected.
+   - **Regression:** on #370's word the same three scripts reproduce #386's `GLOBAL.json`, `AUDIT.json` and the bit, finite and κ fields of `COMBINED.json`, field for field. They also reproduce #425's and #431's κ.
+   - **Comparison:** the same chain prices #376's word (rebuilt in step 1) and #426's word in this layout. Each gives the same κ with #431, since each has c > b.
+7. **B₄ (#381's layout, unsplit).**
+   - #381's `geometry_k.py` on this word: PR234 routes on 9 blocks, idle gap ranks equal to `bridged.py`, the 9-window entrance completion, max child 50 (halving degree 2).
+   - `tile_k.py`: 740 banks of 9 rank-8 residuals with T = 9 replicas.
+   - `certify_bit_k.py` prices this word and the #370, #376 and #417 controls.
+   - `receipts_k.py` and `finite_k.py`: the finite bill at m = 72. The coefficient has 48 bits, below 2⁸⁰; the payload prefix is 64 bits; the internal row coefficient is 10,370.
+   - `kappa_b4.py` computes κ with the cited B₄ suppliers.
+   - **Regression:** `columns_k` at K = 2 gives the five-stage `columns_h` receipt.
+8. **B₃ (informational).** Formal columns at K = 3 (1,460 columns), banks with T = 7, and prices with the #376 and #426 controls.
+9. **Summary** against `EXPECTED.json`.
+
+Locally, the C++ checkers were built against a 128-bit, overflow-checked stand-in for `boost::multiprecision::cpp_int`, because the preparing machine has no Boost. CI compiles them against libboost-dev.
+
+## Retained assumptions and open obligations
+
+- **Everything PR #370 admits:**
+  - 9 retained totals at h = 8;
+  - PR234's banks for a non-paired-cube family;
+  - the inherited all-size weighted bit compiler, prime/tape/precision and analytic interfaces.
+- **The compressed nine-stage layout is PR #386's:**
+  - its window, bank and route arguments (PROOF.txt there);
+  - two-level halving (max child 42 of 64);
+  - its finite charges.
+  Our scripts check this word against those arguments' finite conditions; they add no new argument.
+- **B₄ is PR #381's:** halving degree two on the bit side (#375, #381); no Lean proof of B_K.
+- **The complex suppliers are cited by pinned reference and not rebuilt:**
+  - the headline κ depends on #433's split-centre complex supplier (its PROOF.md), which builds on #425's written scalar-interface extension;
+  - #433's complex b, its six-level tail (#392's refined form, η = β = 10⁻¹⁸) and all its obligations remain #433's.
+  - #431 (a draft) and the other cited suppliers are listed only for comparison.
+- **#433's bit finite charge is adopted for the headline:** the prefix is charged at the next multiple of 64 bits (here 123 bits, charged 128, inside #386's 192-bit allowance), and the two-level coefficient is below 2⁵¹² (here 282 bits).
+- This is a conditional finite construction, not a formal verification of the multiplication theorem. No Lean proof is claimed.
+- **Not measured:** stacking #417's shared-donor kernel on this word. It applies to B_K banks. It does not apply to #386's whole-block banks, whose slots need rank-8 residuals.
+
+## Credits
+
+- **Dylan Crow (utcorvusvolat-dotcom), PR #370:** the E8 bit word format, the producer whose output we reuse, the independent checker and the generalised official checkers.
+- **applecrusher, PR #376:** helper-lifetime reuse, which the elimination reuse generalises.
+- **ai-nanachi:**
+  - PR #389: the frame-retiming idea;
+  - PR #426: clean-reset reuse, the same slot-reuse mechanism, published first (developed independently here), and its R767 word as a comparison.
+- **icekylinx, PR #433:**
+  - the split-centre complex supplier that the headline κ uses;
+  - its bit engine, finite invoice and six-level tail, ported here;
+  - the R758 comparison.
+- **DaysSky:**
+  - PR #381: the B₄ layout and checkers;
+  - PR #375: halving degree two;
+  - PR #363: B_K and `bridged.py`.
+- **Zhihao Chen (jacklightChen):**
+  - PR #386: the compressed nine-stage bit layout and its checkers, generalised here;
+  - PR #425: the mutable-basis complex word.
+- **Chafik Boukhalfa (chafreaky), PR #417:** the B₄ pricing tail port, the #376 rebuild and the kernel-word control.
+- **Rohan Arun (rohanarun):**
+  - PR #431: a cited complex supplier and the two-supplier seed policy;
+  - PR #392: the refined pricing tail.
+- **Jacob Sussman:** the E8 family and the bridged word.
+- **PR #266 and PR #315 (DreamingOfClouds) lineage:** the official checkers, the moment engines and the outer assembly.
+
+Prepared by eumemic with substantial Anthropic Claude assistance. Apache-2.0 (`LICENSE`); see `NOTICE.md`.
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr370.json b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr370.json
new file mode 100644
index 0000000000..db86b22e15
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr370.json
@@ -0,0 +1,105 @@
+{
+ "schema": "source-pins/1",
+ "source": "https://github.com/CrocSwap/integer-mult-bounds/pull/370",
+ "head_repository": "utcorvusvolat-dotcom/e8-bit-kappa-8.7548e-4",
+ "commit": "b7fe9cdf2da009c947ff6b334c562bc190b30373",
+ "note": "PR #370 (Dylan Crow / utcorvusvolat-dotcom): E8 bit word, producer, independent checker, generalised official checkers, PR #315 engines as vendored there. Every file listed has, in this package, the git blob id it has at the commit above (git ls-tree -r <commit> -- <source_path>).",
+ "identical": {
+  "LICENSE": {
+   "source_path": "research/e8-bit/LICENSE",
+   "blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64"
+  },
+  "code/bit/producer/compile.py": {
+   "source_path": "research/e8-bit/code/bit/producer/compile.py",
+   "blob": "86b12507ef86308336833a208a989d56072096d1"
+  },
+  "code/bit/producer/compile2.py": {
+   "source_path": "research/e8-bit/code/bit/producer/compile2.py",
+   "blob": "a7bdfdfbe417c793b2a8c515f5432bdd10472259"
+  },
+  "code/bit/producer/e8lib.py": {
+   "source_path": "research/e8-bit/code/bit/producer/e8lib.py",
+   "blob": "8464b956f6a5aa5061695990a14b7a385d370c2e"
+  },
+  "code/bit/producer/frames.py": {
+   "source_path": "research/e8-bit/code/bit/producer/frames.py",
+   "blob": "b28c3b2413b9767e7ffe0a8b2db93836f3455494"
+  },
+  "code/bit/producer/fullword.py": {
+   "source_path": "research/e8-bit/code/bit/producer/fullword.py",
+   "blob": "104f01b7803481b623809bc8a57682d28f09b5c3"
+  },
+  "code/bit/producer/ham1.py": {
+   "source_path": "research/e8-bit/code/bit/producer/ham1.py",
+   "blob": "8086649a5f71c16698db7059bbada7187d781b56"
+  },
+  "code/bit/producer/ham2.py": {
+   "source_path": "research/e8-bit/code/bit/producer/ham2.py",
+   "blob": "842f76b245a1bfb4150c53a853f6f472511f5a2f"
+  },
+  "code/bit/producer/price.py": {
+   "source_path": "research/e8-bit/code/bit/producer/price.py",
+   "blob": "9014d97d519eea1f8c96e4bfc75afa0febd5903f"
+  },
+  "code/bit/producer/params-r865.json": {
+   "source_path": "research/e8-bit/code/bit/producer/params-r865.json",
+   "blob": "110b4d94d884f03d4d37be22672ab27d836f1275"
+  },
+  "code/bit/independent/checkword.py": {
+   "source_path": "research/e8-bit/code/bit/independent/checkword.py",
+   "blob": "da4e0fe05067184d4dab1e130ae1384c1fa983f5"
+  },
+  "code/bit/independent/mutate.py": {
+   "source_path": "research/e8-bit/code/bit/independent/mutate.py",
+   "blob": "eba592fd468e0d7e7e5100fe99da6eb548c5906b"
+  },
+  "code/bit/checkers/legality_h.cpp": {
+   "source_path": "research/e8-bit/code/bit/checkers/legality_h.cpp",
+   "blob": "cb1233c7e96b1aa8bbf4d2e4165d75ab0dca64b9"
+  },
+  "code/bit/checkers/columns_h.cpp": {
+   "source_path": "research/e8-bit/code/bit/checkers/columns_h.cpp",
+   "blob": "00c5a3a5d81d083582f60f33dd2e7bea5049c37f"
+  },
+  "code/bit/checkers/json.hpp": {
+   "source_path": "research/e8-bit/code/bit/checkers/json.hpp",
+   "blob": "82d69f7c5d044c9887c96b90c97f5639083ecd14"
+  },
+  "code/bit/checkers/gram_frames.py": {
+   "source_path": "research/e8-bit/code/bit/checkers/gram_frames.py",
+   "blob": "b740d47295c02692260d7cc01874a49fe48f78ab"
+  },
+  "code/bit/export_records.py": {
+   "source_path": "research/e8-bit/code/bit/export_records.py",
+   "blob": "3632d370486a02f5456f7643ced03f8c925b2350"
+  },
+  "code/bit/mutate_records.py": {
+   "source_path": "research/e8-bit/code/bit/mutate_records.py",
+   "blob": "6794516f665d36eac189894e350a5ad01113cb4c"
+  },
+  "code/bit/regression/stage_cohort.py": {
+   "source_path": "research/e8-bit/code/bit/regression/stage_cohort.py",
+   "blob": "f6d7afe3e623208c4207b6a683a1e3e49249e31c"
+  },
+  "code/pricing/moment.py": {
+   "source_path": "research/e8-bit/code/pricing/moment.py",
+   "blob": "7d697cb45203fe72d97037403d6da41f71f3b7fd"
+  },
+  "code/pricing/base_two_moment.py": {
+   "source_path": "research/e8-bit/code/pricing/base_two_moment.py",
+   "blob": "14a90fa0e788217856f070382c9e61bd7c603c61"
+  },
+  "code/pricing/outer.py": {
+   "source_path": "research/e8-bit/code/pricing/outer.py",
+   "blob": "43007488ad2c43187c77cc6798beff8b1cd76ad2"
+  },
+  "code/pricing/prime_witnesses.py": {
+   "source_path": "research/e8-bit/code/pricing/prime_witnesses.py",
+   "blob": "7f16d930302ae879c562dd58e085d9747fcac077"
+  },
+  "data/bit/bitE8-r865.json.gz": {
+   "source_path": "research/e8-bit/data/bit/bitE8-r865.json.gz",
+   "blob": "8bec1751f7e33c3a1e4673ef5dbc34d6f205321e"
+  }
+ }
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr376.json b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr376.json
new file mode 100644
index 0000000000..818f17fb6a
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr376.json
@@ -0,0 +1,21 @@
+{
+ "schema": "source-pins/1",
+ "source": "https://github.com/CrocSwap/integer-mult-bounds/pull/376",
+ "head_repository": "applecrusher/integer-mult-bounds",
+ "commit": "92328da595bc688146c79ab8308f0d2012bb491e",
+ "note": "PR #376 (applecrusher): frame and helper-reuse witnesses of the R822 word (here as vendored by PR #417, byte-identical). Every file listed has, in this package, the git blob id it has at the commit above (git ls-tree -r <commit> -- <source_path>).",
+ "identical": {
+  "data/controls/pr376/frame-selection.json": {
+   "source_path": "research/e8-bit-helper-reuse/frame-selection.json",
+   "blob": "647b34368f3f0c7d228c70fa335af872e7946beb"
+  },
+  "data/controls/pr376/reuse-selection.json": {
+   "source_path": "research/e8-bit-helper-reuse/reuse-selection.json",
+   "blob": "a6954dc65f28137ad16d015b42c40dbbde0bd66f"
+  },
+  "data/controls/pr376/LICENSE-pr376": {
+   "source_path": "research/e8-bit-helper-reuse/LICENSE",
+   "blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64"
+  }
+ }
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr381.json b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr381.json
new file mode 100644
index 0000000000..042a26c7c2
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr381.json
@@ -0,0 +1,41 @@
+{
+ "schema": "source-pins/1",
+ "source": "https://github.com/CrocSwap/integer-mult-bounds/pull/381",
+ "head_repository": "DaysSky/integer-mult-bounds",
+ "commit": "00765b291d0f924f337298eb1e2930cb0878b95e",
+ "note": "PR #381 (DaysSky): B_K checkers (formal columns, PR234 geometry, banks, price, finite bill) and PR #363's bridged.py. Every file listed has, in this package, the git blob id it has at the commit above (git ls-tree -r <commit> -- <source_path>).",
+ "identical": {
+  "code/bit/checkers/columns_k.cpp": {
+   "source_path": "research/e8-nine-stage-kappa/code/bit/checkers/columns_k.cpp",
+   "blob": "42bb232fbec4de703e70cc13dc2f39a3b43a3a01"
+  },
+  "code/bit/checkers/geometry_k.py": {
+   "source_path": "research/e8-nine-stage-kappa/code/bit/checkers/geometry_k.py",
+   "blob": "2a052980816d9b56b33c5e41132bb7f86286462b"
+  },
+  "code/bit/checkers/tile_k.py": {
+   "source_path": "research/e8-nine-stage-kappa/code/bit/checkers/tile_k.py",
+   "blob": "a4635e6681c2f1521b44f24364cc457d304cb077"
+  },
+  "code/bit/checkers/certify_bit_k.py": {
+   "source_path": "research/e8-nine-stage-kappa/code/bit/checkers/certify_bit_k.py",
+   "blob": "37ce2ee2b412b3b97a397159f48b912ef893b014"
+  },
+  "code/bit/checkers/finite_k.py": {
+   "source_path": "research/e8-nine-stage-kappa/code/bit/checkers/finite_k.py",
+   "blob": "8781815ee6ee663edc0e0afdf1380186594ec913"
+  },
+  "code/bit/checkers/cost.py": {
+   "source_path": "research/e8-nine-stage-kappa/code/bit/checkers/cost.py",
+   "blob": "677584c1c6b0e959c19f58521b68d4b3e847f97e"
+  },
+  "code/bit/receipts_k.py": {
+   "source_path": "research/e8-nine-stage-kappa/code/bit/receipts_k.py",
+   "blob": "428261488b4af028fd04df4f84eead1dad79a389"
+  },
+  "code/complex/code/bridged.py": {
+   "source_path": "research/e8-nine-stage-kappa/code/complex/code/bridged.py",
+   "blob": "626a28614b07066528fd5f189d87cffa5015ac60"
+  }
+ }
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr386.json b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr386.json
new file mode 100644
index 0000000000..ac24e5d262
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr386.json
@@ -0,0 +1,29 @@
+{
+ "schema": "source-pins/1",
+ "source": "https://github.com/CrocSwap/integer-mult-bounds/pull/386",
+ "head_repository": "jacklightChen/integer-mult-bounds",
+ "commit": "dd11cf8069554f0333afde398f12a56c3a7c29dd",
+ "note": "PR #386 (Zhihao Chen / jacklightChen): compressed nine-stage bit geometry (unchanged), portable header, and the validation receipts used as regression references. Every file listed has, in this package, the git blob id it has at the commit above (git ls-tree -r <commit> -- <source_path>).",
+ "identical": {
+  "code/nine/geometry.py": {
+   "source_path": "research/e8-bit-complex-nine/geometry.py",
+   "blob": "91594e0223e8fac49162b5aef834ffaa8e94a254"
+  },
+  "portable-include/bits/stdc++.h": {
+   "source_path": "research/e8-bit-complex-nine/portable-include/bits/stdc++.h",
+   "blob": "fc5664e929d9a81d9b4926bee049a93330be86ec"
+  },
+  "data/controls/pr386/GLOBAL.json": {
+   "source_path": "research/e8-bit-complex-nine-validation/GLOBAL.json",
+   "blob": "21bc6dcc7bbefedcd3064485d0e82c95e585044c"
+  },
+  "data/controls/pr386/AUDIT.json": {
+   "source_path": "research/e8-bit-complex-nine-validation/AUDIT.json",
+   "blob": "698e827ae87ae9db47fd30cf69537176276cff4e"
+  },
+  "data/controls/pr386/COMBINED.json": {
+   "source_path": "research/e8-bit-complex-nine-validation/COMBINED.json",
+   "blob": "8d6e3f22667fa0f6fa1a5495223e87f90a4cd103"
+  }
+ }
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr417.json b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr417.json
new file mode 100644
index 0000000000..33f0ae053c
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr417.json
@@ -0,0 +1,49 @@
+{
+ "schema": "source-pins/1",
+ "source": "https://github.com/CrocSwap/integer-mult-bounds/pull/417",
+ "head_repository": "chafreaky/integer-mult-bounds",
+ "commit": "3f681fb571036ca4a267570318260b0d083f7b9d",
+ "note": "PR #417 (Chafik Boukhalfa / chafreaky): refined pricing tail (bootstrap.refine), its engine module and PR #315 engine copies, PR #376 rebuild (apply376.py), the vendored PR #376 witnesses, and the final kernel word used as a B_4 control. Every file listed has, in this package, the git blob id it has at the commit above (git ls-tree -r <commit> -- <source_path>).",
+ "identical": {
+  "code/tail/e8core.py": {
+   "source_path": "research/e8-kernel-bit-nine/code/e8core.py",
+   "blob": "78983b368715e89fe8524a6dd2c13585d2b5394e"
+  },
+  "code/tail/bootstrap.py": {
+   "source_path": "research/e8-kernel-bit-nine/code/bootstrap.py",
+   "blob": "1bc17e768259c342fb8b94b919bfeaea10304153"
+  },
+  "code/tail/apply376.py": {
+   "source_path": "research/e8-kernel-bit-nine/code/apply376.py",
+   "blob": "c401a84d8f549e0752464ab8313ce648bb4d14fa"
+  },
+  "code/tail/engines/moment.py": {
+   "source_path": "research/e8-kernel-bit-nine/code/engines/moment.py",
+   "blob": "7d697cb45203fe72d97037403d6da41f71f3b7fd"
+  },
+  "code/tail/engines/base_two_moment.py": {
+   "source_path": "research/e8-kernel-bit-nine/code/engines/base_two_moment.py",
+   "blob": "14a90fa0e788217856f070382c9e61bd7c603c61"
+  },
+  "code/tail/engines/outer.py": {
+   "source_path": "research/e8-kernel-bit-nine/code/engines/outer.py",
+   "blob": "43007488ad2c43187c77cc6798beff8b1cd76ad2"
+  },
+  "data/controls/pr376/frame-selection.json": {
+   "source_path": "research/e8-kernel-bit-nine/data/pr376/frame-selection.json",
+   "blob": "647b34368f3f0c7d228c70fa335af872e7946beb"
+  },
+  "data/controls/pr376/reuse-selection.json": {
+   "source_path": "research/e8-kernel-bit-nine/data/pr376/reuse-selection.json",
+   "blob": "a6954dc65f28137ad16d015b42c40dbbde0bd66f"
+  },
+  "data/controls/pr376/LICENSE-pr376": {
+   "source_path": "research/e8-kernel-bit-nine/data/pr376/LICENSE-pr376",
+   "blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64"
+  },
+  "data/controls/pr417-bitE8-nine-kernel.json.gz": {
+   "source_path": "research/e8-kernel-bit-nine/data/final/bitE8-nine-kernel.json.gz",
+   "blob": "572172b8148538d1937b9f7fa7f3939755008a8c"
+  }
+ }
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr425.json b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr425.json
new file mode 100644
index 0000000000..8d9c976b02
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr425.json
@@ -0,0 +1,13 @@
+{
+ "schema": "source-pins/1",
+ "source": "https://github.com/CrocSwap/integer-mult-bounds/pull/425",
+ "head_repository": "jacklightChen/integer-mult-bounds",
+ "commit": "e11ccea1d092beb1b01b4ee4ce49da478234254c",
+ "note": "PR #425 (Zhihao Chen / jacklightChen): the fresh validation receipt that states the cited complex coarse saving b and kappa. Every file listed has, in this package, the git blob id it has at the commit above (git ls-tree -r <commit> -- <source_path>).",
+ "identical": {
+  "data/controls/pr425/FINAL.json": {
+   "source_path": "research/hamming-mutable-basis-complex-validation/FINAL.json",
+   "blob": "1e9c8784c3cb719acb5274126141fe360af253fa"
+  }
+ }
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr426.json b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr426.json
new file mode 100644
index 0000000000..7c72390e09
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr426.json
@@ -0,0 +1,17 @@
+{
+ "schema": "source-pins/1",
+ "source": "https://github.com/CrocSwap/integer-mult-bounds/pull/426",
+ "head_repository": "ai-nanachi/integer-mult-bounds",
+ "commit": "88d552526893cd15325948bb1487e9a4d4bf32f6",
+ "note": "PR #426 (ai-nanachi): R767 bit word (clean-reset reuse), used only as a priced comparison and B_3 control. Every file listed has, in this package, the git blob id it has at the commit above (git ls-tree -r <commit> -- <source_path>).",
+ "identical": {
+  "data/controls/pr426-bit-candidate.json.gz": {
+   "source_path": "research/e8-clean-reuse-extension/data/bit-candidate.json.gz",
+   "blob": "807cea53ebe1322721463ee2319bcd52b9714f24"
+  },
+  "data/controls/LICENSE-pr426": {
+   "source_path": "research/e8-clean-reuse-extension/LICENSE",
+   "blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64"
+  }
+ }
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr431.json b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr431.json
new file mode 100644
index 0000000000..00f1075773
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr431.json
@@ -0,0 +1,13 @@
+{
+ "schema": "source-pins/1",
+ "source": "https://github.com/CrocSwap/integer-mult-bounds/pull/431",
+ "head_repository": "rohanarun/integer-mult-bounds",
+ "commit": "db4f46579b95bec6e2a0c59e3e1ee2b6584dbab3",
+ "note": "PR #431 (Rohan Arun / rohanarun, draft): the local validation receipt that states the cited complex coarse saving b and kappa. Every file listed has, in this package, the git blob id it has at the commit above (git ls-tree -r <commit> -- <source_path>).",
+ "identical": {
+  "data/controls/pr431/VALIDATION-LOCAL.json": {
+   "source_path": "research/hamming-frame-retiming/VALIDATION-LOCAL.json",
+   "blob": "0f0a80418d7f3e521c980ef0354fc3945eae1795"
+  }
+ }
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr433.json b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr433.json
new file mode 100644
index 0000000000..910a7c3490
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/SOURCE-pr433.json
@@ -0,0 +1,13 @@
+{
+ "schema": "source-pins/1",
+ "source": "https://github.com/CrocSwap/integer-mult-bounds/pull/433",
+ "head_repository": "icekylinx/integer-mult-bounds",
+ "commit": "6d9244518175caf9e0089f92486959bc2c317273",
+ "note": "PR #433 (icekylinx): the certificate that states the cited complex lower bound, the R758 bit lower bound and kappa of the split-centre composition. Every file listed has, in this package, the git blob id it has at the commit above (git ls-tree -r <commit> -- <source_path>).",
+ "identical": {
+  "data/controls/pr433/CERTIFICATE.json": {
+   "source_path": "research/split-centres-global/CERTIFICATE.json",
+   "blob": "7e807079c1ec4907306035c84be1ba2fb1d69d79"
+  }
+ }
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/b4/kappa_b4.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/b4/kappa_b4.py
new file mode 100644
index 0000000000..402a510e15
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/b4/kappa_b4.py
@@ -0,0 +1,31 @@
+"""kappa with cited complex savings when the bit side is this word in B_4 (or B_3).
+
+The bit coarse saving c is read from certify_bit_k.py's receipt (PR #381's checker, unchanged). For every cited
+complex supplier b, kappa is computed by PR #417's bootstrap.refine (chafreaky's reimplementation of rohanarun's PR #392
+refined pricing tail: six fixed bootstrap levels, PR #315's outer assembly, 47 strict constraints, next grid point and
+invalid parameters rejected) and must equal the value cited with b. Since c > b for every cited supplier, the result is
+complex-bound and does not depend on c; it is recomputed with the best previously published bit c as a control.
+usage: kappa_b4.py KAPPA.json (certify_bit_k receipt) CONTROL_C COMPLEX_B.json OUT.json
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import json
+import os
+import sys
+from fractions import Fraction as Q
+
+sys.path.insert(0, os.path.join(os.path.dirname(os.path.abspath(__file__)), "..", "tail"))
+from bootstrap import refine  # noqa: E402  (PR #417, unchanged)
+
+rec = json.load(open(sys.argv[1]))
+c = Q(rec["bit_coarse"])
+c0 = Q(sys.argv[2])
+out = dict(K=rec["K"], m=rec["m"], bit_coarse=str(c), control_bit_coarse=str(c0), kappa={})
+for s in json.load(open(sys.argv[3]))["suppliers"]:
+    b = Q(s["b"])
+    k, rej = refine(b, c)
+    k0, _ = refine(b, c0)
+    assert c > b and c0 > b and k == k0 == Q(s["kappa"]), (s["name"], str(k), s["kappa"])
+    out["kappa"][s["name"]] = dict(b=str(b), kappa=str(k), kappa_float=float(k), binding="complex", rejected=rej,
+                                   bit_headroom_percent=100 * float(c / b - 1), source=s["source"])
+    print("   with %s b = %.12e: kappa = %s = %.15e (complex-bound, equal to the cited value and unchanged with the"
+          " control bit c; bit headroom c/b - 1 = %.3f%%)" % (s["name"], float(b), k, float(k), 100 * float(c / b - 1)))
+json.dump(out, open(sys.argv[4], "w"), indent=1)
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/certify_bit_k.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/certify_bit_k.py
new file mode 100644
index 0000000000..37ce2ee2b4
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/certify_bit_k.py
@@ -0,0 +1,59 @@
+"""Generalized (Dylan Crow, with Anthropic Claude assistance): h, the normalization T and the output path are arguments;
+h = 20, T = 12 is the original.  Bridged word B_K (DaysSky, assisted with Claude): the one-level histogram is
+(2K+1) x the local histogram + 2v x the idle blocks of PR #363's bridged.check(K, h) (split below m/2 for K > 2),
+W = 2Kv + resid/h, m = (2K+1) h; K = 2 is certify_bit_g.py.  With a seventh argument 'unsplit' the idle climbs are
+not split and the least halving degree t (m^t > 2 max child^t) replaces the half-shrink guard.
+usage: certify_bit_k.py WORDDIR B K H T OUT.json [unsplit]
+Exact bit coarse saving + outer assembly for a PR249-format local word, using PR #315's engines
+(moment.py, base_two_moment.py, outer.py) and its math_check.run logic, with a given complex coarse b."""
+import sys, json, importlib.util, os
+from fractions import Fraction as Q
+from collections import Counter
+sys.path.insert(0,os.path.dirname(os.path.abspath(__file__)))
+import cost as C
+sys.path.insert(0,os.path.join(os.path.dirname(os.path.abspath(__file__)),'..','..','complex','code'))
+import bridged
+P=os.environ.get('PR315',os.path.join(os.path.dirname(os.path.abspath(__file__)),'..','..','pricing'))+'/'
+def load(n):
+    s=importlib.util.spec_from_file_location(n,P+n+'.py'); m=importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+moment=load('moment'); other=load('base_two_moment'); outer=load('outer')
+d=sys.argv[1]; b=Q(sys.argv[2]); KP=int(sys.argv[3]); HH=int(sys.argv[4]); T=int(sys.argv[5]); OUT=sys.argv[6]; S=2*KP+1
+s,fr,dim,rec=C.load_snapshot(d)
+H,resid,v=C.local_profile(rec,s,dim,h=HH); m=S*HH
+UNSPLIT=len(sys.argv)>7 and sys.argv[7]=='unsplit'
+lay=bridged.check(KP,HH,split=(m-1)//2 if (KP>2 and not UNSPLIT) else None)
+prof=Counter({j:S*c for j,c in H.items()})
+for r in lay['blocks_per_role_pair']: prof[r]+=2*v
+norm={int(k):int(c)*T for k,c in prof.items() if c}; Wn=Q(2*KP*v*HH+resid,HH)*T; assert Wn.denominator==1; Wn=int(Wn)
+t_half=1
+while m**t_half<=2*max(norm)**t_half: t_half+=1
+assert UNSPLIT or t_half==1, 'half-shrink guard'
+mass=sum(k*c for k,c in norm.items()); print('normalized W',Wn,'calls',sum(norm.values()),'mass',mass,'deficit',m*Wn-mass,'maxchild',max(norm))
+root=moment.certify(dict(norm),m,Wn,True); c=Q(int(Q(root['lower'])*10**18),10**18)
+bm=moment.moment(norm,m,Wn,c,True); nextbm=moment.moment(norm,m,Wn,c+Q(1,10**18),True); assert bm[1]<1<nextbm[0]
+fallback=32*m*m*sum(norm.values())
+_,upper=other.moment(m,Wn,list(norm.items()),c); _,bad=other.moment(m,Wn,[(1,fallback)],c)
+lower,_=other.moment(m,Wn,list(norm.items()),c+Q(1,10**18)); badlower,_=other.moment(m,Wn,[(1,fallback)],c+Q(1,10**18))
+assert upper+Q(1,10**16)*bad<1<lower+Q(1,10**16)*badlower
+print('bit coarse c =',c,float(c),'(two engines + 1e-16 fallback, adjacent grid excluded)')
+grid=Q(1,10**18); eta=Q(1,10**12); beta=Q(1,10**9); cap=(1-beta)*b
+sv=min(c,Q(((cap-grid)*10**18).__floor__(),10**18)); binding='bit' if sv==c else 'complex'
+sm=bm if sv==c else moment.moment(norm,m,Wn,sv,True); assert 0<sv<=c and sm[1]<1
+if binding=='complex': assert sv+grid>cap-grid, 'complex-bound saving not tight against the cap'
+chain=[Q(384599,10**10)]
+for _ in range(3):
+    a=(1-sv)*sv+sv*chain[-1]; assert chain[-1]<a<sv<1-a; chain.append(a)
+bit=chain[-1]
+bridge=dict(proof='PROOF.md',representation='Exact powers with source-bound finite overcharges',semantic=dict(G=dict(base=2,exponent=30000),E=dict(base=2,exponent=100000),B_upper=dict(base=2,exponent=100001),C0=dict(base=2,exponent=210000),C1=1,strict_literal_gap=1,induction_gap_lower=1),rows=dict(coefficient=20161,degree=10**6,suffix_slope=4*10**6,degree_gap=Q(10**6)-Q(51*20161,25)))
+q=bit*(1-2*eta); minimum=(1-eta)*q/(1+q); ticks=minimum*10**18; k=Q((ticks.numerator-1)//ticks.denominator,10**18)
+asm=outer.assembly(bit,b,bridge,k,eta=eta,beta=beta); assert len(asm['strict_constraints'])==47 and min(asm['strict_constraints'].values())>0
+try:
+    outer.assembly(bit,b,bridge,k+Q(1,10**18),eta=eta,beta=beta); raise SystemExit('ADJACENT ADMITTED')
+except AssertionError: pass
+if binding=='complex':
+    try: outer.assembly(cap,b,bridge,k,eta=eta,beta=beta)
+    except AssertionError as e: assert 'leaf_saving_above_bit' in str(e); print('complex leaf cap itself rejected (leaf_saving_above_bit), as in PR #315 math_check')
+    else: raise SystemExit('complex leaf cap admitted')
+print('complex b =',b,float(b),'| binding:',binding)
+print('KAPPA =',k,'=',format(float(k),'.12e'),'| 47 strict constraints positive, adjacent grid point rejected')
+json.dump(dict(word=d,K=KP,stages=S,halving_degree=t_half,idle_blocks_per_role_pair=lay['blocks_per_role_pair'],h=HH,T=T,maxchild=max(norm),bit_moment_interval=[str(x) for x in bm],normalized_histogram=norm,W=Wn,m=m,bit_coarse=str(c),complex_coarse=str(b),binding=binding,kappa=str(k),kappa_float=float(k)),open(OUT,'w'),indent=1)
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/columns_h.cpp b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/columns_h.cpp
new file mode 100644
index 0000000000..00c5a3a5d8
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/columns_h.cpp
@@ -0,0 +1,48 @@
+// Generalization (Dylan Crow, with Anthropic Claude assistance): the copied-centre count is the macro NCOPY, defaulting to
+// HDIM, so the unmodified PR #346/#352 build (no -DNCOPY) is exactly the original checker. The E8 bit word has 9
+// retained totals at h = 8 (-DNCOPY=9).
+#ifndef NCOPY
+#define NCOPY HDIM
+#endif
+#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=VPORTS,r=RHELP,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==NCOPY,"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==NCOPY,"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",5*NCOPY},{"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 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/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/columns_k.cpp b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/columns_k.cpp
new file mode 100644
index 0000000000..42bb232fbe
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/columns_k.cpp
@@ -0,0 +1,62 @@
+// Generalization (Dylan Crow, with Anthropic Claude assistance): the copied-centre count is the macro NCOPY, defaulting to
+// HDIM, so the unmodified PR #346/#352 build (no -DNCOPY) is exactly the original checker. The E8 bit word has 9
+// retained totals at h = 8 (-DNCOPY=9).
+// Bridged word B_K (DaysSky, assisted with Claude): the macro KPAIRS (default 2) sets the number of bank pairs; the
+// schedule, the twin bridges and the terminal exchange are generated from PR #363's bridged.py rule:
+//   stage 0,1,2 pair 1 forward/backward/forward; stage 2p-1, 2p pair p backward/forward (p = 2..K);
+//   after stage 2p-3: X(p-1) += Xp, Yp -= Y(p-1); after stage 2p-2: Yp += Y(p-1), X(p-1) -= Xp;
+//   after the last stage, for p = K..2: Y(p-1) -= Yp, Xp += X(p-1).
+// KPAIRS = 2 reproduces the original five-stage tables and receipt (checked in verify.sh); KPAIRS = 3 is seven stages.
+#ifndef NCOPY
+#define NCOPY HDIM
+#endif
+#ifndef KPAIRS
+#define KPAIRS 2
+#endif
+#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=VPORTS,r=RHELP,loc=2*v+r,global=2*KPAIRS*v+r,temp=global;const int S=2*KPAIRS+1;
+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==NCOPY,"center boundaries");
+std::vector<std::array<int,2>>active;std::vector<bool>backward;std::vector<std::vector<std::array<int,3>>>after(S);
+auto X=[](int p){return 2*(p-1);};auto Y=[](int p){return 2*(p-1)+1;};
+for(int t=0;t<S;t++){int p=t<3?1:(t+1)/2;bool b=(t==1)||(t>=3&&t%2==1);backward.push_back(b);active.push_back(b?std::array<int,2>{Y(p),X(p)}:std::array<int,2>{X(p),Y(p)});}
+for(int q=2;q<=KPAIRS;q++){after[2*q-3].push_back({X(q-1),X(q),1});after[2*q-3].push_back({Y(q),Y(q-1),-1});
+ after[2*q-2].push_back({Y(q),Y(q-1),1});after[2*q-2].push_back({X(q-1),X(q),-1});}
+for(int p=KPAIRS;p>=2;p--){after[S-1].push_back({Y(p-1),Y(p),-1});after[S-1].push_back({X(p),X(p-1),1});}
+int nbridges=0;for(auto&a:after)nbridges+=a.size();need(nbridges==6*(KPAIRS-1),"twin bridge count");
+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 2*KPAIRS*v+i-2*v;return temp;};
+auto t0=std::chrono::steady_clock::now();J stages=J::array();
+for(int stage=0;stage<S;stage++){bool rev=backward[stage];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==NCOPY,"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");}}}
+for(auto q:after[stage])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<2*KPAIRS;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,KPAIRS==2?"five-stage all physical formal columns":"bridged all physical formal columns");}
+// Independent complete four-bank controls, each omitted bridge must change endpoint.
+J controls=J::array();for(int skip=0;skip<nbridges;skip++){std::vector<unsigned>b(2*KPAIRS);for(int z=0;z<2*KPAIRS;z++)b[z]=1u<<z;int j=0;for(int s=0;s<S;s++){b[active[s][1]]^=b[active[s][0]];for(auto q:after[s]){if(j++!=skip)b[q[0]]^=b[q[1]];}}for(int z=0;z<2*KPAIRS;z+=2)std::swap(b[z],b[z+1]);bool failed=false;for(int z=0;z<2*KPAIRS;z++)failed|=b[z]!=(1u<<z);need(failed,"vacuous omitted bridge control");controls.push_back({{"omit_bridge",skip},{"rejected",true}});}
+J out={{"status",KPAIRS==2?"PASS_NEW_COHORT249_ALL_FIVE_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL":"PASS_NEW_COHORT249_ALL_BRIDGED_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},{KPAIRS==2?"five_stage_additions":"stage_additions",S*adds},{"bridge_additions",6*(KPAIRS-1)*v},{"fresh_center_copies",S*NCOPY},{"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 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/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/cost.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/cost.py
new file mode 100644
index 0000000000..677584c1c6
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/cost.py
@@ -0,0 +1,62 @@
+"""Fast exact cost evaluator for a five-stage banked bit core-block word.
+Word format (PR249 snapshot): records = int32 six-tuples
+  MOVE (0, role, old_frame, new_frame, rank, z)
+  ADD  (1, dst, src, coeff, frame, category)
+  COPY (2, center, temp, copy_frame, target_frame, rank)   [paid child of given rank]
+  ERASE(3, ...)
+"""
+import json, struct, collections
+import numpy as np
+from mpmath import mp, mpf, findroot
+mp.dps = 50
+
+def load_snapshot(d):
+    s = json.load(open(f'{d}/249-states.json'))
+    fr = json.load(open(f'{d}/frames.json'))
+    dim = {int(k): len(v['B']) for k, v in fr['frames'].items()}
+    rec = np.frombuffer(open(f'{d}/249-records.bin','rb').read(), dtype='<i4').reshape(-1, 6)
+    return s, fr, dim, rec
+
+def local_profile(rec, s, dim, h=24):
+    """Return (local child histogram incl. copies, sum of helper residuals, v)."""
+    v = s['v']; n = s['n']
+    H = collections.Counter()
+    moves = rec[rec[:, 0] == 0]
+    for r in moves:
+        if r[4] > 0: H[int(r[4])] += 1
+    copies = rec[rec[:, 0] == 2]
+    for r in copies:
+        if r[5] > 0: H[int(r[5])] += 1
+    init = s['initial']
+    resid = sum(h - dim[init[str(r)]] for r in range(2 * v, n))
+    return H, resid, v
+
+def five_stage(H, resid, v, h=24, stages=5):
+    m = stages * h
+    prof = collections.Counter()
+    for j, c in H.items(): prof[j] += stages * c
+    for j in (2*h - 2, h - 1, 2*h + 2, 4): prof[j] += 2 * v
+    W = mpf(4 * v) + mpf(resid) / h
+    mass = sum(j * c for j, c in prof.items())
+    return prof, W, m, W * m - mass
+
+def solve_moment(prof, W, m, bad=mpf('1e-16')):
+    calls = sum(prof.values())
+    items = [(mpf(j) / m, c) for j, c in prof.items()]
+    def mu(sv):
+        t = 1 - sv
+        return (sum(c * x ** t for x, c in items) + bad * 32 * m * m * calls * (mpf(1) / m) ** t) / W - 1
+    return findroot(mu, mpf('0.0007'))
+
+def evaluate(rec, s, dim, h=24):
+    H, resid, v = local_profile(rec, s, dim, h)
+    prof, W, m, deficit = five_stage(H, resid, v, h)
+    sv = solve_moment(prof, W, m)
+    return dict(saving=sv, kappa_approx=sv / (1 + sv), W=W, deficit=deficit, m=m,
+                calls=sum(prof.values()), local=dict(sorted(H.items())), resid=resid)
+
+if __name__ == '__main__':
+    import sys
+    s, fr, dim, rec = load_snapshot(sys.argv[1])
+    r = evaluate(rec, s, dim)
+    print({k: (float(v) if hasattr(v, 'real') and not isinstance(v, dict) else v) for k, v in r.items() if k != 'local'})
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/finite_k.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/finite_k.py
new file mode 100644
index 0000000000..8781815ee6
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/finite_k.py
@@ -0,0 +1,154 @@
+"""Finite bill for the banked five-stage bit word, generalized from the source527/p10 finite_check.run (Dylan Crow, with
+Anthropic Claude assistance).  The arithmetic is the original line by line; the changes are explicit parameters:
+  * h, m = 5h, v, R, replicas T, literal stock, literal paid histogram, weighted/unit additions and the forward and
+    inverse cancellation-free row bounds are inputs (from this package's receipts);
+  * NCOPY, the copied-centre temporaries per invocation and 5*NCOPY copy/erase episodes per replica (the original
+    writes h for both, since the paired cube has h centres; the E8 word has 9 retained totals at h = 8);
+  * the 2h-dimensional rational route template: [[p*, k*], [k*, p*]] for the reference port line q* of the label
+    family under its form (original: a triple line under G = I - J/9, denominators 1,2,3,6; E8: a root line under
+    <x,y>/2), recomputed and factored into elementary operations, exact inverse replay, omitted factor rejected;
+  * K, the conservative extra bank-selector calls, by the original formula 2*5*T*((live-1) + R*m*factors) with
+    factors = maxops + (m-1) + m (maxops of the actual charts; an ungauged word has only the identity chart, 0 ops).
+Bridged word B_K (DaysSky, assisted with Claude): x['Kpairs'] (default 2) gives S = 2K + 1 invocations, m = S h,
+S invocations' additions plus 6(K-1)v twin-bridge additions, route families 2S(2v + R) + 2Kv (each invocation routes
+its 2v data and R helper roles in and out; the terminal exchange moves the 2Kv data roles), S*NCOPY*T copy/erase
+episodes and the selector bill 2*S*T*(...) (receipts_k.py).  K = 2 gives exactly finite_g.py's 5, 6v, 20v + 10R + 4v
+and 5*NCOPY*T; the p = 10 regression path is five-stage and unchanged.
+usage: python3 finite_k.py e8 RECEIPTS.json OUT.json  |  python3 finite_k.py regression P10_RECEIPT_DIR"""
+from fractions import Fraction as Q
+from collections import Counter
+from hashlib import sha256
+import json, sys, os, importlib.util, gzip
+HERE=os.path.dirname(os.path.abspath(__file__))
+def ceilq(x): return -((-x.numerator)//x.denominator)
+def cutoff_log2(delta,C):
+    assert 0<delta<=1 and isinstance(C,int) and C>=1
+    return max(1,ceilq(36/delta**2),ceilq(2*(4+(C-1).bit_length())/delta))
+def mm(A,B): return [[sum(A[i][k]*B[k][j] for k in range(len(B))) for j in range(len(B[0]))] for i in range(len(A))]
+def route_template(h,q,form,g=None,ginv=None):
+    """[[g p* g^-1, g k*], [k* g^-1, p*]] with p* = q q^T G/<q,q>; G given by form(x,y) on coordinate vectors
+    (bilinear); g = I (the original's reference port) unless a port isometry is given."""
+    I=lambda n:[[Q(i==j)for j in range(n)]for i in range(n)]
+    Gq=[sum(form(i,j)*q[j] for j in range(h)) for i in range(h)]; nq=sum(q[i]*Gq[i] for i in range(h))
+    P=[[Q(q[i])*Gq[j]/nq for j in range(h)]for i in range(h)]
+    K=[[Q(i==j)-P[i][j]for j in range(h)]for i in range(h)]
+    if g is None: TL,TR,BL=P,K,K
+    else: TL,TR,BL=mm(mm(g,P),ginv),mm(g,K),mm(K,ginv)
+    rho=[TL[i]+TR[i]for i in range(h)]+[BL[i]+P[i]for i in range(h)]
+    a=[r[:]for r in rho];factors=[]
+    for j in range(2*h):
+        p=next(i for i in range(j,2*h)if a[i][j])
+        if p!=j:a[j],a[p]=a[p],a[j];factors.append(('swap',j,p,None))
+        if a[j][j]!=1:
+            c=1/a[j][j];a[j]=[c*x for x in a[j]];factors.append(('scale',j,None,c))
+        for i in range(2*h):
+            if i!=j and a[i][j]:
+                c=-a[i][j];a[i]=[x+c*y for x,y in zip(a[i],a[j])];factors.append(('add',i,j,c))
+    assert a==I(2*h)
+    def replay(omit=None):
+        a=I(2*h)
+        for z in reversed(range(len(factors))):
+            if z==omit:continue
+            kind,i,j,c=factors[z]
+            if kind=='swap':a[i],a[j]=a[j],a[i]
+            elif kind=='scale':a[i]=[x/c for x in a[i]]
+            else:a[i]=[x-c*y for x,y in zip(a[i],a[j])]
+        return a
+    assert replay()==rho
+    omit=next((i for i,f in enumerate(factors)if f[0]=='add'),0)   # original: the first addition; a route without additions: the first factor
+    assert factors and replay(omit)!=rho
+    counts=dict(Counter(f[0]for f in factors));denoms=sorted({c.denominator for kind,i,j,c in factors if c is not None})
+    serialization=[[kind,i,j,None if c is None else str(c)]for kind,i,j,c in factors]
+    return dict(factors=len(factors),factor_counts=counts,denominators=denoms,
+        factor_program_sha256=sha256(json.dumps(serialization,separators=(',',':')).encode()).hexdigest(),
+        exact_inverse_reconstruction=True,missing_addition_rejected=True)
+def bill(x):
+    """x: dict with h,m,v,R,T,stock,literal(hist),ncopy,weighted,unit,fwd_row,inv_row,K,coarse,moment_module,route."""
+    h,m,v,R,T,stock,ncopy=x['h'],x['m'],x['v'],x['R'],x['T'],x['stock'],x['ncopy']
+    literal=Counter(x['literal']);E=sum(literal.values());mass=sum(r*c for r,c in literal.items())
+    KP=x.get('Kpairs',2);S=2*KP+1
+    assert m==S*h and 0<max(literal)<m
+    t=1
+    while m**t<=2*max(literal)**t: t+=1          # least halving degree; t = 1 is the original half-shrink (PR234: ratio 5/6, degree four)
+    assert m*stock-mass==T*x['deficit']
+    d=m*m;N=2*m
+    weighted=T*(S*x['weighted']+6*(KP-1)*v);unit=T*(S*x['unit']+6*(KP-1)*v)
+    J=T*(2*S*(2*v+R)+2*KP*v);good=8*m*m+8;high=16*(d+1)**2;K=x['K']
+    payload=64*x['fwd_row']**3*x['inv_row']**2;assert payload<2**104
+    fallback=6*N*(N-1)+3*N+6*(N-1);assert fallback<32*m*m
+    coefficient=unit+J*high+J*(stock+ncopy)+E*good+E*(128*N**3)+16*m**3+S*ncopy*T+E+K+1
+    assert coefficient<2**80 and 2*m**3*10**16<2**80 and 0<K<2**40 and stock+ncopy<2**80
+    mod=x['moment_module'];c=Q(x['coarse']);lo,hi=mod.moment(dict(literal),m,stock,c,True)
+    delta_tau=1-hi;delta1=1-Q(mass,m*stock)-Q(1,10**16)*32*m*E/stock;assert delta_tau>0 and delta1>0
+    chain=[Q(384599,10**10)];gaps=[]
+    for j in range(3):
+        old=chain[-1];a=(1-c)*c+c*old;ds=dict(atom=c-a,borrowing=1-a-c,remainder=1-a-c*(1-old),stock=1-c);assert old<a<c<1-a and min(ds.values())>0
+        delta=min(ds.values());L=cutoff_log2(delta,coefficient);assert Q(L)*delta**2>=36 and Q(L)*delta>=2*(4+(coefficient-1).bit_length())
+        gaps.append(dict(stage=j+1,minimum_gap=str(delta),cutoff_log2_at_charged_coefficient=str(L)));chain.append(a)
+    controls=[]
+    for name,test in [('zero cutoff gap',lambda:cutoff_log2(Q(0),coefficient)),('negative constant',lambda:cutoff_log2(Q(1,2),0))]:
+        try:test()
+        except AssertionError:controls.append(name)
+        else:raise AssertionError('bad finite cutoff accepted')
+    return dict(coefficient=coefficient,coefficient_bits=coefficient.bit_length(),low_matrix_power=d,strict_upper='q^'+str(d+1),
+        positive_rank_children=E,rank_mass=mass,weighted_additions=weighted,unit_expanded_additions=unit,route_families=J,
+        copy_erase_episodes=S*ncopy*T,payload_prefix_upper=payload,payload_prefix_bits=payload.bit_length(),
+        delta_tau_lower=str(delta_tau),delta_linear=str(delta1),bootstrap_chain=list(map(str,chain)),gaps=gaps,
+        row_reserve=dict(internal_coefficient=t*(d+1),external_complex_coefficient=20161,**({'halving_degree':t} if t>1 else {})),route=x['route'],rejected_controls=controls)
+def load_moment():
+    s=importlib.util.spec_from_file_location('m',os.path.join(HERE,'..','..','pricing','moment.py'));m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+def hist(x): return Counter({int(k):v for k,v in x.items() if v})
+if __name__=='__main__':
+    mod=load_moment()
+    if sys.argv[1]=='regression':
+        d=sys.argv[2]; raw=json.load(open(d+'/raw.json')); sc=json.load(open(d+'/scalar.json')); bk=json.load(open(d+'/banks.json'))['banks']
+        ma=json.load(open(d+'/math.json'))['mathematics']; fin=json.load(open(d+'/finite.json')); gl=json.load(open(d+'/global_result.json'))
+        h=raw['h'];m=5*h;H=hist(raw['five_stage_profile']['histogram'])
+        for a,cnt in hist(raw.get('completion_rank_histogram',raw['auxiliary_entrance_rank_histogram'])).items():
+            H[5*a]-=cnt
+            if not H[5*a]: del H[5*a]
+        T=bk['physical_replicas']; literal=Counter({r:T*c for r,c in H.items()})
+        q=[int(i<3) for i in range(h)]; form=lambda i,j: Q(int(i==j))-Q(1,9)
+        x=dict(h=h,m=m,v=raw['v'],R=raw['physical_R'],T=T,stock=bk['literal_stock'],literal=literal,ncopy=h,deficit=4*raw['v']-5*h*(h-2),
+               weighted=sc['forward']['weighted_additions'],unit=sc['forward']['literal_unit_additions'],fwd_row=sc['forward']['max_intermediate_row_l1'],
+               inv_row=sc['inverse']['max_intermediate_row_l1'],K=bk['conservative_extra_selector_calls'],coarse=ma['bit_coarse'],moment_module=mod,
+               route=route_template(h,q,form))
+        r=bill(x)
+        assert r['coefficient']==fin['q_power_bound']['coefficient'],(r['coefficient'],fin['q_power_bound'])
+        assert r['bootstrap_chain']==fin['bootstrap']['chain'] and r['delta_tau_lower']==fin['moment']['delta_tau_lower'] and r['delta_linear']==fin['moment']['delta_linear']
+        assert r['route']['factor_counts']==fin['rational_route']['factor_counts'] and r['route']['factor_program_sha256']==fin['rational_route']['factor_program_sha256']
+        assert r['route']['denominators']==[1,2,3,6]
+        print('PASS regression: on the p = 10 receipts in',d,'the generalized bill reproduces the coefficient',r['coefficient'],
+              ', the moment gaps, the bootstrap chain and the 40-dimensional route program (sha',r['route']['factor_program_sha256'][:12]+'...)')
+    else:
+        x=json.load(open(sys.argv[2]))
+        q=x['qstar']; form=lambda i,j: Q(int(i==j),2)       # E8 form <x,y>/2 in Construction-A coordinates
+        x['route']=route_template(x['h'],q,form); x['moment_module']=mod; x['literal']=hist(x['literal'])
+        # every port: route conjugated by its W(E8) reflection word (the original's coordinate permutations are free
+        # relabelings; here the isometry is a rational program and is charged as part of the port route)
+        w=json.load(gzip.open(x['word'],'rt')); Lw=w['lines']; h=x['h']
+        ip=lambda a,b: Q(sum(u*t for u,t in zip(a,b)),2)
+        def refl(r):
+            return [[Q(int(i==j))-Q(r[i]*r[j],2)*2/ip(r,r) for j in range(h)] for i in range(h)]
+        isom={0:[[Q(int(i==j)) for j in range(h)] for i in range(h)]}; fr=[0]
+        while fr:
+            nx=[]
+            for a_ in fr:
+                for b_ in range(len(Lw)):
+                    if b_ in isom or abs(ip(Lw[a_],Lw[b_]))!=1: continue
+                    d_=[u-t for u,t in zip(Lw[a_],Lw[b_])] if ip(Lw[a_],Lw[b_])==1 else [u+t for u,t in zip(Lw[a_],Lw[b_])]
+                    isom[b_]=mm(refl(d_),isom[a_]); nx.append(b_)
+            fr=nx
+        assert len(isom)==len(Lw) and Lw[0]==q
+        ports=[]; allden=set(); maxf=0
+        for t,g in isom.items():
+            ginv=[[g[j][i]*1 for j in range(h)] for i in range(h)]          # G = I/2 is scalar, so g^-1 = g^T
+            assert mm(g,ginv)==[[Q(int(i==j)) for j in range(h)] for i in range(h)]
+            gq=[sum(g[i][j]*q[j] for j in range(h)) for i in range(h)]; assert gq==Lw[t] or gq==[-u for u in Lw[t]]
+            r_=route_template(h,q,form,g,ginv); allden|=set(r_['denominators']); maxf=max(maxf,r_['factors'])
+        assert all(d_&(d_-1)==0 for d_ in allden), allden          # powers of two: units modulo every odd prime q
+        x['route']['all_ports']=dict(ports=len(isom),max_factors=maxf,denominators=sorted(allden))
+        r=bill(x); r.pop('route') if False else None
+        json.dump({k:(v if not isinstance(v,Counter) else dict(v)) for k,v in r.items()},open(sys.argv[3],'w'),indent=1,default=str)
+        print('PASS finite bill (E8, K = %d, m = %d): coefficient %d (%d bits) < 2^80, q-power bound %s, payload prefix %d bits < 104, delta_tau %s, reference route %s; all %d port routes exact elementary programs, at most %d factors, denominators %s (powers of two: units modulo every odd q)'%(
+            x.get('Kpairs',2),x['m'],r['coefficient'],r['coefficient_bits'],r['strict_upper'],r['payload_prefix_bits'],r['delta_tau_lower'][:14],r['route']['factor_counts'],r['route']['all_ports']['ports'],r['route']['all_ports']['max_factors'],r['route']['all_ports']['denominators']))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/geometry_k.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/geometry_k.py
new file mode 100644
index 0000000000..2a05298081
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/geometry_k.py
@@ -0,0 +1,163 @@
+"""PR234's route and idle geometry for the bridged word B_K (DaysSky, assisted with Claude), generalizing PR #370's
+geometry_g.py (five stages) to 2K + 1 stages.  Every formula is geometry_g.py's; only the number of blocks and the idle
+chronology change.
+
+    H^S with S = 2K + 1 blocks, ambient form G (+) ... (+) G; p* = q* q*^T G / <q*,q*>, k* = I - p*
+    route rho(i,t)     [[g p* g^-1, g k*], [k* g^-1, p*]] on blocks (0, i), identity elsewhere; rho(0,t) = I   (i < S)
+    stage projector    P (+) K (+) ... (+) K   (K = k* on blocks 1..i)
+    data(i,kind)       rho(i,t) * stage_projector(i, frame(kind)) * rho(i,t),  kinds P (port line), K, H, 0
+Checks for every port t: rho^2 = I; data(i-1,H) = data(i,P) and data(i-1,K) = data(i,0) for i = 1..S-1; the idle
+boundary pairs of B_K (PR #363's bridged.py chronology), each commuting with a*b = a and an idempotent gap whose rank
+equals bridged.check(K, h)'s idle climb:
+    pair q = 2..K, X: (p, data(2q-3,H)) and (data(2q-2,P), data(2q-1,P));  Y: (0, data(2q-3,K)) and (data(2q-2,0), data(2q-1,0))
+    pair 1, final:  (data(2,H), I) and (data(2,K), I - p);   pair q, final: (data(2q,H), I) and (data(2q,K), I - p)
+For K = 2 this is geometry_g.py's list of eight pairs, in the same order.  Every gap of rank above floor((m - 1)/2)
+gets an explicit intermediate frame Q = b - D, D a sum of mutually orthogonal E8 root projectors r r^T G/<r,r> in a
+diagonal block where the gap is block-diagonal (dyadic entries only, so the prime-witness set stays {2}):
+a Q = Q a = a, Q b = b Q = Q, Q^2 = Q, ranks (split, rest), so the paid children obey the half-shrink guard
+2 max child < m.  Entrance census (every helper starts at frame 0): the S tau-conjugates of
+(I_h - P_sigma) (+) 0 are pairwise orthogonal and sum to I - completion(sigma); a duplicated window is rejected.
+With the third argument 'unsplit' no climb is split: the idle children are the whole climbs, and the least halving
+degree t (m^t > 2 max child^t) is reported instead of the half-shrink guard.
+usage: python3 geometry_k.py K WORD.json[.gz] [unsplit]"""
+import sys, os, json, gzip, time
+import sympy as sp
+sys.path.insert(0, os.path.join(os.path.dirname(os.path.abspath(__file__)), '..', '..', 'complex', 'code'))
+import bridged
+def eye(n): return sp.eye(n)
+class Geo:
+    def __init__(self, h, G, qstar, S):
+        self.h = h; self.S = S; self.M = S * h; self.G = G; self.q = qstar
+        nq = (qstar.T * G * qstar)[0]; assert nq != 0
+        self.pstar = qstar * (qstar.T * G) / nq; self.kstar = eye(h) - self.pstar
+        self.GG = sp.diag(*([G] * S))
+    def frame_projector(self, B):
+        if B.rows == 0: return sp.zeros(self.h)
+        return B.T * (B * self.G * B.T).inv() * B * self.G
+    def rho(self, stage, g, ginv):
+        h, M = self.h, self.M; I = eye(M)
+        if stage == 0: return I
+        I[:h, :h] = g * self.pstar * ginv; I[stage*h:(stage+1)*h, stage*h:(stage+1)*h] = self.pstar
+        I[:h, stage*h:(stage+1)*h] = g * self.kstar; I[stage*h:(stage+1)*h, :h] = self.kstar * ginv
+        return I
+    def tau(self, stage):
+        I = eye(self.M)
+        if stage:
+            for j in range(self.h): I.row_swap(j, stage * self.h + j)
+        return I
+    def stage_projector(self, stage, P):
+        A = sp.zeros(self.M); A[:self.h, :self.h] = P
+        for j in range(1, stage + 1): A[j*self.h:(j+1)*self.h, j*self.h:(j+1)*self.h] = self.kstar
+        return A
+    def intermediate(self, a, b, split, lines):
+        """Q = b - D with D a sum of mutually G-orthogonal root projectors r r^T G/<r,r> (dyadic) inside diagonal blocks
+        on which the gap b - a is block-diagonal; rank(Q - a) = split."""
+        h, M = self.h, self.M; gap = b - a; need = int(gap.trace()) - split; D = sp.zeros(M); got = 0
+        proj = [r * (r.T * self.G) / (r.T * self.G * r)[0] for r in lines]
+        for j in range(self.S - 1, 0, -1):
+            blk = slice(j * h, (j + 1) * h)
+            off = gap.copy(); off[blk, blk] = sp.zeros(h)
+            if not (off[blk, :].is_zero_matrix and off[:, blk].is_zero_matrix): continue
+            Gj = gap[blk, blk]; chosen = []
+            for e in proj:
+                if got == need: break
+                if Gj * e == e and all(e * f == sp.zeros(h) for f in chosen):
+                    chosen.append(e); D[blk, blk] = D[blk, blk] + e; got += 1
+            if got == need: break
+        assert got == need, ('no dyadic intermediate frame', need, got)
+        Q = b - D
+        assert D * D == D and D * a == a * D == sp.zeros(M) and b * D == D * b == D and Q * Q == Q
+        assert a * Q == Q * a == a and Q * b == b * Q == Q
+        assert int((Q - a).trace()) == split and int((b - Q).trace()) == need
+        assert all(sp.Rational(x).q & (sp.Rational(x).q - 1) == 0 for x in Q), 'intermediate frame not dyadic'
+        return Q
+    def check_port(self, K, qt, g, ginv, split, lines):
+        h, M, S = self.h, self.M, self.S; I = eye(M); Z = sp.zeros(M)
+        assert g * ginv == eye(h) and g.T * self.G * g == self.G, 'port map is not a G-isometry'
+        assert g * self.q == qt or g * self.q == -qt, 'port map does not send q* to the port line'
+        routes = [self.rho(i, g, ginv) for i in range(S)]
+        assert all(r * r == I for r in routes)
+        P = self.frame_projector(qt.T); assert P * P == P and P.trace() == 1
+        Ph = {'P': P, 'K': eye(h) - P, 'H': eye(h), '0': sp.zeros(h)}
+        cache = {}
+        def data(i, kind):
+            if (i, kind) not in cache: cache[i, kind] = routes[i] * self.stage_projector(i, Ph[kind]) * routes[i]
+            return cache[i, kind]
+        for i in range(1, S):
+            assert data(i-1, 'H') == data(i, 'P'); assert data(i-1, 'K') == data(i, '0')
+        p = data(0, 'P'); pairs = []
+        for q in range(2, K + 1):
+            pairs += [(p, data(2*q-3, 'H')), (Z, data(2*q-3, 'K')), (data(2*q-2, 'P'), data(2*q-1, 'P')), (data(2*q-2, '0'), data(2*q-1, '0'))]
+        pairs += [(data(2, 'H'), I), (data(2, 'K'), I - p)]
+        for q in range(2, K + 1):
+            pairs += [(data(2*q, 'H'), I), (data(2*q, 'K'), I - p)]
+        ranks = []; children = []
+        for a, b in pairs:
+            assert a * b == b * a == a; gap = b - a; assert gap * gap == gap; r = int(gap.trace()); ranks.append(r)
+            if r > split:
+                Q = self.intermediate(a, b, split, lines); children += [split, r - split]
+            else:
+                children.append(r)
+        assert p * (I - p) == Z and p + (I - p) == I
+        return ranks, children
+    def check_entrance(self, Psigma):
+        h, M, S = self.h, self.M, self.S; Z = sp.zeros(M)
+        completion = sp.diag(*([Psigma] * S)); residual = eye(M) - completion
+        assert completion * completion == completion and completion.trace() == S * Psigma.trace()
+        actual = []
+        for i in range(S):
+            t = self.tau(i); local = sp.zeros(M); local[:h, :h] = eye(h) - Psigma; actual.append(t * local * t)
+        assert sum(actual, Z) == residual
+        assert all(a * b == Z for i, a in enumerate(actual) for j, b in enumerate(actual) if i != j)
+        assert sum(actual[:S-1] + [actual[S-2]], Z) != residual
+        return True
+def expected(K, h):
+    """idle climbs of bridged.check in the order of check_port's pair list (X and Y of each climb)"""
+    idle = bridged.check(K, h)['per_pair_idle']; out = []
+    for q in range(2, K + 1):
+        a, b, _ = idle[q]; out += [a, a, b, b]
+    out += [idle[1][0]] * 2
+    for q in range(2, K + 1): out += [idle[q][2]] * 2
+    return out
+def main(K, word, unsplit=False):
+    c = json.load(gzip.open(word, 'rt') if word.endswith('.gz') else open(word))
+    assert c['form'] == '<x,y>/2' and c['h'] == 8
+    h = 8; S = 2 * K + 1; m = S * h; split = m if unsplit else (m - 1) // 2
+    G = eye(h) / 2; L = [sp.Matrix(x) for x in c['lines']]; v = len(L)
+    ip = lambda a, b: (a.T * G * b)[0]
+    def refl(r): return eye(h) - r * (r.T * G) * 2 / ip(r, r)
+    star = 0; geo = Geo(h, G, L[star], S)
+    isom = {star: (eye(h), [])}; frontier = [star]
+    while frontier:
+        nxt = []
+        for a in frontier:
+            for r in range(v):
+                if r == a: continue
+                if abs(ip(L[a], L[r])) == 1:
+                    d = L[a] - L[r] if ip(L[a], L[r]) == 1 else L[a] + L[r]
+                    if r not in isom:
+                        isom[r] = (refl(d) * isom[a][0], isom[a][1] + [d]); nxt.append(r)
+        frontier = nxt
+    assert len(isom) == v
+    want = expected(K, h); idle = None; kids = None; t0 = time.time()
+    for t in range(v):
+        g, w_ = isom[t]
+        ranks, children = geo.check_port(K, L[t], g, g.inv(), split, L)
+        if idle is None: idle, kids = ranks, children
+        assert ranks == idle == want, (ranks, want)
+        assert children == kids and (unsplit or 2 * max(children) < m)
+        if t % 30 == 0: print('  port %d/%d checked (%d reflections) %.0fs' % (t + 1, v, len(w_), time.time() - t0), flush=True)
+    nreg = 2 * v + c['R']; starts = {c['start'][r] for r in range(2 * v, nreg)}
+    assert starts == {c['start'][v]} and len(c['frames'][c['start'][v]]) == 0
+    geo.check_entrance(sp.zeros(h))
+    lay = bridged.check(K, h, split=None if (unsplit or K <= 2) else split)['blocks_per_role_pair']
+    t = 1
+    while m ** t <= 2 * max(kids) ** t: t += 1
+    assert sorted(kids) == sorted(lay * 2), (kids, lay)     # X and Y of every role pair: PR #363's priced idle blocks
+    print('PASS E8 geometry in B_%d (%d stages, m = %d): all %d ports (W(E8) reflection words), routes involutive, %d stage boundaries chained,'
+          ' idle gap ranks %s (= bridged.py), paid idle children %s (%s); entrance census {0: %d helpers}:'
+          ' %d-window completion exact, duplicate window rejected' % (K, S, m, v, S - 1, idle, kids,
+          'unsplit, halving degree %d' % t if unsplit else 'explicit dyadic intermediate frames, 2 x %d < %d' % (max(kids), m), c['R'], S))
+    if unsplit: print('   unsplit: largest idle child %d of m = %d, least halving degree t = %d (%d^%d > 2 * %d^%d)' % (max(kids), m, t, m, t, max(kids), t))
+if __name__ == '__main__':
+    main(int(sys.argv[1]), sys.argv[2], len(sys.argv) > 3 and sys.argv[3] == 'unsplit')
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/gram_frames.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/gram_frames.py
new file mode 100644
index 0000000000..b740d47295
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/gram_frames.py
@@ -0,0 +1,54 @@
+"""Exact nondegeneracy and PR #315's prime-witness rule for every frame of a PR249-format word, with the ambient Gram
+matrix as a parameter.  Generalizes PR #346's exactnd_h.py and prime_new.py (Dylan Crow, with Anthropic Claude assistance).
+  --gram triple9 : the paired-cube form G = I - J/9, integer Gram 9 B G B^t = 9 B B^t - s s^t  (exactnd_h/prime_new, verbatim)
+  --gram e8ham   : the E8 form <x,y>/2 in Construction-A (Hamming) coordinates, integer Gram 2 B G B^t = B B^t
+Checks per frame: rank(B) = dim, A.B = 0 and |A| + dim = h (when A given), det(integer Gram) != 0 (exact Bareiss), and
+the prime witness: |det| = residual * prod p^e over PR #315's allowed primes with 0 < residual < 2^80.  With --new BASE
+only frames absent from BASE are checked (prime_new.py's scope); otherwise every frame.
+usage: python3 gram_frames.py WORDDIR --gram {triple9,e8ham} --h H [--new BASEDIR] [--positive]"""
+import json, sys, argparse, importlib.util, os, collections
+ap=argparse.ArgumentParser(); ap.add_argument('word'); ap.add_argument('--gram',required=True); ap.add_argument('--h',type=int,required=True)
+ap.add_argument('--new'); ap.add_argument('--positive',action='store_true'); a=ap.parse_args()
+HERE=os.path.dirname(os.path.abspath(__file__))
+s=importlib.util.spec_from_file_location('pw',os.path.join(HERE,'..','..','pricing','prime_witnesses.py')); pw=importlib.util.module_from_spec(s); s.loader.exec_module(pw)
+def validate_record(row, dimension, determinant, allowed_primes):   # PR #315 prime_check.validate_record, verbatim logic
+    assert type(row['dimension']) is int and type(row['determinant']) is int and type(row['residual']) is int, 'exact integer witness fields'
+    assert row['dimension'] == dimension and row['determinant'] == determinant != 0, 'exact determinant mismatch or singular basis'
+    assert 0 < row['residual'] < 2**80, 'retained prime lower bound'
+    product = row['residual']
+    for prime, exponent in row['factors'].items():
+        q = int(prime); assert q in allowed_primes and type(exponent) is int and exponent > 0, 'factor shape'; product *= q**exponent
+    assert product == abs(determinant), 'factor identity'
+def gram(B):
+    if a.gram=='triple9':
+        s_=list(map(sum,B)); return [[9*sum(x*y for x,y in zip(B[i],B[j]))-s_[i]*s_[j] for j in range(len(B))] for i in range(len(B))]
+    if a.gram=='e8ham':
+        return [[sum(x*y for x,y in zip(B[i],B[j])) for j in range(len(B))] for i in range(len(B))]
+    raise SystemExit('unknown gram')
+def rank_int(B):
+    M=[r[:] for r in B]; 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]!=0),None)
+        if p is None: continue
+        M[r],M[p]=M[p],M[r]
+        for i in range(len(M)):
+            if i!=r and M[i][c]!=0: x,y=M[r][c],M[i][c]; M[i]=[u*x-w*y for u,w in zip(M[i],M[r])]
+        r+=1
+    return r
+fr=json.load(open(a.word+'/frames.json'))['frames']
+old=json.load(open(a.new+'/frames.json'))['frames'] if a.new else {}
+keys=[k for k in fr if k not in old]
+stats=collections.Counter(); primes=set(); bits=0; nonpos=0
+for k in keys:
+    B=fr[k]['B']; A=fr[k].get('A',[]); d=len(B); assert fr[k]['dim']==d
+    assert d==0 or rank_int(B)==d,('basis rank',k)
+    if A: assert all(sum(x*y for x,y in zip(r,b))==0 for r in A for b in B) and len(A)+d==a.h,('annihilator',k)
+    M=gram(B) if d else []; det=pw.det(M); assert det!=0,('degenerate frame',k)
+    if a.positive:   # positive-definite ambient form: every leading principal minor positive
+        for j in range(1,d+1):
+            if pw.det([r[:j] for r in M[:j]])<=0: nonpos+=1; break
+    powers,residual=pw.factor_witness(det); row=dict(dimension=d,determinant=det,residual=residual,factors={p:e for p,e in powers.items() if e})
+    validate_record(row,d,det,pw.PRIMES); primes.update(map(int,row['factors'])); bits=max(bits,abs(det).bit_length()); stats[d]+=1
+assert nonpos==0
+print('PASS %s Gram: %d frames checked, all nondegenerate%s; prime witnesses valid; max determinant bits %d; primes %s; by dim %s'%(
+    a.gram,sum(stats.values()),' and positive definite' if a.positive else '',bits,sorted(primes),dict(sorted(stats.items()))))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/json.hpp b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/json.hpp
new file mode 100644
index 0000000000..82d69f7c5d
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/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/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/legality_h.cpp b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/legality_h.cpp
new file mode 100644
index 0000000000..cb1233c7e9
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/legality_h.cpp
@@ -0,0 +1,13 @@
+// Generalization (Dylan Crow, with Anthropic Claude assistance): the copied-centre count is the macro NCOPY, defaulting to
+// HDIM, so the unmodified PR #346/#352 build (no -DNCOPY) is exactly the original checker. The E8 bit word has 9
+// retained totals at h = 8 (-DNCOPY=9).
+#ifndef NCOPY
+#define NCOPY HDIM
+#endif
+#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<HDIM;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()!=HDIM-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<HDIM;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!=NCOPY||era!=NCOPY)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/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/tile_k.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/tile_k.py
new file mode 100644
index 0000000000..a4635e6681
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/checkers/tile_k.py
@@ -0,0 +1,41 @@
+"""Generalized (Dylan Crow, with Anthropic Claude assistance): h, m = 5h and the replica count are arguments
+(defaults h = 20, m = 100, 60 replicas: the original).  Bridged word B_K (DaysSky, assisted with Claude): the bank
+width is m = (2K + 1) h; K = 2 is tile_g.py.  usage: tile_k.py WORDDIR K h replicas
+Exact zero-padding width-m bank tiling of the word's entrance residuals (PR #315's bank_template.tile, verbatim logic)."""
+import json, sys
+from collections import Counter
+def tile(blocks, m):
+    blocks = {w: n for w, n in blocks.items() if n}
+    assert all(0 < w <= m for w in blocks)
+    mixed = sorted(x for x in blocks if m % x)
+    def search(i, left, out):
+        if i == len(mixed):
+            if any(left[w] % (m // w) for w in left): return None
+            return out + [(tuple([w]*(m // w)), left[w]//(m // w)) for w in sorted(left) if left[w]]
+        w = mixed[i]; n = blocks[w]
+        for f in sorted(left, key=lambda x: (-left[x], x)):
+            a = next((a for a in range(m // w, 0, -1) if (m - w*a) % f == 0), None)
+            if a is None: continue
+            b = (m - w*a)//f; q, r = divmod(n, a)
+            if r and (m - w*r) % f: continue
+            t = (m - w*r)//f if r else 0
+            if q*b + t > left[f]: continue
+            rest = dict(left); rest[f] -= q*b + t
+            found = search(i + 1, rest, out + ([(tuple([w]*a + [f]*b), q)] if q else []) + ([(tuple([w]*r + [f]*t), 1)] if r else []))
+            if found is not None: return found
+        return None
+    out = search(0, {w: n for w, n in blocks.items() if not m % w}, [])
+    assert out is not None, ('no exact zero-padding tiling', blocks, m)
+    used = Counter()
+    for widths, count in out:
+        assert sum(widths) == m and count > 0
+        for x in widths: used[x] += count
+    assert used == Counter(blocks), 'every block used exactly once'
+    return tuple(out)
+d = sys.argv[1]; K = int(sys.argv[2]); h = int(sys.argv[3]); m = (2*K + 1)*h; replicas = int(sys.argv[4])
+s = json.load(open(d + '/249-states.json')); fr = json.load(open(d + '/frames.json'))
+dim = {int(k): len(v['B']) for k, v in fr['frames'].items()}; v = s['v']; n = s['n']
+res = Counter(h - dim[s['initial'][str(r)]] for r in range(2*v, n))
+pat = tile({r: replicas*c for r, c in res.items() if r > 0}, m)
+print('residual census', dict(sorted(res.items())), '| freed roles (r = 0) are deleted, not banked')
+print('PASS exact width-%d tiling with %d replicas:' % (m, replicas), pat)
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/export_records.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/export_records.py
new file mode 100644
index 0000000000..3632d37048
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/export_records.py
@@ -0,0 +1,72 @@
+"""Export a bitE8/1 word to the PR249 record format read by PR #266's official cohort checkers and PR #315's engines.
+usage: python3 export_records.py word.json[.gz] OUTDIR   ->  OUTDIR/{249-records.bin,249-states.json,frames.json}
+Records are int32 six-tuples: MOVE(0,role,old,new,rank,0), ADD(1,dst,src,1,frame,phase), COPY(2,centre,temp,frame,ZERO,rank),
+ERASE(3,centre,temp,frame,ZERO,0).  A multi-source gate becomes one ADD per source, preceded by the MOVEs of every
+register of the gate to the gate frame.  Frames: integer basis rows B (label vectors of the frame's root lines in the
+word's coordinates, a rational basis) and integer annihilator rows A (standard dot product), as PR #266 expects.
+Dylan Crow, with Anthropic Claude assistance; Apache-2.0."""
+import sys, json, gzip, struct, os
+from fractions import Fraction as Fr
+from math import gcd
+def load(p):
+    with (gzip.open(p,'rt') if p.endswith('.gz') else open(p)) as f: return json.load(f)
+c=load(sys.argv[1]); out=sys.argv[2]; os.makedirs(out,exist_ok=True)
+v,R,h=c['v'],c['R'],c['h']; n=2*v+R; lines=c['lines']
+def basis(idx):
+    rows=[]; piv=[]; B=[]
+    for i in idx:
+        x=[Fr(a) for a in lines[i]]
+        for p,r in zip(piv,rows):
+            if x[p]: f=x[p]/r[p]; x=[a-f*b for a,b in zip(x,r)]
+        nz=[k for k in range(h) if x[k]]
+        if nz: rows.append(x); piv.append(nz[0]); B.append(list(lines[i]))
+    return B,rows,piv
+def annihilator(rows,piv):
+    # rows in echelon (pivot columns piv); free columns give the null space of the row space under the dot product
+    # reduce to RREF
+    R_=[r[:] for r in rows]
+    for i,(p,r) in enumerate(zip(piv,R_)):
+        R_[i]=[a/r[p] for a in r]
+    for i,p in enumerate(piv):
+        for j in range(len(R_)):
+            if j!=i and R_[j][p]: f=R_[j][p]; R_[j]=[a-f*b for a,b in zip(R_[j],R_[i])]
+    free=[k for k in range(h) if k not in piv]; A=[]
+    for f in free:
+        a=[Fr(0)]*h; a[f]=Fr(1)
+        for i,p in enumerate(piv): a[p]=-R_[i][f]
+        L=1
+        for x in a: L=L*x.denominator//gcd(L,x.denominator)
+        ai=[int(x*L) for x in a]; g=0
+        for x in ai: g=gcd(g,abs(x))
+        A.append([x//g for x in ai])
+    return A
+frames={}
+for k,idx in enumerate(c['frames']):
+    B,rows,piv=basis(idx); A=annihilator(rows,piv) if B else [[int(i==j) for j in range(h)] for i in range(h)]
+    assert all(sum(a*b for a,b in zip(x,y))==0 for x in A for y in B) and len(A)+len(B)==h
+    frames[str(k)]=dict(dim=len(B),B=B,A=A)
+dim=[frames[str(k)]['dim'] for k in range(len(c['frames']))]
+ZERO=[k for k in range(len(dim)) if dim[k]==0]; assert len(ZERO)==1; ZERO=ZERO[0]
+cur=list(c['start']); rec=[]
+def move(r,f):
+    if cur[r]!=f: rec.append((0,r,cur[r],f,dim[f]-dim[cur[r]],0)); cur[r]=f
+def run(gates,ph):
+    for f,d,srcs in gates:
+        for r in [d]+srcs: move(r,f)
+        for s in srcs: rec.append((1,d,s,1,f,ph))
+run(c['D'],1); run(c['A'],2)
+temp=n
+for k,q in enumerate(c['ret']):
+    fq=cur[q]; rec.append((2,q,temp,fq,ZERO,dim[fq]))
+    for t,row in enumerate(c['scatter']):
+        if k in row: rec.append((1,v+t,temp,1,ZERO,3))
+    rec.append((3,q,temp,fq,ZERO,0))
+run(c['B'],4); run(c['C'],5)
+for r in range(n): move(r,c['final'][r])
+with open(out+'/249-records.bin','wb') as f:
+    for e in rec: f.write(struct.pack('<6i',*e))
+st=dict(n=n,v=v,h=h,R=R,ZERO=ZERO,initial={str(r):c['start'][r] for r in range(n)},final={str(r):c['final'][r] for r in range(n)},
+        retained_totals=c['ret'],source_owned_roles=[],regs=[])
+json.dump(st,open(out+'/249-states.json','w'),sort_keys=True,separators=(',',':'))
+json.dump(dict(frames=frames),open(out+'/frames.json','w'),sort_keys=True,separators=(',',':'))
+print('exported',len(rec),'records,',len(frames),'frames, n',n,'ZERO',ZERO)
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/independent/checkword.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/independent/checkword.py
new file mode 100644
index 0000000000..da4e0fe050
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/independent/checkword.py
@@ -0,0 +1,143 @@
+#!/usr/bin/env python3
+"""Dylan Crow, with Anthropic Claude assistance; Apache-2.0.
+usage: checkword.py WORD.json.gz PRICING_DIR
+Independent checker for 'bitE8/1' bit words (no import of the design/compile code).
+Checks: (1) labels are the 120 root lines of an even unimodular rank-8 lattice (E8);
+(2) frame legality: every register's frames nested (exact rational ranks), every gate at one common frame,
+    retained totals present and y at frame 0 at the scatter, start/final frames as required;
+(3) exact F2 semantics on all 2v+R columns (x, y, helper dirt): y_t += x_t, x and helpers restored;
+(4) Gram determinants of every frame basis (nondegeneracy) and their prime factors;
+(5) five-stage price: histogram, deficit, exact moment root (repo's moment.certify, with and without
+    the inherited 1e-16 bad envelope)."""
+import sys, json, gzip, math
+from fractions import Fraction as Fr
+from collections import Counter
+def load(p):
+    with (gzip.open(p,'rt') if p.endswith('.gz') else open(p)) as f: return json.load(f)
+c=load(sys.argv[1])
+v,h,R=c['v'],c['h'],c['R']; nreg=2*v+R
+lines=[tuple(x) for x in c['lines']]
+den=2 if c['form']=='<x,y>/2' else 4
+def ip(a,b):
+    s=sum(x*y for x,y in zip(a,b)); assert s%den==0; return s//den
+# (1) labels
+assert len(lines)==v==120 and h==8
+assert all(ip(a,a)==2 for a in lines)
+assert all(abs(ip(lines[i],lines[j]))<=1 for i in range(v) for j in range(i+1,v)), 'not distinct root lines'
+def rank(vecs):
+    rows=[[Fr(x) for x in r] for r in vecs]; rk=0; n=len(rows[0]) if rows else 0
+    for col in range(n):
+        p=next((i for i in range(rk,len(rows)) if rows[i][col]!=0),None)
+        if p is None: continue
+        rows[rk],rows[p]=rows[p],rows[rk]
+        for i in range(len(rows)):
+            if i!=rk and rows[i][col]!=0:
+                f=rows[i][col]/rows[rk][col]; rows[i]=[a-f*b for a,b in zip(rows[i],rows[rk])]
+        rk+=1
+    return rk
+def basis(idx):
+    B=[]
+    for i in idx:
+        if rank([lines[j] for j in B]+[lines[i]])>len(B): B.append(i)
+    return B
+def det(M):
+    M=[[Fr(x) for x in r] for r in M]; n=len(M); d=Fr(1)
+    for col in range(n):
+        p=next((i for i in range(col,n) if M[i][col]!=0),None)
+        if p is None: return Fr(0)
+        if p!=col: M[col],M[p]=M[p],M[col]; d=-d
+        d*=M[col][col]
+        for i in range(col+1,n):
+            f=M[i][col]/M[col][col]; M[i]=[a-f*b for a,b in zip(M[i],M[col])]
+    return d
+full=basis(range(v)); assert len(full)==8
+G8=det([[ip(lines[a],lines[b]) for b in full] for a in full])
+# lattice generated by roots: unimodular check via a Z-basis is heavier; we check det of Gram of an integral basis
+# found greedily among roots whose Gram has det 1 (exists for E8)
+import itertools
+print('labels: 120 distinct lines of norm 2 (pairwise |ip| <= 1), spanning rank 8')
+# (2) frames
+fr=c['frames']
+fb=[basis(f) for f in fr]
+fdim=[len(b) for b in fb]
+assert fdim[c['start'][v]]==0
+FULLID=[i for i,d in enumerate(fdim) if d==8]
+def inside(a,b):
+    if fdim[a]>fdim[b]: return False
+    return rank([lines[j] for j in fb[a]+fb[b]])==fdim[b]
+cache={}
+def nested(a,b):
+    k=(a,b)
+    if k not in cache: cache[k]=inside(a,b)
+    return cache[k]
+cur=list(c['start']); steps=[[] for _ in range(nreg)]
+for r in range(v): assert fdim[cur[r]]==1 and rank([lines[r]]+[lines[j] for j in fb[cur[r]]])==1, 'x start is its line'
+for r in range(v,nreg): assert fdim[cur[r]]==0
+def climb(r,f):
+    if cur[r]==f: return
+    assert nested(cur[r],f) and fdim[cur[r]]<fdim[f], ('frame not nested',r,cur[r],f)
+    steps[r].append(fdim[f]-fdim[cur[r]]); cur[r]=f
+val=[1<<i for i in range(nreg)]   # column i: x_i (i<v), y0 (v..2v-1), dirt of helper (2v..)
+def run(gates,tag):
+    for k,(f,d,srcs) in enumerate(gates):
+        regs=[d]+srcs
+        assert len(set(regs))==len(regs) and all(0<=x<nreg for x in regs),(tag,k)
+        assert all(x>=v for x in [d]), ('x register written',tag,k)   # x registers are never destinations
+        for x in regs: climb(x,f)
+        for s in srcs: val[d]^=val[s]
+run(c['D'],'D')
+assert all(fdim[cur[r]]==0 for r in range(v,nreg)),'dirt compensation must be at frame 0'
+run(c['A'],'A')
+# scatter
+ret=c['ret']; cent_rank=[]
+for q in ret: assert q>=2*v; cent_rank.append(fdim[cur[q]])
+assert all(fdim[cur[v+t]]==0 for t in range(v)),'y left frame 0 before the scatter'
+copies=[val[q] for q in ret]
+for t,row in enumerate(c['scatter']):
+    for k in row: val[v+t]^=copies[k]
+run(c['B'],'B')
+run(c['C'],'C')
+for r in range(nreg): climb(r,c['final'][r])
+for r in range(v): assert fdim[c['final'][r]]==8
+for t in range(v):
+    f=c['final'][v+t]; assert fdim[f]==7
+    assert all(ip(lines[t],lines[j])==0 for j in fb[f]),'y final frame is the cap of its label'
+for r in range(2*v,nreg): assert fdim[c['final'][r]]==8
+# (3) F2 semantics
+for s in range(v): assert val[s]==1<<s
+for t in range(v): assert val[v+t]==(1<<(v+t))|(1<<t),('target',t)
+for r in range(2*v,nreg): assert val[r]==1<<r,('helper not restored',r)
+print('legality + exact F2 on all %d columns: PASS (gates D/A/B/C = %d/%d/%d/%d)'%(nreg,len(c['D']),len(c['A']),len(c['B']),len(c['C'])))
+# (4) nondegeneracy
+used=set(c['start'])|set(c['final'])|{f for g in c['D']+c['A']+c['B']+c['C'] for f in [g[0]]}
+primes=Counter(); dets={}
+def factor(n):
+    n=abs(n); out=Counter(); p=2
+    while p*p<=n:
+        while n%p==0: out[p]+=1; n//=p
+        p+=1
+    if n>1: out[n]+=1
+    return out
+for f in used:
+    if fdim[f]==0: continue
+    B=fb[f]; d=det([[ip(lines[a],lines[b]) for b in B] for a in B])
+    assert d>0
+    dets[f]=d
+    for p in factor(d.numerator): primes[p]+=1
+print('nondegeneracy: %d used frames, all Gram dets > 0 (positive-definite form); primes in dets:'%len(dets),sorted(primes))
+# (5) price
+H=Counter()
+for r in range(nreg):
+    for s in steps[r]: H[s]+=5
+for rk in cent_rank: H[rk]+=5
+for rr in (2*h-2,h-1,2*h+2,4): H[rr]+=2*v
+m=5*h; W=4*v+R
+mass=sum(r*n for r,n in H.items())
+L=sum(cent_rank)
+print('histogram',dict(sorted(H.items())),'m',m,'W',W,'mass',mass,'deficit',m*W-mass,'(4v-5L =',4*v-5*L,')','maxchild',max(H))
+assert m*W-mass==4*v-5*L and 2*max(H)<m
+sys.path.insert(0,sys.argv[2])
+import moment
+for bad in (False,True):
+    r=moment.certify(H,m,W,bad)
+    print('bad envelope' if bad else 'no envelope ','saving in [%s, %s]'%(r['lower'][:22],r['upper'][:22]))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/independent/mutate.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/independent/mutate.py
new file mode 100644
index 0000000000..eba592fd46
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/independent/mutate.py
@@ -0,0 +1,31 @@
+"""Mutation controls for checkword.py: each mutated word must be rejected."""
+import json, gzip, subprocess, copy, sys, random, os, tempfile
+HERE=os.path.dirname(os.path.abspath(__file__))
+src=sys.argv[1]
+c=json.load(gzip.open(src,'rt'))
+rng=random.Random(3)
+muts=[]
+def m1(c):  # drop one phase-B delivery gate
+    c['B'].pop(len(c['B'])//2); return 'drop a phase-B gate'
+def m2(c):  # deliver a junk sum at a frame outside the cap: move a B gate to the full frame
+    g=c['B'][-1]; g[0]=c['final'][0]; return 'phase-B gate at the full frame (y beyond its cap)'
+def m3(c):  # remove one dirt compensation source
+    c['D'][0][2].pop(); return 'drop a dirt compensation read'
+def m4(c):  # skip a cleanup gate
+    c['C'].pop(10); return 'drop a cleanup gate'
+def m5(c):  # wrong scatter row
+    c['scatter'][5]=c['scatter'][5][1:]; return 'wrong scatter row'
+def m6(c):  # an A gate at a smaller frame than one operand already reached
+    for g in c['A']:
+        if len(c['frames'][g[0]])>3:
+            g[0]=c['start'][0]; break
+    return 'phase-A gate frame not nested'
+for f in (m1,m2,m3,m4,m5,m6):
+    cc=copy.deepcopy(c); name=f(cc)
+    tmp=os.path.join(tempfile.mkdtemp(),'mut.json.gz')
+    with gzip.open(tmp,'wt') as fh: json.dump(cc,fh)
+    r=subprocess.run([sys.executable,'-B',os.path.join(HERE,'checkword.py'),tmp,sys.argv[2]],capture_output=True,text=True)
+    ok=r.returncode!=0
+    assert ok, 'mutant accepted: '+name
+    print(('REJECTED ' if ok else 'ACCEPTED!! ')+name+' :: '+(r.stderr.strip().splitlines()[-1][:100] if ok else ''))
+print('PASS all 6 word-level negative controls rejected')
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/mutate_records.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/mutate_records.py
new file mode 100644
index 0000000000..6794516f66
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/mutate_records.py
@@ -0,0 +1,34 @@
+"""Negative controls for the official checkers on the exported E8 records: every mutant must be rejected.
+usage: mutate_records.py RECORDDIR COHORT_IN COHORT_OUT LEGALITY_BIN COLUMNS_BIN LEGALITY_NCOPY8_BIN"""
+import sys, struct, shutil, subprocess, os
+rd,cin,cout,leg,col,leg8=sys.argv[1:7]
+rec=bytearray(open(rd+'/249-records.bin','rb').read()); n=len(rec)//24
+get=lambda i: list(struct.unpack_from('<6i',rec,24*i))
+def run(mut,which):
+    tmp=cout+'-mut'; shutil.rmtree(tmp,ignore_errors=True); shutil.copytree(cout,tmp)
+    open(tmp+'/COHORT249-RECORDS.bin','wb').write(bytes(mut))
+    if which=='legality': r=subprocess.run([leg,cin,tmp,tmp+'/x.json'],capture_output=True,text=True)
+    elif which=='legality8': r=subprocess.run([leg8,cin,tmp,tmp+'/x.json'],capture_output=True,text=True)
+    else: r=subprocess.run([col,tmp+'/COHORT249-RECORDS.bin',tmp+'/x.json'],capture_output=True,text=True)
+    shutil.rmtree(tmp,ignore_errors=True)
+    return r.returncode!=0, (r.stderr.strip().splitlines() or ['?'])[-1][:70]
+def mutate(pred,change):
+    m=bytearray(rec)
+    for i in range(n):
+        e=get(i)
+        if pred(e,i):
+            change(e); struct.pack_into('<6i',m,24*i,*e); return m
+    raise SystemExit('no mutation site')
+B4=[i for i in range(n) if get(i)[0]==1 and get(i)[5]==4]
+cases=[('drop a phase-B delivery ADD (columns: defining decoder)','columns',bytes(rec[:24*B4[len(B4)//2]]+rec[24*(B4[len(B4)//2]+1):])),
+       ('ADD at a frame its registers do not stand at','legality',mutate(lambda e,i:e[0]==1 and e[5]==4,lambda e:e.__setitem__(4,0))),
+       ('MOVE with a wrong rank','legality',mutate(lambda e,i:e[0]==0 and e[4]>1,lambda e:e.__setitem__(4,e[4]-1))),
+       ('COPY with a cheaper rank','legality',mutate(lambda e,i:e[0]==2,lambda e:e.__setitem__(5,7))),
+       ('drop a dirt-compensation ADD (columns)','columns',bytes(rec[:24*[i for i in range(n) if get(i)[0]==1 and get(i)[5]==1][0]]+rec[24*([i for i in range(n) if get(i)[0]==1 and get(i)[5]==1][0]+1):])),
+       ('unchanged word with the copy count pinned to h = 8 (NCOPY unset)','legality8',bytes(rec))]
+ok=True
+for name,which,m in cases:
+    rej,msg=run(m,which); ok&=rej
+    print(('   REJECTED  ' if rej else '   ACCEPTED!! ')+name+'  ['+msg+']')
+assert ok, 'a mutant was accepted'
+print('PASS all %d record-level negative controls rejected'%len(cases))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/compile.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/compile.py
new file mode 100644
index 0000000000..86b12507ef
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/compile.py
@@ -0,0 +1,201 @@
+"""Dylan Crow, with Anthropic Claude assistance; Apache-2.0. Compile a Re-Pair hierarchy into an explicit bit word (frames = root masks) and price it.
+Registers: x 0..119, y 120..239, helpers 240.. .  Gate: (phase, frame, dst, [srcs])  dst += sum(srcs) over F2."""
+import e8lib as E, frames as Fm, price as P
+from collections import defaultdict, Counter
+V=E.V
+class Word:
+    def __init__(self):
+        self.nh=0; self.A=[]; self.B=[]; self.ret=[]
+    def helper(self):
+        r=2*V+self.nh; self.nh+=1; return r
+def X(s): return s
+def Y(t): return V+t
+def compile_h(h, low=True, drop=frozenset(), centres=None):
+    need=h.need
+    needed=set(); todo=[u for t in range(V) for u in need[t]]
+    while todo:
+        u=todo.pop()
+        if u in needed: continue
+        needed.add(u)
+        if h.kids[u]: todo.extend(h.kids[u])
+    rules=sorted((u for u in needed if h.kids[u]), key=lambda u:(h.dim[u],u))
+    # low reads: longest nested chain of needed symbols per target
+    lowset=set()
+    if low:
+        for t in range(V):
+            it=sorted(need[t], key=lambda u:(h.dim[u],u)); best={}
+            for j,u in enumerate(it):
+                b=[u]
+                for i in range(j):
+                    v=it[i]
+                    if (h.dim[v]<h.dim[u] and Fm.inside(h.frame[v],h.frame[u])) and len(best[v])+1>len(b): b=best[v]+[u]
+                best[u]=b
+            ch=max(best.values(),key=len) if best else []
+            for u in ch:
+                if h.dim[u]<7 and (t,u) not in drop: lowset.add((t,u))
+    uses=defaultdict(list)
+    for w in rules:
+        for c in h.kids[w]: uses[c].append((0,h.dim[w],h.frame[w],w))
+    for t in range(V):
+        for u in need[t]:
+            if (t,u) in lowset: uses[u].append((1,h.dim[u],h.frame[u],t))
+            else: uses[u].append((1,7,Fm.HYP[t],t))
+    chains={}; chain_of={}
+    for u in needed:
+        ev=sorted(uses[u]); cl=[]
+        for e in ev:
+            best=None
+            for i,ch in enumerate(cl):
+                last=ch[-1]
+                if last[0]==1 and last[1]==7 and last[2]!=e[2]: continue
+                if last[2]==e[2] or (last[1]<e[1] and Fm.inside(last[2],e[2])):
+                    if best is None or cl[best][-1][1]<last[1]: best=i
+            if best is None: cl.append([e]); best=len(cl)-1
+            else: cl[best].append(e)
+            chain_of[(u,e[0],e[3])]=best
+        chains[u]=cl
+    W=Word(); reg={}
+    # phase A: sources
+    for s in range(V):
+        if s not in needed: continue
+        cl=chains[s]
+        xi=None
+        for i,ch in enumerate(cl):
+            if all(e[0]==0 for e in ch): xi=i; break
+        car=[]
+        for i,ch in enumerate(cl):
+            if i==xi: reg[(s,i)]=X(s)
+            else:
+                q=W.helper(); car.append(q); reg[(s,i)]=q
+        if car: W.A.append((Fm.LINE[s],X(s),None,car))   # fan-out copy: each carrier += x_s at line
+    inplace=0
+    for w in rules:
+        F=h.frame[w]; ks=h.kids[w]
+        info=[]
+        for c in ks:
+            i=chain_of[(c,0,w)]; ch=chains[c][i]
+            info.append((c,i,ch[-1][0]==0 and ch[-1][3]==w))
+        host=None
+        for c,i,end in info:
+            if end and reg[(c,i)]>=2*V: host=(c,i); break
+        if host:
+            q=reg.pop(host); srcs=[reg[(c,i)] for c,i,_ in info if (c,i)!=host]
+            W.A.append((F,q,srcs,None)); inplace+=1
+        else:
+            q=W.helper(); W.A.append((F,q,[reg[(c,i)] for c,i,_ in info],None))
+        reg[(w,0)]=q
+        n=len(chains[w])
+        if n>1:
+            qs=[W.helper() for _ in range(n-1)]
+            W.A.append((F,q,None,qs))
+            for i,qq in enumerate(qs): reg[(w,i+1)]=qq
+    # totals
+    cent=centres or default_centres()
+    for sup in cent:
+        q=W.helper(); W.A.append((Fm.FULL,q,[X(s) for s in range(V) if sup>>s&1],None)); W.ret.append(q)
+    # phase B: deliveries sorted by frame dim
+    ev=[]
+    for t in range(V):
+        hyp=[]
+        for u in need[t]:
+            r=reg[(u,chain_of[(u,1,t)])]
+            if (t,u) in lowset: ev.append((h.dim[u],h.frame[u],Y(t),[r]))
+            else: hyp.append(r)
+        if hyp: ev.append((7,Fm.HYP[t],Y(t),hyp))
+    ev.sort(key=lambda e:(e[0],e[2]))
+    for d,F,yt,srcs in ev: W.B.append((F,yt,srcs,None))
+    W.stats=dict(R=W.nh,rules=len(rules),inplace=inplace,low=len(lowset),chains=sum(len(c) for c in chains.values()))
+    return W
+_DC=None
+def default_centres():
+    """T0 = all lines; T_i = {S : B(a_i,S)=1} for a basis a_i of E8/2E8 given by 8 lines spanning it mod 2."""
+    global _DC
+    if _DC: return _DC
+    # pick 8 lines whose images are independent mod 2 : use B-matrix rank
+    B=[[E.G[a][b]&1 for b in range(V)] for a in range(V)]
+    rows=[]; basis=[]; piv={}
+    for a in range(V):
+        m=sum(B[a][b]<<b for b in range(V)); m0=m
+        while m:
+            p=m.bit_length()-1
+            if p in piv: m^=piv[p]
+            else: piv[p]=m; basis.append(a); break
+        if len(basis)==8: break
+    _DC=[(1<<V)-1]+[sum(B[a][b]<<b for b in range(V)) for a in basis]
+    return _DC
+def decoder(cent):
+    """for each target t, the set of centres it reads so that sum = 1 + B(t,.) (as masks); verify."""
+    import itertools
+    full=(1<<V)-1
+    B=[sum((E.G[a][b]&1)<<b for b in range(V)) for a in range(V)]
+    reads=[]
+    for t in range(V):
+        want=full^B[t]
+        found=None
+        for k in range(len(cent)+1):
+            for C in itertools.combinations(range(len(cent)),k):
+                m=0
+                for c in C: m^=cent[c]
+                if m==want: found=C; break
+            if found is not None: break
+        assert found is not None
+        reads.append(found)
+    return reads
+def chains_of_word(W, cent_reads=None):
+    """legality replay: returns per-register list of frame dims, asserts nesting and common frame."""
+    nreg=2*V+W.nh
+    cur=[Fm.LINE[s] for s in range(V)]+[0]*V+[0]*W.nh
+    dims=[[1] for _ in range(V)]+[[0] for _ in range(V+W.nh)]
+    def climb(r,F):
+        if cur[r]==F: return
+        assert Fm.inside(cur[r],F) and cur[r]!=F, ('not nested',r)
+        cur[r]=F; dims[r].append(Fm.dim(F))
+    for ph in ('A','B'):
+        if ph=='B':
+            for q in W.ret: assert cur[q]==Fm.FULL
+            assert all(cur[Y(t)]==0 for t in range(V))
+        for F,dst,srcs,outs in getattr(W,ph):
+            regs=[dst]+(srcs or [])+(outs or [])
+            assert len(set(regs))==len(regs)
+            for r in regs: climb(r,F)
+    for s in range(V): climb(X(s),Fm.FULL)
+    for t in range(V): climb(Y(t),Fm.HYP[t])
+    for q in range(2*V,nreg): climb(q,Fm.FULL)
+    return dims
+def f2_check(W, need_low=None):
+    """forward F2 replay on source columns only (no dirt): y_t must end with exactly x_t (after centre reads)."""
+    val=[1<<s for s in range(V)]+[0]*V+[0]*W.nh
+    for F,dst,srcs,outs in W.A:
+        if srcs is not None:
+            for s in srcs: val[dst]^=val[s]
+        if outs is not None:
+            for o in outs: val[o]^=val[dst]
+    cent=[val[q] for q in W.ret]
+    reads=decoder(cent)
+    for t in range(V):
+        for c in reads[t]: val[Y(t)]^=cent[c]
+    for F,dst,srcs,outs in W.B:
+        if srcs is not None:
+            for s in srcs: val[dst]^=val[s]
+        if outs is not None:
+            for o in outs: val[o]^=val[dst]
+    bad=[t for t in range(V) if val[Y(t)]!=1<<t]
+    xbad=[s for s in range(V) if val[s]!=1<<s]
+    return bad,xbad
+def evaluate(W):
+    dims=chains_of_word(W)
+    steps=Counter()
+    for d in dims:
+        for a,b in zip(d,d[1:]): steps[b-a]+=1
+    s,deficit,D=P.price(steps,W.nh)
+    return s,deficit,D,steps
+if __name__=='__main__':
+    import pickle,sys
+    from repair import Hier
+    import __main__; __main__.Hier=Hier
+    h=pickle.load(open(sys.argv[1],'rb'))
+    W=compile_h(h)
+    print(W.stats)
+    print('f2 check bad targets/x:',[len(z) for z in f2_check(W)])
+    s,deficit,D,steps=evaluate(W)
+    print('R',W.nh,'saving %.6e'%s,'deficit',deficit,'D %.0f'%D,sorted(steps.items()))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/compile2.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/compile2.py
new file mode 100644
index 0000000000..a7bdfdfbe4
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/compile2.py
@@ -0,0 +1,142 @@
+"""Dylan Crow, with Anthropic Claude assistance; Apache-2.0. Compile v2: A-rules (built from sources) before the scatter, B-rules (helpers only) and deliveries after,
+interleaved by frame dimension.  Low reads at the symbol's own frame along one nested chain per target."""
+import e8lib as E, frames as Fm, price as P, compile as C
+from collections import defaultdict, Counter
+V=E.V
+def needed_symbols(h):
+    needed=set(); todo=[u for t in range(V) for u in h.need[t]]
+    while todo:
+        u=todo.pop()
+        if u in needed: continue
+        needed.add(u)
+        if h.kids[u]: todo.extend(h.kids[u])
+    return needed
+PHASEMODE=['allA']
+def phases(h,needed):
+    ph={}
+    def get(u):
+        if u<V: return 'S'
+        if u in ph: return ph[u]
+        ks=[get(c) for c in h.kids[u]]
+        if PHASEMODE[0]=='allA':
+            ph[u]='A' if all(k in ('S','A') for k in ks) else 'B'
+        else:
+            ph[u]='A' if ('S' in ks and all(k in ('S','A') for k in ks)) else 'B'
+        return ph[u]
+    for u in needed:
+        if u>=V: get(u)
+    return ph
+def choose_low(h, needed, ph, drop=frozenset(), mode='longest'):
+    lowset=set()
+    for t in range(V):
+        it=sorted(h.need[t], key=lambda u:(h.dim[u],u)); best={}
+        for j,u in enumerate(it):
+            b=[u]
+            for i in range(j):
+                v=it[i]
+                if h.dim[v]<h.dim[u] and Fm.inside(h.frame[v],h.frame[u]) and len(best[v])+1>len(b): b=best[v]+[u]
+            best[u]=b
+        ch=max(best.values(),key=len) if best else []
+        for u in ch:
+            if h.dim[u]<7 and (t,u) not in drop: lowset.add((t,u))
+    return lowset
+def compile2(h, lowset=None, drop=frozenset(), centres=None):
+    needed=needed_symbols(h); ph=phases(h,needed)
+    if lowset is None: lowset=choose_low(h,needed,ph,drop)
+    # uses: (phaseorder, dim, kind, frame, who)   phaseorder 0=A 1=B ; kind 0 rule-child 1 delivery
+    uses=defaultdict(list)
+    for w in needed:
+        if w<V: continue
+        po=0 if ph[w]=='A' else 1
+        for c in h.kids[w]: uses[c].append((po,h.dim[w],0,h.frame[w],w))
+    for t in range(V):
+        for u in h.need[t]:
+            if (t,u) in lowset: uses[u].append((1,h.dim[u],1,h.frame[u],t))
+            else: uses[u].append((1,7,1,Fm.HYP[t],t))
+    chains={}; chain_of={}
+    for u in needed:
+        ev=sorted(uses[u],key=lambda e:(e[0],e[1],e[2],e[4]))
+        cl=[]
+        for e in ev:
+            best=None
+            for i,ch in enumerate(cl):
+                last=ch[-1]
+                if last[2]==1 and last[1]==7 and last[3]!=e[3]: continue
+                if last[3]==e[3] or (last[1]<e[1] and Fm.inside(last[3],e[3])):
+                    if best is None or cl[best][-1][1]<last[1]: best=i
+            if best is None: cl.append([e]); best=len(cl)-1
+            else: cl[best].append(e)
+            chain_of[(u,e[2],e[4])]=best
+        chains[u]=cl
+    W=C.Word(); reg={}
+    # sources: x takes a chain made only of A-uses (prefer the longest); others carriers
+    for s in range(V):
+        if s not in needed: continue
+        cl=chains[s]; xi=None
+        cand=[i for i,ch in enumerate(cl) if all(e[0]==0 for e in ch)]
+        if cand: xi=max(cand,key=lambda i:len(cl[i]))
+        car=[]
+        for i in range(len(cl)):
+            if i==xi: reg[(s,i)]=C.X(s)
+            else: q=W.helper(); car.append(q); reg[(s,i)]=q
+        if car: W.A.append((Fm.LINE[s],C.X(s),None,car))
+    W.ncarrier=sum(1 for k,r in reg.items() if r>=2*V)
+    inplace=[0]; ncopy=[0]
+    def form(w,lst):
+        F=h.frame[w]; info=[]
+        for c in h.kids[w]:
+            i=chain_of[(c,0,w)]; ch=chains[c][i]
+            info.append((c,i,ch[-1][2]==0 and ch[-1][4]==w))
+        host=None
+        for c,i,end in info:
+            if end and reg[(c,i)]>=2*V: host=(c,i); break
+        if host:
+            q=reg.pop(host); lst.append((F,q,[reg[(c,i)] for c,i,_ in info if (c,i)!=host],None)); inplace[0]+=1
+        else:
+            q=W.helper(); lst.append((F,q,[reg[(c,i)] for c,i,_ in info],None))
+        reg[(w,0)]=q; n=len(chains[w])
+        if n>1:
+            qs=[W.helper() for _ in range(n-1)]; ncopy[0]+=n-1
+            lst.append((F,q,None,qs))
+            for i,qq in enumerate(qs): reg[(w,i+1)]=qq
+    Arules=sorted((w for w in needed if w>=V and ph[w]=='A'),key=lambda w:(h.dim[w],w))
+    for w in Arules: form(w,W.A)
+    cent=centres or C.default_centres()
+    for sup in cent:
+        q=W.helper(); W.A.append((Fm.FULL,q,[C.X(s) for s in range(V) if sup>>s&1],None)); W.ret.append(q)
+    # phase B events
+    ev=[]
+    for w in needed:
+        if w>=V and ph[w]=='B': ev.append((h.dim[w],0,w))
+    lowby=defaultdict(list)
+    for (t,u) in lowset: lowby[u].append(t)
+    for u in lowby: ev.append((h.dim[u],1,u))
+    for t in range(V): ev.append((7,2,t))
+    ev.sort()
+    for d,k,a in ev:
+        if k==0: form(a,W.B)
+        elif k==1:
+            u=a
+            for t in sorted(lowby[u]):
+                W.B.append((h.frame[u],C.Y(t),[reg[(u,chain_of[(u,1,t)])]],None))
+        else:
+            t=a; srcs=[reg[(u,chain_of[(u,1,t)])] for u in h.need[t] if (t,u) not in lowset]
+            if srcs: W.B.append((Fm.HYP[t],C.Y(t),srcs,None))
+    W.stats=dict(R=W.nh,carriers=W.ncarrier,Arules=len(Arules),Brules=sum(1 for w in needed if w>=V and ph[w]=='B'),
+                 inplace=inplace[0],copies=ncopy[0],low=len(lowset),chains=sum(len(c) for c in chains.values()))
+    return W
+if __name__=='__main__':
+    import pickle,sys
+    from repair import Hier
+    import __main__; __main__.Hier=Hier
+    try:
+        import ham1; __main__.SH=ham1.SH
+    except Exception: pass
+    h=pickle.load(open(sys.argv[1],'rb'))
+    if len(sys.argv)>2: PHASEMODE[0]=sys.argv[2]
+    W=compile2(h)
+    print(W.stats)
+    print('f2 check bad targets/x:',[len(z) for z in C.f2_check(W)])
+    s,deficit,D,steps=C.evaluate(W)
+    print('R',W.nh,'saving %.6e'%s,'deficit',deficit,'D %.0f'%D,sorted(steps.items()))
+    import diag; diag.diag(W)
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/e8lib.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/e8lib.py
new file mode 100644
index 0000000000..8464b956f6
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/e8lib.py
@@ -0,0 +1,79 @@
+"""Dylan Crow, with Anthropic Claude assistance; Apache-2.0. E8 root lines in Q^8 (standard coordinates, doubled to integers), F2 images, basic linear algebra."""
+import itertools
+from fractions import Fraction as Fr
+
+def roots2():
+    """E8 roots times 2 (integer vectors): 2(±e_i±e_j) and (±1)^8 with even number of minus signs."""
+    R=[]
+    for i,j in itertools.combinations(range(8),2):
+        for a in (2,-2):
+            for b in (2,-2):
+                v=[0]*8; v[i]=a; v[j]=b; R.append(tuple(v))
+    for signs in itertools.product((1,-1),repeat=8):
+        if signs.count(-1)%2==0: R.append(tuple(signs))
+    return R
+
+def ip(u,v):  # true inner product of roots given doubled coordinates
+    return sum(a*b for a,b in zip(u,v))//4
+
+import os
+def roots_hamming():
+    """E8 via Construction A from the [8,4,4] extended Hamming code: x in Z^8, x mod 2 in H8, |x|^2=4.
+    Inner product of roots = <x,y>/2. Returned scaled so that ip() (which divides by 4) works: multiply by sqrt2? no:
+    we return 2*x/sqrt... -> use integer vectors y=x and a separate scale."""
+    H=[]
+    for a in itertools.product((0,1),repeat=4):
+        g=[(1,1,1,1,0,0,0,0),(1,1,0,0,1,1,0,0),(1,0,1,0,1,0,1,0),(0,1,1,0,1,0,0,1)]
+        w=[sum(a[k]*g[k][i] for k in range(4))%2 for i in range(8)]
+        H.append(tuple(w))
+    R=[]
+    for i in range(8):
+        for sg in (2,-2):
+            v=[0]*8; v[i]=sg; R.append(tuple(v))
+    for w in H:
+        if sum(w)==4:
+            idx=[i for i in range(8) if w[i]]
+            for sg in itertools.product((1,-1),repeat=4):
+                v=[0]*8
+                for i,s_ in zip(idx,sg): v[i]=s_
+                R.append(tuple(v))
+    return R
+COORD=os.environ.get('E8COORD','std')
+if COORD=='ham':
+    ALL=[tuple(a for a in r) for r in roots_hamming()]
+    def ip(u,v): return sum(a*b for a,b in zip(u,v))//2
+else:
+    ALL=roots2()
+assert len(ALL)==240
+LINES=[]
+seen=set()
+for r in ALL:
+    if r in seen: continue
+    neg=tuple(-a for a in r); seen.add(r); seen.add(neg)
+    # canonical: first nonzero coordinate positive
+    LINES.append(r if [a for a in r if a][0]>0 else neg)
+V=len(LINES); assert V==120
+G=[[ip(LINES[a],LINES[b]) for b in range(V)] for a in range(V)]
+ORTH=[[b for b in range(V) if G[a][b]==0] for a in range(V)]
+NEIGH=[[b for b in range(V) if abs(G[a][b])==1] for a in range(V)]
+assert all(len(o)==63 and len(n)==56 for o,n in zip(ORTH,NEIGH))
+
+def rank_q(vecs):
+    """rank over Q of integer vectors"""
+    rows=[list(map(Fr,v)) for v in vecs]
+    r=0; n=len(rows[0]) if rows else 0
+    for c in range(n):
+        p=None
+        for i in range(r,len(rows)):
+            if rows[i][c]!=0: p=i;break
+        if p is None: continue
+        rows[r],rows[p]=rows[p],rows[r]
+        for i in range(len(rows)):
+            if i!=r and rows[i][c]!=0:
+                f=rows[i][c]/rows[r][c]
+                rows[i]=[x-f*y for x,y in zip(rows[i],rows[r])]
+        r+=1
+    return r
+
+def span_dim(idx):
+    return rank_q([LINES[i] for i in idx]) if idx else 0
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/frames.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/frames.py
new file mode 100644
index 0000000000..b28c3b2413
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/frames.py
@@ -0,0 +1,45 @@
+"""Dylan Crow, with Anthropic Claude assistance; Apache-2.0. Root-spanned rational subspaces of Q^8, represented by the bitmask of E8 root lines they contain."""
+import e8lib as E
+from fractions import Fraction as Fr
+V=E.V
+L=E.LINES
+_cache={}
+def _basis(idx):
+    rows=[]
+    piv=[]
+    for i in idx:
+        v=[Fr(a) for a in L[i]]
+        for (p,b) in zip(piv,rows):
+            if v[p]!=0:
+                f=v[p]/b[p]; v=[x-f*y for x,y in zip(v,b)]
+        nz=[k for k in range(8) if v[k]!=0]
+        if nz:
+            rows.append(v); piv.append(nz[0])
+    return rows,piv
+def _inspan(v,rows,piv):
+    v=[Fr(a) for a in v]
+    for (p,b) in zip(piv,rows):
+        if v[p]!=0:
+            f=v[p]/b[p]; v=[x-f*y for x,y in zip(v,b)]
+    return all(x==0 for x in v)
+def closure(mask):
+    """mask of all root lines in the rational span of the lines in mask; returns (closed_mask, dim)"""
+    r=_cache.get(mask)
+    if r is not None: return r
+    idx=[i for i in range(V) if mask>>i&1]
+    rows,piv=_basis(idx)
+    cm=0
+    for i in range(V):
+        if mask>>i&1 or _inspan(L[i],rows,piv): cm|=1<<i
+    r=(cm,len(rows))
+    _cache[mask]=r; _cache[cm]=r
+    return r
+def dim(mask): return closure(mask)[1]
+FULL=(1<<V)-1
+ZERO=0
+HYP=[sum(1<<s for s in E.ORTH[t]) for t in range(V)]
+LINE=[1<<s for s in range(V)]
+def join(a,b): return closure(a|b)[0]
+def inside(a,b): return a&~b==0   # for closed masks
+for t in range(V): assert closure(HYP[t])==(HYP[t],7)
+assert closure(FULL)==(FULL,8)
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/fullword.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/fullword.py
new file mode 100644
index 0000000000..104f01b780
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/fullword.py
@@ -0,0 +1,75 @@
+"""Producer of the bitE8 word (Dylan Crow, with Anthropic Claude assistance; Apache-2.0).
+usage: E8COORD=ham python3 fullword.py params-r865.json out.json[.gz]
+Turn a compiled Word into a complete reversible bit word (JSON 'bitE8/1'):
+   D: dirt compensation at frame 0 (y_t += helper r for every helper whose initial value reaches y_t)
+   A: phase A (word), S: scatter (y_t += copies of retained totals at frame 0), B: phase B,
+   C: cleanup at the full frame (reverse of every helper-destination gate of A and B).
+Gate = [frame_id, dst, [srcs]] meaning dst += sum(srcs) over F2."""
+import json, gzip, sys
+import e8lib as E, frames as Fm, compile as C
+V=E.V
+def build(W):
+    nreg=2*V+W.nh
+    frames={}
+    def fid(mask):
+        if mask not in frames: frames[mask]=len(frames)
+        return frames[mask]
+    fid(0); fid(Fm.FULL)
+    def flat(lst):
+        out=[]
+        for F,dst,srcs,outs in lst:
+            f=fid(F)
+            if srcs is not None: out.append([f,dst,list(srcs)])
+            if outs is not None:
+                for o in outs: out.append([f,o,[dst]])
+        return out
+    A=flat(W.A); B=flat(W.B)
+    # decoder reads
+    vals=[0]*nreg
+    cent_sup=None
+    # compute retained totals' x-content after A to derive scatter table
+    val=[1<<s for s in range(V)]+[0]*V+[0]*W.nh
+    for f,d,srcs in A:
+        for s in srcs: val[d]^=val[s]
+    cent=[val[q] for q in W.ret]
+    reads=C.decoder(cent)
+    scat=[list(r) for r in reads]
+    # dirt reaching y: symbolic over dirt columns only
+    dv=[0]*nreg
+    for r in range(2*V,nreg): dv[r]=1<<(r-2*V)
+    for f,d,srcs in A:
+        for s in srcs: dv[d]^=dv[s]
+    cdirt=[dv[q] for q in W.ret]
+    for t in range(V):
+        for c in reads[t]: dv[V+t]^=cdirt[c]
+    for f,d,srcs in B:
+        for s in srcs: dv[d]^=dv[s]
+    D=[]
+    for t in range(V):
+        m=dv[V+t]; srcs=[]
+        while m:
+            b=m&-m; r=b.bit_length()-1; m^=b; srcs.append(2*V+r)
+        if srcs: D.append([fid(0),V+t,srcs])
+    Cl=[]
+    for f,d,srcs in reversed(A+B):
+        if d>=2*V: Cl.append([fid(Fm.FULL),d,srcs])
+    fr=[None]*len(frames)
+    for mk,i in frames.items(): fr[i]=[s for s in range(V) if mk>>s&1]
+    start=[fid(Fm.LINE[s]) for s in range(V)]+[fid(0)]*V+[fid(0)]*W.nh
+    final=[fid(Fm.FULL)]*V+[fid(Fm.HYP[t]) for t in range(V)]+[fid(Fm.FULL)]*W.nh
+    return dict(format='bitE8/1',coords=E.COORD,h=8,v=V,R=W.nh,lines=[list(r) for r in E.LINES],
+                form='<x,y>/2' if E.COORD=='ham' else '<x,y>/4',frames=fr,start=start,final=final,
+                ret=list(W.ret),scatter=scat,D=D,A=A,B=B,C=Cl)
+def save(cert,path):
+    data=json.dumps(cert,separators=(',',':'),sort_keys=True).encode()
+    if path.endswith('.gz'):
+        with open(path,'wb') as fh:
+            with gzip.GzipFile(filename='',mode='wb',fileobj=fh,mtime=0) as gz: gz.write(data)
+    else: open(path,'wb').write(data)
+if __name__=='__main__':
+    import ast, ham2, compile2 as C2
+    Pd={ast.literal_eval(k):v for k,v in json.load(open(sys.argv[1]))} if sys.argv[1]!='-' else {}
+    ham2.P.clear(); ham2.P.update(Pd)
+    h=ham2.build(0,True); W=C2.compile2(h)
+    cert=build(W); save(cert,sys.argv[2])
+    print('R',W.nh,'gates D/A/B/C',len(cert['D']),len(cert['A']),len(cert['B']),len(cert['C']),'frames',len(cert['frames']))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/ham1.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/ham1.py
new file mode 100644
index 0000000000..8086649a5f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/ham1.py
@@ -0,0 +1,81 @@
+"""Dylan Crow, with Anthropic Claude assistance; Apache-2.0. Hand-structured bit-E8 hierarchy in Hamming coordinates (E8COORD=ham)."""
+import os, sys, itertools, pickle
+assert os.environ.get('E8COORD')=='ham'
+import e8lib as E, frames as Fm
+from collections import defaultdict
+V=E.V
+L=E.LINES
+idx={}
+for i,r in enumerate(L): idx[r]=i; idx[tuple(-a for a in r)]=i
+frame_line=[idx[tuple(2 if k==i else 0 for k in range(8))] for i in range(8)]
+blocks=sorted(set(tuple(k for k in range(8) if r[k]) for r in L if sum(1 for a in r if a)==4))
+assert len(blocks)==14
+def cw_lines(c): return [i for i,r in enumerate(L) if tuple(k for k in range(8) if r[k])==c]
+class SH:
+    """hierarchy with XOR semantics"""
+    def __init__(self):
+        self.content=[1<<s for s in range(V)]; self.frame=[Fm.LINE[s] for s in range(V)]; self.dim=[1]*V
+        self.kids=[None]*V; self.key={c:i for i,c in enumerate(self.content)}; self.need=[set() for _ in range(V)]
+    def sym(self,parts):
+        """symbol = XOR of parts (symbols), built left to right as a binary chain"""
+        cur=parts[0]
+        for p in parts[1:]:
+            c=self.content[cur]^self.content[p]
+            w=self.key.get(c)
+            if w is None:
+                w=len(self.content); self.content.append(c); f,d=Fm.closure(self.frame[cur]|self.frame[p])
+                self.frame.append(f); self.dim.append(d); self.kids.append((cur,p)); self.key[c]=w
+            cur=w
+        return cur
+def build(variant=0):
+    h=SH()
+    # relative sign of line r on pair (i,j)
+    def rel(r,i,j): return 1 if r[i]*r[j]>0 else -1
+    Lsym={}; Psym={}
+    for c in blocks:
+        ls=cw_lines(c)
+        for (i,j) in itertools.combinations(c,2):
+            for rho in (1,-1):
+                mem=[s for s in ls if rel(L[s],i,j)==rho]
+                assert len(mem)==4
+                # split into two pairs: pair lines that agree on the remaining pair (k,l) relative sign
+                k,l=[q for q in c if q not in (i,j)]
+                a=[s for s in mem if rel(L[s],k,l)==1]; b=[s for s in mem if rel(L[s],k,l)==-1]
+                pa=h.sym(sorted(a)); pb=h.sym(sorted(b))
+                Lsym[(c,i,j,rho)]=h.sym([pa,pb])
+    Dsym={}
+    for c in blocks:
+        i,j=c[0],c[1]
+        Dsym[c]=h.sym([Lsym[(c,i,j,1)],Lsym[(c,i,j,-1)]]+[frame_line[q] for q in c])
+    Msym={}
+    for c in blocks:
+        for (i,j) in itertools.combinations(c,2):
+            others=[c2 for c2 in blocks if c2!=c and i in c2 and j in c2]
+            assert len(others)==2
+            for rho in (1,-1):
+                Msym[(c,i,j,rho)]=h.sym([Lsym[(others[0],i,j,rho)],Lsym[(others[1],i,j,rho)]])
+    comp={c:[c2 for c2 in blocks if not set(c)&set(c2)][0] for c in blocks}
+    for c in blocks:
+        cb=comp[c]
+        for t in cw_lines(c):
+            r=L[t]
+            def rho(i,j): return -rel(r,i,j)
+            i,j,k,l=c   # level-5 pair (i,j), level-6 triangle (i,j,k)
+            need=[Dsym[cb], Msym[(c,i,j,rho(i,j))], h.sym([Msym[(c,i,k,rho(i,k))],Msym[(c,j,k,rho(j,k))]]),
+                  Msym[(c,i,l,rho(i,l))],Msym[(c,j,l,rho(j,l))],Msym[(c,k,l,rho(k,l))]]
+            need+=[s for s in cw_lines(c) if E.G[t][s]==0]
+            h.need[t]=set(need)
+    for m in range(8):
+        t=frame_line[m]
+        need=[Dsym[c] for c in blocks if m not in c]+[frame_line[q] for q in range(8) if q!=m]
+        h.need[t]=set(need)
+    # verify XOR
+    for t in range(V):
+        x=0
+        for u in h.need[t]: x^=h.content[u]
+        assert x==Fm.HYP[t],(t,bin(x^Fm.HYP[t]).count('1'))
+    return h
+if __name__=='__main__':
+    h=build()
+    pickle.dump(h,open('hier_ham1.pkl','wb'))
+    print('symbols',len(h.content)-V,'reads',sum(len(n) for n in h.need))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/ham2.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/ham2.py
new file mode 100644
index 0000000000..842f76b245
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/ham2.py
@@ -0,0 +1,131 @@
+"""Dylan Crow, with Anthropic Claude assistance; Apache-2.0. Hamming-coordinate bit-E8 design with pi-coset pairing (E8COORD=ham)."""
+import os, sys, itertools, pickle
+assert os.environ.get('E8COORD')=='ham'
+import e8lib as E, frames as Fm
+from ham1 import SH, blocks, cw_lines, frame_line, idx
+V=E.V; L=E.LINES
+def proj_dir(S,c):
+    """projection of line S onto C_c as a normalized tuple (sign-canonical) or None if zero"""
+    v=[L[S][k] if k in c else 0 for k in range(8)]
+    if not any(v): return None
+    f=[a for a in v if a][0]
+    return tuple(a if f>0 else -a for a in v)
+FRAMEOPT=[True,0,0]
+P={}
+LSKEYS=set()
+def par(k,n):
+    return P.get(k,0)%n
+def build(pairing=0, fold=True):
+    h=SH()
+    comp={c:[c2 for c2 in blocks if not set(c)&set(c2)][0] for c in blocks}
+    # L sets: lines of block c2 with projection onto C_c (c != c2, |c&c2|=2) along b-line p
+    Lsets={}
+    for c2 in blocks:
+        for c in blocks:
+            if len(set(c)&set(c2))!=2: continue
+            for S in cw_lines(c2):
+                p=proj_dir(S,c)
+                Lsets.setdefault((c2,p),set()).add(S)
+    Lsets={k:sorted(v) for k,v in Lsets.items()}
+    for k,v in Lsets.items(): assert len(v)==4,(k,v)
+    Lsym={}
+    for (c2,p),mem in Lsets.items():
+        # split into two pairs by the relative sign on the other two coordinates of c2
+        oth=[q for q in c2 if p[q]==0]
+        sp=par(('ls',c2,p),3); LSKEYS.add(('ls',c2,p))
+        if sp==0:
+            a=[s for s in mem if L[s][oth[0]]*L[s][oth[1]]>0]; b=[s for s in mem if L[s][oth[0]]*L[s][oth[1]]<0]
+        else:
+            q0=[q for q in c2 if p[q]!=0][0]
+            a=[s for s in mem if L[s][q0]*L[s][oth[sp-1]]>0]; b=[s for s in mem if L[s][q0]*L[s][oth[sp-1]]<0]
+        Lsym[(c2,p)]=h.sym([h.sym(sorted(a)),h.sym(sorted(b))])
+    Msym={}
+    for c in blocks:
+        for (c2,p),s in Lsets.items():
+            pass
+    for (c2,p) in Lsets:
+        # p is a b-line of the block c for which p's support pair lies: find blocks c containing supp(p) other than c2
+        supp=tuple(q for q in range(8) if p[q])
+        for c in blocks:
+            if c!=c2 and set(supp)<=set(c):
+                Msym.setdefault((c,p),[]).append(Lsym[(c2,p)])
+    for k in list(Msym):
+        assert len(Msym[k])==2
+        Msym[k]=h.sym(sorted(Msym[k]))
+    Dsym={}; Bcw={}
+    for c in blocks:
+        ls=cw_lines(c)
+        # E(D4(c)) = all 8 codeword lines of c + 4 frame lines
+        p=None
+        for (c2,pp),s in Lsym.items():
+            pass
+        # use two complementary L-like halves: split by relative sign on (c0,c1)
+        i,j=c[0],c[1]
+        A=[s for s in ls if L[s][i]*L[s][j]>0]; B=[s for s in ls if L[s][i]*L[s][j]<0]
+        Bcw[c]=h.sym([h.sym(sorted(A[:2])+sorted(A[2:])), h.sym(sorted(B)) ])
+        Dsym[c]=h.sym([Bcw[c]]+[frame_line[q] for q in c])
+    def bdir(u,w):
+        """the two b-line directions in the plane span(L[u],L[w]) (vectors a+-b normalized)"""
+        out=[]
+        for sg in (1,-1):
+            v=tuple(x+sg*y for x,y in zip(L[u],L[w]))
+            f=[a for a in v if a][0]
+            v=tuple(a//2 if f>0 else -a//2 for a in v)
+            out.append(v)
+        return out
+    for c in blocks:
+        cb=comp[c]
+        ls=cw_lines(c)
+        # pi-cosets: 4 mutually orthogonal lines
+        cos=[]
+        rem=set(ls)
+        while rem:
+            t=min(rem); Q=[t]+[s for s in rem if s!=t and E.G[t][s]==0]
+            assert len(Q)==4 and all(E.G[a][b]==0 for a in Q for b in Q if a!=b)
+            cos.append(Q); rem-=set(Q)
+        for Q in cos:
+            pr_=(pairing+par(('pair',c,min(Q)),3))%3
+            pairs=[(Q[0],Q[1+pr_]),tuple(q for q in Q[1:] if q!=Q[1+pr_])]
+            partner={}
+            for x,y in pairs: partner[x]=y; partner[y]=x
+            for t in Q:
+                d=partner[t]; a,b=[q for q in Q if q not in (t,d)]
+                p5,p6=sorted(bdir(a,b))
+                if par(('l5',min(t,d)),2): p5,p6=p6,p5
+                M=lambda p: Msym[(c,p)]
+                need=[Dsym[cb], M(p5), h.sym([M(p6),a,b])]
+                q1,q2=sorted(bdir(a,d)); r1,r2=sorted(bdir(b,d))
+                fo=par(('fold',t),2) if fold else 2
+                if fo==0:
+                    need+=[h.sym([M(q1),M(q2),d]), h.sym([M(r1),M(r2)])]
+                elif fo==1:
+                    need+=[h.sym([M(q1),M(q2)]), h.sym([M(r1),M(r2),d])]
+                else:
+                    need+=[h.sym([M(q1),M(q2)]), h.sym([M(r1),M(r2)]), d]
+                h.need[t]=set(need)
+    for m in range(8):
+        t=frame_line[m]
+        if not FRAMEOPT[0]:
+            h.need[t]=set([Dsym[c] for c in blocks if m not in c]+[frame_line[q] for q in range(8) if q!=m]); continue
+        avoid=[c for c in blocks if m not in c]
+        c0=avoid[(FRAMEOPT[1]+par(('fc0',m),7))%len(avoid)]
+        ns=[q for q in range(8) if q!=m and q not in c0]
+        n=ns[(FRAMEOPT[2]+par(('fn',m),3))%len(ns)]
+        A6=[q for q in range(8) if q not in (m,n)]
+        in6=[c for c in avoid if set(c)<=set(A6) and c!=c0]; assert len(in6)==2
+        top=[c for c in avoid if n in c]; assert len(top)==4
+        # pair top blocks so each pair spans a 6-dim coordinate space (always true)
+        need=[Dsym[c0], h.sym([Bcw[in6[0]],Bcw[in6[1]]]+[frame_line[q] for q in A6 if q not in c0]),
+              h.sym([Bcw[top[0]],Bcw[top[1]],frame_line[n]]), h.sym([Bcw[top[2]],Bcw[top[3]]])]
+        h.need[t]=set(need)
+    for t in range(V):
+        x=0
+        for u in h.need[t]: x^=h.content[u]
+        assert x==Fm.HYP[t],(t,bin(x^Fm.HYP[t]).count('1'))
+    return h
+if __name__=='__main__':
+    pr=int(sys.argv[1]) if len(sys.argv)>1 else 0
+    fold=(sys.argv[2]!='nofold') if len(sys.argv)>2 else True
+    h=build(pr,fold)
+    pickle.dump(h,open('hier_ham2_%d_%s.pkl'%(pr,fold),'wb'))
+    print('symbols',len(h.content)-V,'reads',sum(len(n) for n in h.need))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/params-r865.json b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/params-r865.json
new file mode 100644
index 0000000000..110b4d94d8
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/params-r865.json
@@ -0,0 +1,2082 @@
+[
+[
+"('fc0', 0)",
+3
+],
+[
+"('fc0', 1)",
+3
+],
+[
+"('fc0', 2)",
+0
+],
+[
+"('fc0', 3)",
+0
+],
+[
+"('fc0', 4)",
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+],
+[
+"('fc0', 5)",
+0
+],
+[
+"('fc0', 6)",
+2
+],
+[
+"('fc0', 7)",
+0
+],
+[
+"('fn', 0)",
+1
+],
+[
+"('fn', 1)",
+1
+],
+[
+"('fn', 2)",
+0
+],
+[
+"('fn', 3)",
+0
+],
+[
+"('fn', 4)",
+0
+],
+[
+"('fn', 5)",
+0
+],
+[
+"('fn', 6)",
+0
+],
+[
+"('fn', 7)",
+2
+],
+[
+"('fold', 10)",
+1
+],
+[
+"('fold', 100)",
+1
+],
+[
+"('fold', 101)",
+0
+],
+[
+"('fold', 102)",
+1
+],
+[
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+[
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+[
+"('fold', 11)",
+1
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+1
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+[
+"('fold', 113)",
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+[
+"('fold', 114)",
+0
+],
+[
+"('fold', 115)",
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+[
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+[
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+[
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+1
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+[
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+"('fold', 12)",
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+[
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+[
+"('fold', 18)",
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+[
+"('fold', 19)",
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+[
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+[
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+[
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+[
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+[
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+[
+"('fold', 32)",
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+[
+"('fold', 33)",
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+[
+"('fold', 34)",
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+[
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+[
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+[
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+[
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+[
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+[
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+[
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+[
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+[
+"('fold', 48)",
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+[
+"('fold', 49)",
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+[
+"('fold', 50)",
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+[
+"('fold', 51)",
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+[
+"('fold', 52)",
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+[
+"('fold', 53)",
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+[
+"('fold', 54)",
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+[
+"('fold', 55)",
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+[
+"('fold', 56)",
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+[
+"('fold', 57)",
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+[
+"('fold', 58)",
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+[
+"('fold', 59)",
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+[
+"('fold', 60)",
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+[
+"('fold', 61)",
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+[
+"('fold', 62)",
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+[
+"('fold', 63)",
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+[
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+[
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+[
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+[
+"('ls', (2, 3, 4, 5), (0, 0, 1, 0, 1, 0, 0, 0))",
+0
+],
+[
+"('ls', (2, 3, 4, 5), (0, 0, 1, 1, 0, 0, 0, 0))",
+0
+],
+[
+"('ls', (2, 3, 6, 7), (0, 0, 0, 0, 0, 0, 1, -1))",
+0
+],
+[
+"('ls', (2, 3, 6, 7), (0, 0, 0, 0, 0, 0, 1, 1))",
+0
+],
+[
+"('ls', (2, 3, 6, 7), (0, 0, 0, 1, 0, 0, -1, 0))",
+0
+],
+[
+"('ls', (2, 3, 6, 7), (0, 0, 0, 1, 0, 0, 0, -1))",
+0
+],
+[
+"('ls', (2, 3, 6, 7), (0, 0, 0, 1, 0, 0, 0, 1))",
+0
+],
+[
+"('ls', (2, 3, 6, 7), (0, 0, 0, 1, 0, 0, 1, 0))",
+0
+],
+[
+"('ls', (2, 3, 6, 7), (0, 0, 1, -1, 0, 0, 0, 0))",
+0
+],
+[
+"('ls', (2, 3, 6, 7), (0, 0, 1, 0, 0, 0, -1, 0))",
+0
+],
+[
+"('ls', (2, 3, 6, 7), (0, 0, 1, 0, 0, 0, 0, -1))",
+0
+],
+[
+"('ls', (2, 3, 6, 7), (0, 0, 1, 0, 0, 0, 0, 1))",
+0
+],
+[
+"('ls', (2, 3, 6, 7), (0, 0, 1, 0, 0, 0, 1, 0))",
+0
+],
+[
+"('ls', (2, 3, 6, 7), (0, 0, 1, 1, 0, 0, 0, 0))",
+0
+],
+[
+"('ls', (4, 5, 6, 7), (0, 0, 0, 0, 0, 0, 1, -1))",
+0
+],
+[
+"('ls', (4, 5, 6, 7), (0, 0, 0, 0, 0, 0, 1, 1))",
+0
+],
+[
+"('ls', (4, 5, 6, 7), (0, 0, 0, 0, 0, 1, -1, 0))",
+0
+],
+[
+"('ls', (4, 5, 6, 7), (0, 0, 0, 0, 0, 1, 0, -1))",
+0
+],
+[
+"('ls', (4, 5, 6, 7), (0, 0, 0, 0, 0, 1, 0, 1))",
+0
+],
+[
+"('ls', (4, 5, 6, 7), (0, 0, 0, 0, 0, 1, 1, 0))",
+0
+],
+[
+"('ls', (4, 5, 6, 7), (0, 0, 0, 0, 1, -1, 0, 0))",
+0
+],
+[
+"('ls', (4, 5, 6, 7), (0, 0, 0, 0, 1, 0, -1, 0))",
+0
+],
+[
+"('ls', (4, 5, 6, 7), (0, 0, 0, 0, 1, 0, 0, -1))",
+0
+],
+[
+"('ls', (4, 5, 6, 7), (0, 0, 0, 0, 1, 0, 0, 1))",
+0
+],
+[
+"('ls', (4, 5, 6, 7), (0, 0, 0, 0, 1, 0, 1, 0))",
+0
+],
+[
+"('ls', (4, 5, 6, 7), (0, 0, 0, 0, 1, 1, 0, 0))",
+0
+],
+[
+"('pair', (0, 1, 2, 3), 64)",
+0
+],
+[
+"('pair', (0, 1, 2, 3), 65)",
+0
+],
+[
+"('pair', (0, 1, 2, 3), 66)",
+0
+],
+[
+"('pair', (0, 1, 2, 3), 67)",
+1
+],
+[
+"('pair', (0, 1, 2, 3), 68)",
+0
+],
+[
+"('pair', (0, 1, 2, 3), 69)",
+0
+],
+[
+"('pair', (0, 1, 2, 3), 70)",
+2
+],
+[
+"('pair', (0, 1, 2, 3), 71)",
+1
+],
+[
+"('pair', (0, 1, 4, 5), 32)",
+0
+],
+[
+"('pair', (0, 1, 4, 5), 33)",
+0
+],
+[
+"('pair', (0, 1, 4, 5), 34)",
+1
+],
+[
+"('pair', (0, 1, 4, 5), 35)",
+1
+],
+[
+"('pair', (0, 1, 4, 5), 36)",
+1
+],
+[
+"('pair', (0, 1, 4, 5), 37)",
+1
+],
+[
+"('pair', (0, 1, 4, 5), 38)",
+1
+],
+[
+"('pair', (0, 1, 4, 5), 39)",
+1
+],
+[
+"('pair', (0, 1, 6, 7), 24)",
+0
+],
+[
+"('pair', (0, 1, 6, 7), 25)",
+0
+],
+[
+"('pair', (0, 1, 6, 7), 26)",
+2
+],
+[
+"('pair', (0, 1, 6, 7), 27)",
+0
+],
+[
+"('pair', (0, 1, 6, 7), 28)",
+2
+],
+[
+"('pair', (0, 1, 6, 7), 29)",
+2
+],
+[
+"('pair', (0, 1, 6, 7), 30)",
+2
+],
+[
+"('pair', (0, 1, 6, 7), 31)",
+2
+],
+[
+"('pair', (0, 2, 4, 6), 16)",
+0
+],
+[
+"('pair', (0, 2, 4, 6), 17)",
+0
+],
+[
+"('pair', (0, 2, 4, 6), 18)",
+2
+],
+[
+"('pair', (0, 2, 4, 6), 19)",
+0
+],
+[
+"('pair', (0, 2, 4, 6), 20)",
+2
+],
+[
+"('pair', (0, 2, 4, 6), 21)",
+0
+],
+[
+"('pair', (0, 2, 4, 6), 22)",
+0
+],
+[
+"('pair', (0, 2, 4, 6), 23)",
+1
+],
+[
+"('pair', (0, 2, 5, 7), 40)",
+0
+],
+[
+"('pair', (0, 2, 5, 7), 41)",
+0
+],
+[
+"('pair', (0, 2, 5, 7), 42)",
+0
+],
+[
+"('pair', (0, 2, 5, 7), 43)",
+2
+],
+[
+"('pair', (0, 2, 5, 7), 44)",
+1
+],
+[
+"('pair', (0, 2, 5, 7), 45)",
+1
+],
+[
+"('pair', (0, 2, 5, 7), 46)",
+0
+],
+[
+"('pair', (0, 2, 5, 7), 47)",
+2
+],
+[
+"('pair', (0, 3, 4, 7), 72)",
+0
+],
+[
+"('pair', (0, 3, 4, 7), 73)",
+0
+],
+[
+"('pair', (0, 3, 4, 7), 74)",
+0
+],
+[
+"('pair', (0, 3, 4, 7), 75)",
+0
+],
+[
+"('pair', (0, 3, 4, 7), 76)",
+0
+],
+[
+"('pair', (0, 3, 4, 7), 77)",
+2
+],
+[
+"('pair', (0, 3, 4, 7), 78)",
+1
+],
+[
+"('pair', (0, 3, 4, 7), 79)",
+2
+],
+[
+"('pair', (0, 3, 5, 6), 112)",
+0
+],
+[
+"('pair', (0, 3, 5, 6), 113)",
+0
+],
+[
+"('pair', (0, 3, 5, 6), 114)",
+2
+],
+[
+"('pair', (0, 3, 5, 6), 115)",
+0
+],
+[
+"('pair', (0, 3, 5, 6), 116)",
+0
+],
+[
+"('pair', (0, 3, 5, 6), 117)",
+1
+],
+[
+"('pair', (0, 3, 5, 6), 118)",
+0
+],
+[
+"('pair', (0, 3, 5, 6), 119)",
+2
+],
+[
+"('pair', (1, 2, 4, 7), 10)",
+2
+],
+[
+"('pair', (1, 2, 4, 7), 11)",
+0
+],
+[
+"('pair', (1, 2, 4, 7), 12)",
+2
+],
+[
+"('pair', (1, 2, 4, 7), 13)",
+0
+],
+[
+"('pair', (1, 2, 4, 7), 14)",
+1
+],
+[
+"('pair', (1, 2, 4, 7), 15)",
+1
+],
+[
+"('pair', (1, 2, 4, 7), 8)",
+0
+],
+[
+"('pair', (1, 2, 4, 7), 9)",
+0
+],
+[
+"('pair', (1, 2, 5, 6), 48)",
+0
+],
+[
+"('pair', (1, 2, 5, 6), 49)",
+0
+],
+[
+"('pair', (1, 2, 5, 6), 50)",
+2
+],
+[
+"('pair', (1, 2, 5, 6), 51)",
+1
+],
+[
+"('pair', (1, 2, 5, 6), 52)",
+2
+],
+[
+"('pair', (1, 2, 5, 6), 53)",
+0
+],
+[
+"('pair', (1, 2, 5, 6), 54)",
+1
+],
+[
+"('pair', (1, 2, 5, 6), 55)",
+2
+],
+[
+"('pair', (1, 3, 4, 6), 80)",
+0
+],
+[
+"('pair', (1, 3, 4, 6), 81)",
+0
+],
+[
+"('pair', (1, 3, 4, 6), 82)",
+1
+],
+[
+"('pair', (1, 3, 4, 6), 83)",
+2
+],
+[
+"('pair', (1, 3, 4, 6), 84)",
+1
+],
+[
+"('pair', (1, 3, 4, 6), 85)",
+1
+],
+[
+"('pair', (1, 3, 4, 6), 86)",
+1
+],
+[
+"('pair', (1, 3, 4, 6), 87)",
+2
+],
+[
+"('pair', (1, 3, 5, 7), 104)",
+0
+],
+[
+"('pair', (1, 3, 5, 7), 105)",
+0
+],
+[
+"('pair', (1, 3, 5, 7), 106)",
+0
+],
+[
+"('pair', (1, 3, 5, 7), 107)",
+2
+],
+[
+"('pair', (1, 3, 5, 7), 108)",
+2
+],
+[
+"('pair', (1, 3, 5, 7), 109)",
+1
+],
+[
+"('pair', (1, 3, 5, 7), 110)",
+2
+],
+[
+"('pair', (1, 3, 5, 7), 111)",
+1
+],
+[
+"('pair', (2, 3, 4, 5), 100)",
+0
+],
+[
+"('pair', (2, 3, 4, 5), 101)",
+2
+],
+[
+"('pair', (2, 3, 4, 5), 102)",
+1
+],
+[
+"('pair', (2, 3, 4, 5), 103)",
+2
+],
+[
+"('pair', (2, 3, 4, 5), 96)",
+0
+],
+[
+"('pair', (2, 3, 4, 5), 97)",
+0
+],
+[
+"('pair', (2, 3, 4, 5), 98)",
+2
+],
+[
+"('pair', (2, 3, 4, 5), 99)",
+1
+],
+[
+"('pair', (2, 3, 6, 7), 88)",
+0
+],
+[
+"('pair', (2, 3, 6, 7), 89)",
+0
+],
+[
+"('pair', (2, 3, 6, 7), 90)",
+0
+],
+[
+"('pair', (2, 3, 6, 7), 91)",
+0
+],
+[
+"('pair', (2, 3, 6, 7), 92)",
+1
+],
+[
+"('pair', (2, 3, 6, 7), 93)",
+2
+],
+[
+"('pair', (2, 3, 6, 7), 94)",
+0
+],
+[
+"('pair', (2, 3, 6, 7), 95)",
+1
+],
+[
+"('pair', (4, 5, 6, 7), 56)",
+0
+],
+[
+"('pair', (4, 5, 6, 7), 57)",
+0
+],
+[
+"('pair', (4, 5, 6, 7), 58)",
+0
+],
+[
+"('pair', (4, 5, 6, 7), 59)",
+2
+],
+[
+"('pair', (4, 5, 6, 7), 60)",
+0
+],
+[
+"('pair', (4, 5, 6, 7), 61)",
+1
+],
+[
+"('pair', (4, 5, 6, 7), 62)",
+0
+],
+[
+"('pair', (4, 5, 6, 7), 63)",
+0
+]
+]
\ No newline at end of file
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/price.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/price.py
new file mode 100644
index 0000000000..9014d97d51
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/producer/price.py
@@ -0,0 +1,23 @@
+# Dylan Crow, with Anthropic Claude assistance; Apache-2.0.
+import math
+from collections import Counter
+def price(steps, R, v=120, h=8, L=72, ncent=9, exact=True):
+    """steps: Counter of step ranks over x, y, helpers for ONE invocation (centres added here).
+    Five-stage: H5 = 5*(steps + centres) + 2v*(2h-2,h-1,2h+2,4); W = 4v+R; m=5h."""
+    m=5*h
+    H=Counter()
+    for r,n in steps.items(): H[r]+=5*n
+    H[h]+=5*ncent  # centres at full frame (rank = frame dim = h)
+    for r in (2*h-2,h-1,2*h+2,4): H[r]+=2*v
+    W=4*v+R
+    mass=sum(r*n for r,n in H.items())
+    g=lambda r:r*math.log(m/r)
+    D=sum(n*g(r) for r,n in H.items())
+    s1=(W*m-mass)/D
+    if not exact: return s1,W*m-mass,D
+    lo,hi=0.0,0.01
+    for _ in range(80):
+        s=(lo+hi)/2
+        if sum(n*(r/m)**(1-s) for r,n in H.items())>W: hi=s
+        else: lo=s
+    return lo,W*m-mass,D
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/receipts_k.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/receipts_k.py
new file mode 100644
index 0000000000..428261488b
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/receipts_k.py
@@ -0,0 +1,24 @@
+"""Assemble the finite-bill input for the E8 bit word from this run's receipts (no pinned numbers are trusted:
+every value is read from a receipt written earlier in verify.sh, and cross-checked).
+Bridged word B_K (DaysSky, assisted with Claude): K and the literal replica count T are read from kappa.json; S = 2K+1.
+usage: receipts_k.py WORD.json.gz RECORDDIR legality.json columns.json kappa.json OUT.json"""
+import sys, json, gzip, struct
+from collections import Counter
+w=json.load(gzip.open(sys.argv[1],'rt')); rd=sys.argv[2]; leg=json.load(open(sys.argv[3])); col=json.load(open(sys.argv[4])); kap=json.load(open(sys.argv[5]))
+v,R,h=w['v'],w['R'],w['h']; KP=kap.get('K',2); S=2*KP+1; m=S*h; T=kap['T']; assert kap['m']==m and kap['h']==h and (T*R)%S==0
+rec=open(rd+'/249-records.bin','rb').read(); n=len(rec)//24
+adds=sum(1 for i in range(n) if struct.unpack_from('<6i',rec,24*i)[0]==1)
+assert adds==leg['common_frame_ADDs']==col['local_scalar_additions'] and col['local_odd_scalar_additions']==adds   # every coefficient is 1
+ncopy=len(w['ret']); assert ncopy==leg['copies']==leg['erasures']==col['fresh_center_copies']//S==9
+fwd=int(col['signed_lift_prefix'][0]['cancellation_free_signed_row_l1_upper']); inv=int(col['signed_lift_prefix'][1]['cancellation_free_signed_row_l1_upper'])
+assert col['signed_lift_prefix'][0]['reverse'] is False and col['signed_lift_prefix'][1]['reverse'] is True
+stock=kap['W']; maxops=0     # W and the histogram of kappa.json already carry the T literal replicas; identity chart only
+factors=maxops+(m-1)+m; K=2*S*T*((stock-1)+R*m*factors)
+deficit=2*KP*v-S*ncopy*h
+out=dict(Kpairs=KP,h=h,m=m,v=v,R=R,T=T,stock=stock,literal=dict(kap['normalized_histogram']),ncopy=ncopy,deficit=deficit,
+         weighted=adds,unit=adds,fwd_row=fwd,inv_row=inv,K=K,coarse=kap['bit_coarse'],qstar=w['lines'][0],word=sys.argv[1],
+         provenance=dict(adds='ADD records of the exported word = legality common_frame_ADDs = columns local_scalar_additions',
+                         rows='columns_h signed_lift_prefix', K='2*S*T*((stock-1)+R*m*(maxops+(m-1)+m)), S = 2K+1, identity chart maxops 0',
+                         ncopy='retained totals of the word = COPY = ERASE count'))
+json.dump(out,open(sys.argv[6],'w'),indent=1)
+print('finite-bill input: K %d, m %d, v %d, R %d, T %d, stock %d, NCOPY %d, unit additions %d, rows %d/%d, K %d'%(KP,m,v,R,T,stock,ncopy,adds,fwd,inv,K))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/regression/stage_cohort.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/regression/stage_cohort.py
new file mode 100644
index 0000000000..f6d7afe3e6
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/bit/regression/stage_cohort.py
@@ -0,0 +1,12 @@
+"""Stage a PR249-format word for PR266's official cohort checkers (empty kernel selection, no source owners/donors)."""
+import json, os, shutil, sys
+base, word, IN, OUT = sys.argv[1:5]
+os.makedirs(IN, exist_ok=True); os.makedirs(OUT, exist_ok=True)
+st = json.load(open(word + '/249-states.json')); st.setdefault('source_owned_roles', []); st.setdefault('regs', [])
+json.dump(st, open(IN + '/249-states.json', 'w'))
+bf = json.load(open(base + '/frames.json')); wf = json.load(open(word + '/frames.json'))
+json.dump(bf, open(IN + '/frames.json', 'w')); json.dump({'donor_keys': []}, open(IN + '/249-DONOR-OWNERSHIP.json', 'w'))
+json.dump({k: v for k, v in wf['frames'].items() if k not in bf['frames']}, open(OUT + '/COHORT249-FRAMES.json', 'w'))
+json.dump({k: int(v) for k, v in st['initial'].items()}, open(OUT + '/COHORT249-INITIAL.json', 'w'))
+json.dump([], open(OUT + '/COHORT249-SELECTION.json', 'w'))
+shutil.copy(word + '/249-records.bin', OUT + '/COHORT249-RECORDS.bin')
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/complex/code/bridged.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/complex/code/bridged.py
new file mode 100644
index 0000000000..626a28614b
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/complex/code/bridged.py
@@ -0,0 +1,105 @@
+"""The bridged word B_k: k bank pairs per class, s = 2k + 1 stages of invocations, on the label space
+H + (s - 1) x H (m = s h).  Generalises Jacob Sussman's B_2 (Work/Bridge/Net.lean, Work/BridgeGeom/Net.lean; k = 2,
+five stages) to any k.
+
+Schedule (pair 1 as in B_2; every further pair borrows its first forward invocation from the pair before it):
+    stage 0  forward  pair 1   window block 0
+    stage 1  backward pair 1   window block F0
+    stage 2  forward  pair 1   window block F1
+    stage 2p-1 backward pair p   window block F(2p-2)      (p = 2..k)
+    stage 2p   forward  pair p   window block F(2p-1)
+Free twin gates (scalar +-1 additions between equal-frame roles of pairs p-1 and p):
+    after stage 2p-3:  X(p-1) += X(p),  Y(p) -= Y(p-1)
+    after stage 2p-2:  Y(p) += Y(p-1),  X(p-1) -= X(p)
+    at the end, for p = k down to 2:  Y(p-1) -= Y(p),  X(p) += X(p-1)
+
+Frames are coordinate sets in the one orthonormal basis of the class (Sussman's BBB, Work/BridgeGeom/Stage.lean:
+every bank frame of the class is a coordinate frame JB s q):
+    X enters stage t >= 1 at  block0 + qS(F0..F(t-2)),  leaves at  + qS(F(t-1));  stage 0: {l} -> block0
+    Y enters stage t >= 1 at  block0 - l + qS(F0..F(t-2)), leaves at + qS(F(t-1)); stage 0: {} -> block0 - l
+    X ends at every coordinate, Y at every coordinate but (block0, l).
+check(k, h) verifies: every climb nested; every gate between roles at equal frames; every invocation entered at its
+stage frame; final frames; each data role makes m - 1 moves; the exchange identity X_i = -y_i, Y_i = x_i (sympy).
+It returns the idle climbs (moves of data roles outside invocations) per class, as blocks."""
+import itertools
+
+def qS(blocks, h, l=0):
+    return frozenset((c, j) for c in blocks for j in range(h) if j != l)
+
+def check(k, h, l=0, split=None):
+    s = 2 * k + 1; m = s * h
+    B0 = frozenset(('b0', j) for j in range(h))
+    F = ['F%d' % i for i in range(s - 1)]
+    allc = B0 | frozenset((c, j) for c in F for j in range(h))
+    assert len(allc) == m
+    def stage_in(t, role):
+        if t == 0: return frozenset([('b0', l)]) if role == 'X' else frozenset()
+        base = B0 if role == 'X' else B0 - {('b0', l)}
+        return base | qS(F[:t - 1], h, l)
+    def stage_out(t, role):
+        if t == 0: return B0 if role == 'X' else B0 - {('b0', l)}
+        return stage_in(t, role) | qS([F[t - 1]], h, l)
+    final = {'X': allc, 'Y': allc - {('b0', l)}}
+    stages = [(0, 'F', 1), (1, 'B', 1), (2, 'F', 1)] + [x for p in range(2, k + 1) for x in ((2 * p - 1, 'B', p), (2 * p, 'F', p))]
+    cur = {(r, p): stage_in(0, r) for p in range(1, k + 1) for r in 'XY'}
+    inv_moves = {key: 0 for key in cur}; idle = {key: [] for key in cur}; log = []
+    def climb(key, new, idle_flag):
+        old = cur[key]
+        assert old <= new, ('not nested', key, len(old), len(new))
+        if new != old:
+            if idle_flag: idle[key].append(len(new) - len(old))
+            else: inv_moves[key] += len(new) - len(old)
+        cur[key] = new
+    def gate(dst, src, sign):
+        assert cur[dst] == cur[src], ('gate at unequal frames', dst, src)
+        log.append(('G', dst, src, sign))
+    for t, kind, p in stages:
+        for r in 'XY':
+            climb((r, p), stage_in(t, r), True)          # pair p reaches its stage frame (idle climb if needed)
+            climb((r, p), stage_out(t, r), False)        # the invocation
+        log.append((kind, p))
+        # twin gates of pairs (q-1, q) after stages 2q-3 and 2q-2
+        for q in range(2, k + 1):
+            if t == 2 * q - 3:
+                for r in 'XY': climb((r, q), cur[(r, q - 1)], True)
+                gate(('X', q - 1), ('X', q), 1); gate(('Y', q), ('Y', q - 1), -1)
+            if t == 2 * q - 2:
+                for r in 'XY': climb((r, q), cur[(r, q - 1)], True)
+                gate(('Y', q), ('Y', q - 1), 1); gate(('X', q - 1), ('X', q), -1)
+    for key in cur: climb(key, final[key[0]], True)
+    for q in range(k, 1, -1):
+        gate(('Y', q - 1), ('Y', q), -1); gate(('X', q), ('X', q - 1), 1)
+    for key in cur:
+        assert inv_moves[key] + sum(idle[key]) == m - 1, (key, inv_moves[key], idle[key])
+    # exchange identity (Sussman's abstraction: forward Y += X, backward X -= Y, gates are +-1 additions)
+    import sympy as sp
+    S = {}
+    for p in range(1, k + 1):
+        S[('X', p)] = sp.Symbol('x%d' % p); S[('Y', p)] = sp.Symbol('y%d' % p)
+    for op in log:
+        if op[0] == 'F': S[('Y', op[1])] = sp.expand(S[('Y', op[1])] + S[('X', op[1])])
+        elif op[0] == 'B': S[('X', op[1])] = sp.expand(S[('X', op[1])] - S[('Y', op[1])])
+        else: S[op[1]] = sp.expand(S[op[1]] + op[3] * S[op[2]])
+    for p in range(1, k + 1):
+        assert S[('X', p)] == -sp.Symbol('y%d' % p) and S[('Y', p)] == sp.Symbol('x%d' % p), (p, S[('X', p)], S[('Y', p)])
+    # idle blocks per class: X and Y of every pair have equal idle ranks
+    for p in range(1, k + 1): assert idle[('X', p)] == idle[('Y', p)], (p, idle[('X', p)], idle[('Y', p)])
+    blocks = [r for p in range(1, k + 1) for r in idle[('X', p)]]
+    if split:
+        out = []
+        for r in blocks:
+            while r > split: out.append(split); r -= split
+            if r: out.append(r)
+        blocks = out
+    return dict(stages=s, m=m, blocks_per_role_pair=blocks, gates=sum(1 for x in log if x[0] == 'G'),
+                invocations=sum(1 for x in log if x[0] in 'FB'), per_pair_idle={p: idle[('X', p)] for p in range(1, k + 1)})
+
+if __name__ == '__main__':
+    import sys
+    h = int(sys.argv[1]) if len(sys.argv) > 1 else 9
+    for k in (1, 2, 3, 4):
+        if k == 1:
+            continue
+        r = check(k, h)
+        print('k=%d stages=%d m=%d invocations=%d twin gates=%d idle per pair %s  (sum %d per role pair)' % (
+            k, r['stages'], r['m'], r['invocations'], r['gates'], r['per_pair_idle'], sum(r['blocks_per_role_pair'])))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/audit_g.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/audit_g.py
new file mode 100644
index 0000000000..719b378a0e
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/audit_g.py
@@ -0,0 +1,127 @@
+"""Independent audit of the emitted compressed nine-stage bit template, including mutation controls.
+
+Port of PR #386's audit.py (Zhihao Chen, with OpenAI Codex assistance; Apache-2.0); generalisation by eumemic with
+Anthropic Claude assistance (Apache-2.0). Every check and every mutation of the original is kept. The literals of
+PR #370's word are replaced by the given word's values: 944 frames -> the number of frames of the exported word,
+1105 local registers -> 2v + R, 865 helpers -> R, 15,465 live families -> 64v + 9R, 7,785 bank families -> 9R.
+With --regression the original literals are asserted as well.
+usage: audit_g.py --local-check DIR --out DIR [--regression]"""
+import argparse, copy, gzip, hashlib, json, struct, time
+from collections import Counter, defaultdict
+from pathlib import Path
+import sympy as S
+
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    ap.add_argument('--regression',action='store_true')
+    a=ap.parse_args(); start=time.monotonic(); out=a.out
+    blob=gzip.decompress((out/'GLOBAL-TEMPLATE.json.gz').read_bytes()); t=json.loads(blob)
+    g=json.loads((out/'GLOBAL.json').read_text()); geo=json.loads((out/'GEOMETRY.json').read_text())
+    assert hashlib.sha256(blob).hexdigest()==g['template_sha256']
+    assert t['geometry_sha256']==sha(out/'GEOMETRY.json') and t['source_record_sha256']==sha(a.local_check/'records/249-records.bin')
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    records=list(struct.iter_unpack('<6i',(a.local_check/'records/249-records.bin').read_bytes()))
+    V,R=g['v'],g['R']; LOCAL=2*V+R; DATA=2*4*V*8; LIVE=DATA+9*R      # 4 data pairs, 8 replicas, 9 stages
+    assert V==120 and DATA==7680 and g['live']==LIVE
+    I=S.eye(8); proj={}; dimensions={}
+    for key,f in fs.items():
+        k=int(key); B=S.Matrix(f['B']) if f['B'] else S.zeros(0,8)
+        P=B.T*(B*B.T).inv()*B if B.rows else S.zeros(8)
+        assert P.T==P and P*P==P and P.trace()==f['dim']
+        proj[k]=P; dimensions[k]=f['dim']
+    pairs={}
+    for op,x,y,c,r,z in records:
+        if op==0:
+            key=(y,c)
+            if key not in pairs:
+                D=proj[c]-proj[y]
+                assert proj[c]*proj[y]==proj[y] and proj[y]*proj[c]==proj[y]
+                assert D*D==D and D.trace()==r
+                # Reflected reverse has exactly the same positive projector.
+                assert (I-proj[y])-(I-proj[c])==D
+                pairs[key]=r
+    assert len(proj)==len(fs)
+    if a.regression: assert len(proj)==944
+    print('exact frame projectors',len(proj),'nested pairs',len(pairs),flush=True)
+    expected={}
+    for rev in (False,True):
+        es=[]
+        for op,x,y,c,f,z in (reversed(records) if rev else records):
+            if op==0: es.append([0,x,c if rev else y,y if rev else c,f,int(rev)])
+            elif op==1: es.append([1,x,y,-c if rev else c,f,int(rev)])
+            elif op==(3 if rev else 2): es.append([2,x,y,c,f,abs(dimensions[c]-dimensions[f]),int(rev)])
+            else: es.append([3,x,y,c,f,z,int(rev)])
+        expected['reverse' if rev else 'forward']=es
+    assert t['local_programs']==expected
+
+    def validate(q,check_profile=True):
+        assert (q['m'],q['live'],q['replicas'],q['stages'])==(64,LIVE,8,9)
+        assert q['bank_padding'] is None and q['local_programs']==expected
+        hist=Counter(); occupation=defaultdict(set); calls=set()
+        for c in q['calls']:
+            st,rep,p=c['stage'],c['replica'],c['pair']; rev=c['orientation']=='reverse'
+            assert 0<=st<9 and 0<=rep<8 and p==max(0,(st-1)//2)
+            assert rev==(st in (1,3,5,7)) and (st,rep) not in calls; calls.add((st,rep))
+            own=c['owners']; assert len(own)==LOCAL
+            assert len({(f,tuple(r)) for f,r in own})==LOCAL
+            for i,(family,route) in enumerate(own):
+                assert 0<=family<LIVE
+                if i<2*V:
+                    side=i//V; side=1-side if rev else side
+                    assert family==rep*960+(2*p+side)*120+i%120 and route==['data',st,i%120]
+                else:
+                    j=i-2*V; bank,slot=divmod(rep*R+j,8)
+                    assert family==DATA+st*R+bank and route==['bank',slot]
+                    assert slot not in occupation[family]; occupation[family].add(slot)
+            for e in q['local_programs'][c['orientation']]:
+                if e[0]==0 and e[4]: hist[e[4]]+=1
+                if e[0]==2: hist[e[5]]+=1
+        assert calls=={(s,r) for s in range(9) for r in range(8)}
+        assert set(occupation)==set(range(DATA,LIVE)) and all(s==set(range(8)) for s in occupation.values())
+        levels=[-1]*4; scalar=[1<<i for i in range(8)]; seen=[]; br=0; exchanged=False
+        for e in q['schedule']:
+            if e['kind']=='local_cover_sweep':
+                s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1 and not exchanged
+                src,dst=(2*p+1,2*p) if rev else (2*p,2*p+1)
+                scalar[dst]^=scalar[src]; levels[p]=s; seen.append(s)
+            elif e['kind']=='idle':
+                p,src,dst,r=e['pair'],e['source_level'],e['target_level'],e['rank']
+                assert levels[p]==src and src<=dst<=8
+                assert r==7*(dst-src); levels[p]=dst
+                if r: hist[r]+=1920
+            elif e['kind']=='bridge':
+                d,s=e['dst'],e['src']; assert levels[d]==levels[s] and e['coefficient'] in (-1,1)
+                scalar[2*d]^=scalar[2*s]; scalar[2*s+1]^=scalar[2*d+1]; br+=1
+            else:
+                assert e['kind']=='exchange' and levels==[8]*4 and not exchanged
+                for p in range(4): scalar[2*p],scalar[2*p+1]=scalar[2*p+1],scalar[2*p]
+                exchanged=True
+        assert exchanged and scalar==[1<<i for i in range(8)] and seen==list(range(9)) and br==9
+        assert 64*LIVE-sum(r*n for r,n in hist.items())==2496
+        if check_profile: assert hist==Counter({int(k):v for k,v in g['profile'].items()})
+        return hist
+    hist=validate(t)
+    controls=[]
+    def rejects(name,mutator):
+        q=copy.deepcopy(t); mutator(q)
+        try: validate(q)
+        except (AssertionError,KeyError,IndexError): controls.append(name)
+        else: raise AssertionError('mutation accepted: '+name)
+    rejects('omit an idle child',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='idle')))
+    rejects('omit a bridge',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='bridge')))
+    rejects('omit terminal exchange',lambda q:q['schedule'].pop())
+    rejects('remove a local invocation',lambda q:q['calls'].pop())
+    rejects('re-use a helper bank slot',lambda q:q['calls'][0]['owners'].__setitem__(241,q['calls'][0]['owners'][240]))
+    rejects('understate live stock',lambda q:q.__setitem__('live',LIVE-1))
+    rejects('omit a local paid move',lambda q:q['local_programs']['forward'].pop(next(i for i,e in enumerate(q['local_programs']['forward']) if e[0]==0)))
+    rejects('wrong reflected copy charge',lambda q:q['local_programs']['reverse'][next(i for i,e in enumerate(q['local_programs']['reverse']) if e[0]==2)].__setitem__(5,0))
+    result=dict(status='PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT',template_sha256=g['template_sha256'],
+                source_frames=len(proj),exact_nested_frame_pairs=len(pairs),exact_reflected_pairs=len(pairs),
+                orthogonal_lift_argument='Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.',
+                exact_bank_families=9*R,slots_per_bank=8,mutations_rejected=controls,
+                profile=dict(sorted(hist.items())),seconds=time.monotonic()-start)
+    (out/'AUDIT.json').write_text(json.dumps(result,indent=2)+'\n'); print(json.dumps(result),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/certify_g.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/certify_g.py
new file mode 100644
index 0000000000..9f4ae1600a
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/certify_g.py
@@ -0,0 +1,118 @@
+"""Two rational engines, finite overcharges and the strict outer assembly for the compressed nine-stage bit supplier.
+
+Port of PR #386's certify.py (Zhihao Chen, with OpenAI Codex assistance; Apache-2.0); generalisation by eumemic with
+Anthropic Claude assistance (Apache-2.0). The bit side is the original, line by line, with R and the live stock read
+from GLOBAL.json instead of PR #370's literals (865, 15,465, rank mass 987,264). The complex side is not rebuilt here:
+each cited complex coarse saving b (data/complex-b-nine.json) goes through the original selection, three-step
+bootstrap, cutoff and 47-constraint assembly, and the resulting kappa must equal the value cited with it.
+With --regression (PR #370's word) the original literals are asserted, including #386's c, b and kappa.
+usage: certify_g.py --pricing DIR --out DIR --complex-b FILE [--regression]"""
+import argparse, hashlib, importlib.util, json, math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+def load(path,name):
+    s=importlib.util.spec_from_file_location(name,path); m=importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--pricing',type=Path,required=True)
+    ap.add_argument('--out',type=Path,required=True); ap.add_argument('--complex-b',type=Path,required=True)
+    ap.add_argument('--regression',action='store_true')
+    a=ap.parse_args(); out=a.out
+    g=json.loads((out/'GLOBAL.json').read_text()); geo=json.loads((out/'GEOMETRY.json').read_text())
+    assert g['status']=='PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE'
+    assert g['geometry_sha256']==sha(out/'GEOMETRY.json')
+    audit=json.loads((out/'AUDIT.json').read_text())
+    assert audit['status']=='PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT' and audit['template_sha256']==g['template_sha256']
+    pricing=a.pricing
+    moment=load(pricing/'moment.py','bit9_moment'); other=load(pricing/'base_two_moment.py','bit9_other'); outer=load(pricing/'outer.py','bit9_outer')
+    P={int(r):n for r,n in g['profile'].items()}; m=g['m']; W=g['live']; E=sum(P.values()); mass=sum(r*n for r,n in P.items())
+    assert (m,W,m*W-mass)==(64,64*120+9*g['R'],2496)
+    if a.regression: assert (m,W,mass,m*W-mass)==(64,15465,987264,2496)
+    root=moment.certify(P,m,W,True); grid=Q(1,10**18); c=Q(int(Q(root['lower'])*10**18),10**18)
+    bm=moment.moment(P,m,W,c,True); nm=moment.moment(P,m,W,c+grid,True); assert bm[1]<1<nm[0]
+    fallback=32*m*m*E
+    _,up=other.moment(m,W,list(P.items()),c); _,bad=other.moment(m,W,[(1,fallback)],c)
+    lo,_=other.moment(m,W,list(P.items()),c+grid); lobad,_=other.moment(m,W,[(1,fallback)],c+grid)
+    assert up+Q(1,10**16)*bad<1<lo+Q(1,10**16)*lobad
+    # Compose two identical weighted recurrences. Both exact moments contract,
+    # and every grandchild is at most (42/64)^2 < 1/2 of its grandparent.
+    assert 2*max(P)**2<m*m and bm[1]**2<1
+    assert not 2*max(P)<m
+    # Conservative finite bill: inherited polynomial compiler bounds, every
+    # local/owner/copy/idle/bridge item, actual rational route factors, and the
+    # explicitly increased nine-stage payload-prefix allowance.
+    T,L,R,V,K=8,9,g['R'],120,4; physical=g['physical']; d=m*m; N=2*m
+    unit=L*T*g['local_additions']+g['bridge_additions']
+    J=8*T*L*(2*V+R)+8*(2*K*V*T)+2*g['bank_assignments']+2*g['copy_erase_episodes']
+    high=16*(d+1)**2; good=8*m*m+8; compiler=128*N**3
+    selectors=2*L*T*((W-1)+R*m*(geo['max_route_factors']+(m-1)+m))
+    prefix=int(g['global_prefix_bound']); assert prefix<1<<192
+    coefficient=unit+J*high+J*physical+E*(good+compiler)+16*m**3+g['copy_erase_episodes']+selectors+prefix+1
+    two_level_coefficient=(coefficient+1)**2*(E+1)**2
+    assert coefficient<1<<192 and two_level_coefficient<1<<512
+    row=2*(m*m+1)+9909+252; assert row==18355<20161
+    assert geo['bad_prime_factors']==[2] and geo['route_denominators']==[1,2,4]
+    # Existing complex bridge dominates the changed bit finite constants.
+    assert two_level_coefficient<1<<30000
+    if a.regression: assert c==Q(1057833103534317,10**18)
+    kappas={}
+    for s_ in json.loads(a.complex_b.read_text())['suppliers']:
+        b=Q(s_['b'])
+        eta=Q(1,10**12); beta=Q(1,10**9); cap=(1-beta)*b
+        # Seed: PR #431's two-supplier policy, strictly below (1 - beta) times both suppliers. When the bit side
+        # is the larger (c > b) it is exactly PR #386's/#425's complex-bound selection min(c, cap - grid).
+        sv=Q(int(((1-beta)*min(b,c)-grid)*10**18),10**18); assert sv<c and sv<cap
+        if c>b: assert sv==min(c,Q(int((cap-grid)*10**18),10**18))
+        binding='complex' if c>b else 'bit'
+        selected=moment.moment(P,m,W,sv,True); assert selected[1]<1
+        chain=[Q(384599,10**10)]; cutoff=[]
+        def ceilq(x): return -((-x.numerator)//x.denominator)
+        for _ in range(3):
+            old=chain[-1]; z=(1-sv)*sv+sv*old
+            gaps=[sv-z,1-z-sv,1-z-sv*(1-old),1-sv]
+            gap=min(gaps); assert old<z<sv<1-z and gap>0
+            bound=max(1,ceilq(36/gap**2),ceilq(2*(4+(two_level_coefficient-1).bit_length())/gap))
+            assert Q(bound)*gap**2>=36 and Q(bound)*gap>=2*(4+(two_level_coefficient-1).bit_length())
+            cutoff.append(dict(gap=str(gap),cutoff_log2=str(bound))); chain.append(z)
+        bridge=dict(semantic=dict(C0=dict(base=2,exponent=210000),strict_literal_gap=1),
+                    rows=dict(degree_gap=Q(10**6)-Q(51*20161,25)))
+        q=chain[-1]*(1-2*eta); bound=(1-eta)*q/(1+q); ticks=bound/grid
+        k=Q((ticks.numerator-1)//ticks.denominator,10**18)
+        asm=outer.assembly(chain[-1],b,bridge,k,eta=eta,beta=beta)
+        assert len(asm['strict_constraints'])==47 and min(asm['strict_constraints'].values())>0
+        try: outer.assembly(chain[-1],b,bridge,k+grid,eta=eta,beta=beta)
+        except AssertionError: pass
+        else: raise AssertionError('next combined grid point admitted')
+        if a.regression: assert k==Q(s_['kappa_with_pr370_bit']), (s_['name'],str(k),s_['kappa_with_pr370_bit'])
+        kappas[s_['name']]=dict(complex_coarse=str(b),selected_bit_coarse=str(sv),kappa=str(k),kappa_decimal=format(float(k),'.18f'),
+                               binding=binding,bit_headroom_percent=float(c/b-1)*100,bootstrap_chain=list(map(str,chain)),
+                               cutoff=cutoff,strict_constraints={n:str(z) for n,z in asm['strict_constraints'].items()},
+                               minimum_strict_constraint=str(min(asm['strict_constraints'].values())),
+                               next_kappa_grid_rejected=True,cited_kappa_with_pr370_bit=s_['kappa_with_pr370_bit'],source=s_['source'])
+        print('   with %s b = %.15e: kappa = %s = %.15e (%s-bound; %s; 47 strict constraints positive, next grid point rejected)'
+              % (s_['name'],float(b),k,float(k),binding,'equal to the cited value' if k==Q(s_['kappa_with_pr370_bit'])
+                 else 'cited with the PR #370 bit: %.15e, change %+.6f%%' % (float(Q(s_['kappa_with_pr370_bit'])),100*float(k/Q(s_['kappa_with_pr370_bit'])-1))),flush=True)
+    if a.regression: assert kappas['pr386']['kappa']=='998243154231047/1000000000000000000'
+    result=dict(status='PASS_COMPRESSED_NINE_STAGE_BIT_SUPPLIER',
+                bit_coarse=str(c),bit_coarse_decimal=format(float(c),'.18f'),m=m,live=W,R=R,
+                bit_moment_interval=list(map(str,bm)),next_bit_grid_rejected=True,
+                two_rational_engines=True,composed_moment_upper=str(bm[1]**2),halving_depth=2,maxchild=max(P),
+                local_and_global_bit_sha256=sha(out/'GLOBAL.json'),independent_bit_audit_sha256=sha(out/'AUDIT.json'),
+                finite=dict(unit_additions=unit,route_items=J,selector_calls=selectors,coefficient=str(coefficient),
+                            coefficient_bits=coefficient.bit_length(),two_level_coefficient=str(two_level_coefficient),
+                            two_level_coefficient_bits=two_level_coefficient.bit_length(),charged_bound_bits=512,
+                            payload_prefix_bits=prefix.bit_length(),charged_payload_prefix_bits=192,
+                            row_coefficient=row,retained_row_coefficient=20161),
+                kappa_with_cited_complex=kappas,
+                retained_obligations=['PR370 E8 local bit and nine copied-total admission',
+                    'All-size weighted bit compiler, prime/tape/precision and analytic transfer interfaces',
+                    'The cited complex suppliers and their own interfaces (not rebuilt here)'],
+                scope='Conditional finite construction and exact arithmetic assembly. No Lean proof or priority claim; no enumeration of the entire orthogonal cover.')
+    (out/'BIT-NINE.json').write_text(json.dumps(result,indent=2)+'\n')
+    print('PASS compressed nine-stage bit coarse saving c = %s = %.15e (m 64, live %d, two engines, next grid point rejected, two-level halving, finite coefficient %d bits)'
+          % (c,float(c),W,two_level_coefficient.bit_length()),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/cited.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/cited.py
new file mode 100644
index 0000000000..3aedb7a5c5
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/cited.py
@@ -0,0 +1,26 @@
+"""Bind the cited complex suppliers of data/complex-b-nine.json to the PRs' own receipts (vendored byte-identical,
+git blob ids in SOURCE-pr386.json, SOURCE-pr425.json, SOURCE-pr431.json): b and the PR's own kappa must equal the
+receipt fields exactly.
+usage: cited.py COMPLEX_B.json CONTROLS_DIR
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import json
+import sys
+from fractions import Fraction as Q
+from pathlib import Path
+
+cited = {s["name"]: s for s in json.loads(Path(sys.argv[1]).read_text())["suppliers"]}
+d = Path(sys.argv[2])
+receipts = {
+    "pr386": (d / "pr386/COMBINED.json", "complex_coarse", "kappa", "PASS_CONDITIONAL_COMBINED_KAPPA_ABOVE_2_POW_MINUS_10"),
+    "pr425": (d / "pr425/FINAL.json", "complex_b", "kappa", "PASS_FRESH_CONDITIONAL_MUTABLE_BASIS_HAMMING_COMPLEX"),
+    "pr431": (d / "pr431/VALIDATION-LOCAL.json", "complex_b", "kappa", "PASS_FULL_HAMMING_FRAME_RETIMING_AND_SOURCE425_REPLAY"),
+}
+assert set(cited) == set(receipts)
+for name, (path, kb, kk, status) in receipts.items():
+    r = json.loads(path.read_text())
+    assert r["status"] == status, (name, r["status"])
+    assert Q(r[kb]) == Q(cited[name]["b"]) and Q(r[kk]) == Q(cited[name]["kappa_with_pr370_bit"]), name
+    bit = r.get("bit_c", r.get("bit_coarse"))
+    assert Q(bit) == Q(1057833103534317, 10 ** 18), (name, bit)
+    print("   %s: b = %s and kappa = %s equal %s/%s (status %s; paired there with PR #370's bit c = %s)"
+          % (name, cited[name]["b"], cited[name]["kappa_with_pr370_bit"], path.parent.name, path.name, status, bit))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/compose433.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/compose433.py
new file mode 100644
index 0000000000..b2f3fb6ba1
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/compose433.py
@@ -0,0 +1,173 @@
+"""This word's bit side composed with PR #433's complex supplier, with PR #433's own bit pricing, finite invoice and
+outer tail (icekylinx's code/bit_price.py and code/combined.py, ported line by line onto this package's receipts).
+
+Bit price (#433 bit_price.py): PR #315's moment.certify with the inherited 10^-16 bad-branch allowance; c is its
+  10^-24-grid lower endpoint; the second engine (base_two_moment, same allowance) must put the lower endpoint below 1
+  and the upper endpoint above 1.
+Finite invoice (#433 combined.py): #386's coefficient with the fresh prefix bound charged at the next multiple of 64
+  bits (at most 256), two-level coefficient below 2^512, row coefficient 18,355 < 20,161.
+Tail (#433 combined.py): eta = beta = 10^-18, seed s = min(c, (1 - beta) b) - 10^-24, six bootstrap levels with the
+  512-bit cutoff, kappa = the last 10^-18 grid point below (1 - eta) q / (1 + q), q = a_6 (1 - 2 eta); PR #315's outer
+  assembly with its 47 strict inequalities; next grid point, zero eta, zero beta and unit beta rejected.
+Controls: PR #433's stated R758 profile must price to PR #433's bit c, and (that c, PR #433's b) must give PR #433's
+  kappa, before this word is composed.
+usage: compose433.py --pricing DIR --out DIR --cited FILE --receipt CERTIFICATE.json
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import argparse
+import hashlib
+import importlib.util
+import json
+from fractions import Fraction as Q
+from pathlib import Path
+
+
+def load(path, name):
+    s = importlib.util.spec_from_file_location(name, path)
+    m = importlib.util.module_from_spec(s)
+    s.loader.exec_module(m)
+    return m
+
+
+def sha(p):
+    return hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+ap = argparse.ArgumentParser()
+ap.add_argument("--pricing", type=Path, required=True)
+ap.add_argument("--out", type=Path, required=True)
+ap.add_argument("--cited", type=Path, required=True)
+ap.add_argument("--receipt", type=Path, required=True)
+a = ap.parse_args()
+M = load(a.pricing / "moment.py", "c433_moment")
+Other = load(a.pricing / "base_two_moment.py", "c433_other")
+Outer = load(a.pricing / "outer.py", "c433_outer")
+cited = json.loads(a.cited.read_text())
+cert = json.loads(a.receipt.read_text())
+assert cert["status"] == "PASS_CONDITIONAL_SPLIT_CENTRE_ASSEMBLY" and cert["binding_component"] == "bit"
+assert (cert["complex_lower"], cert["bit_lower"], cert["kappa"]) == (cited["b"], cited["bit_c"], cited["kappa"])
+grid = Q(1, 10 ** 18)
+
+
+def price(P, m, W):
+    """#433 bit_price.py: 10^-24 lower endpoint of PR #315's certify (bad-branch allowance), second engine check"""
+    root = M.certify(P, m, W, True)
+    lo, hi = Q(root["lower"]), Q(root["upper"])
+    fb = 32 * m * m * sum(P.values())
+
+    def other(x):
+        l, u = Other.moment(m, W, list(P.items()), x)
+        p, q = Other.moment(m, W, [(1, fb)], x)
+        return l + p / 10 ** 16, u + q / 10 ** 16
+    assert other(lo)[1] < 1 < other(hi)[0]
+    lo2, hi2 = Other.moment(m, W, list(P.items()), lo)
+    bl, bh = Other.moment(m, W, [(1, fb)], lo)
+    assert hi2 + bh / 10 ** 16 < 1                      # #433 combined.py's check at c
+    return lo, hi
+
+
+def tail(c, b):
+    """#433 combined.py: six fixed bootstrap levels and the 47-inequality outer assembly"""
+    eta = beta = Q(1, 10 ** 18)
+    s = min(c, (1 - beta) * b) - Q(1, 10 ** 24)
+    assert 0 < s < c and s < (1 - beta) * b
+    chain = [Q(384599, 10 ** 10)]
+    cutoffs = []
+
+    def ceil(x):
+        return -((-x.numerator) // x.denominator)
+    for _ in range(6):
+        old = chain[-1]
+        z = (1 - s) * s + s * old
+        gap = min(s - z, 1 - z - s, 1 - z - s * (1 - old), 1 - s)
+        assert old < z < s < 1 - z and gap > 0
+        cutoff = max(ceil(36 / gap ** 2), ceil(2 * (4 + 512) / gap))
+        assert cutoff * gap ** 2 >= 36 and cutoff * gap >= 2 * (4 + 512)
+        cutoffs.append(dict(gap=str(gap), cutoff_log2=str(cutoff)))
+        chain.append(z)
+    q = chain[-1] * (1 - 2 * eta)
+    ticks = (1 - eta) * q / (1 + q) / grid
+    k = grid * ((ticks.numerator - 1) // ticks.denominator)
+    bridge = {"semantic": {"C0": {"base": 2, "exponent": 210000}, "strict_literal_gap": 1},
+              "rows": {"degree_gap": Q(10 ** 6) - Q(51 * 20161, 25)}}
+    asm = Outer.assembly(chain[-1], b, bridge, k, eta=eta, beta=beta)
+    assert len(asm["strict_constraints"]) == 47 and all(x > 0 for x in asm["strict_constraints"].values())
+    rejected = []
+    for name, kk, ee, bb in [("next_grid", k + grid, eta, beta), ("zero_eta", k, Q(0), beta),
+                             ("zero_beta", k, eta, Q(0)), ("unit_beta", k, eta, Q(1))]:
+        try:
+            Outer.assembly(chain[-1], b, bridge, kk, eta=ee, beta=bb)
+        except AssertionError:
+            rejected.append(name)
+        else:
+            raise AssertionError(name)
+    binding = "bit" if c < (1 - beta) * b else "complex"
+    return k, binding, rejected, cutoffs, asm
+
+
+b = Q(cited["b"])
+# control 1: PR #433's stated R758 profile, priced by the same code, gives PR #433's bit c
+L433 = {int(r): n for r, n in cited["bit_local_profile"].items()}
+R433 = cited["bit_R"]
+P433 = {r: 72 * n for r, n in L433.items()}
+for r, n in ((7, 48 * 120), (14, 32 * 120), (28, 32 * 120), (42, 32 * 120)):
+    P433[r] = P433.get(r, 0) + n
+W433 = 64 * 120 + 9 * R433
+assert sum(r * n for r, n in L433.items()) == 8 * R433 + 72 + 2 * 120 * 7
+assert 64 * W433 - sum(r * n for r, n in P433.items()) == 2496
+c433, _ = price(P433, 64, W433)
+assert c433 == Q(cited["bit_c"]), (str(c433), cited["bit_c"])
+# control 2: PR #433's (c, b) through the tail gives PR #433's kappa
+k433, bind433, _, _, _ = tail(c433, b)
+assert k433 == Q(cited["kappa"]) and bind433 == "bit", str(k433)
+print("   control: PR #433's R758 profile prices to c = %s (= PR #433 bit_lower); with b = %s the tail gives kappa = %s"
+      " (= PR #433, bit-bound)" % (c433, b, k433), flush=True)
+# this word: the compressed nine-stage receipts of global_word_g.py / audit_g.py, #433's invoice and tail
+out = a.out
+g = json.loads((out / "GLOBAL.json").read_text())
+geo = json.loads((out / "GEOMETRY.json").read_text())
+audit = json.loads((out / "AUDIT.json").read_text())
+assert audit["template_sha256"] == g["template_sha256"] and len(audit["mutations_rejected"]) == 8
+P = {int(r): z for r, z in audit["profile"].items()}
+m, W = 64, g["live"]
+E = sum(P.values())
+T, L, R, V, K = 8, 9, g["R"], 120, 4
+mass = sum(r * z for r, z in P.items())
+assert m * W - mass == 2496 and W == 64 * V + 9 * R
+physical = g["physical"]
+d = m * m
+N = 2 * m
+unit = L * T * g["local_additions"] + g["bridge_additions"]
+J = 8 * T * L * (2 * V + R) + 8 * (2 * K * V * T) + 2 * g["bank_assignments"] + 2 * g["copy_erase_episodes"]
+high = 16 * (d + 1) ** 2
+good = 8 * m * m + 8
+compiler = 128 * N ** 3
+selectors = 2 * L * T * ((W - 1) + R * m * (geo["max_route_factors"] + (m - 1) + m))
+prefix = int(g["global_prefix_bound"])
+charged_prefix = 64 * ((prefix.bit_length() + 63) // 64)
+assert prefix < 1 << charged_prefix <= 1 << 256
+coefficient = unit + J * high + J * physical + E * (good + compiler) + 16 * m ** 3 + g["copy_erase_episodes"] + selectors + prefix + 1
+two = (coefficient + 1) ** 2 * (E + 1) ** 2
+assert two < 1 << 512 and 2 * max(P) ** 2 < m * m
+row = 2 * (m * m + 1) + 9909 + 252
+assert row == 18355 < 20161
+assert geo["bad_prime_factors"] == [2] and geo["route_denominators"] == [1, 2, 4]
+c, chi = price(P, m, W)
+k, binding, rejected, cutoffs, asm = tail(c, b)
+result = dict(status="PASS_BIT_SIDE_COMPOSED_WITH_PR433_COMPLEX", bit_lower=str(c), bit_upper=str(chi),
+              bit_lower_decimal=format(float(c), ".24f"), complex_lower=str(b), kappa=str(k),
+              kappa_decimal=format(float(k), ".18f"), binding_component=binding,
+              gain_over_pr433_percent=float(100 * (k / Q(cited["kappa"]) - 1)),
+              bit_gain_over_pr433_percent=float(100 * (c / Q(cited["bit_c"]) - 1)),
+              bit_invoice=dict(prefix_bits=prefix.bit_length(), charged_prefix_bits=charged_prefix,
+                               coefficient_bits=coefficient.bit_length(), two_level_coefficient_bits=two.bit_length(),
+                               charged_two_level_coefficient_bits=512, row_coefficient=row, live=W, physical=physical),
+              strict_outer_constraints={n: str(x) for n, x in asm["strict_constraints"].items()},
+              minimum_strict_constraint=str(min(asm["strict_constraints"].values())), outer_controls=rejected,
+              bootstrap=cutoffs, bit_global_sha256=sha(out / "GLOBAL.json"), bit_audit_sha256=sha(out / "AUDIT.json"),
+              controls=dict(pr433_bit_c=str(c433), pr433_kappa=str(k433)), source=cited["source"])
+(out / "COMPOSED-433.json").write_text(json.dumps(result, indent=2) + "\n")
+print("PASS this word with PR #433's bit engine and invoice: c = %s = %.24f (prefix %d bits, charged %d; two-level %d"
+      " bits < 512)" % (c, float(c), prefix.bit_length(), charged_prefix, two.bit_length()), flush=True)
+print("PASS composed with PR #433's complex b = %s: kappa = %s = %.18f (%s-bound; PR #433: %s, %+.6f%%; 47 strict"
+      " inequalities, next grid point, zero eta, zero beta and unit beta rejected)"
+      % (b, k, float(k), binding, cited["kappa"], result["gain_over_pr433_percent"]), flush=True)
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/geometry.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/geometry.py
new file mode 100644
index 0000000000..91594e0223
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/geometry.py
@@ -0,0 +1,121 @@
+"""Exact compressed nine-stage E8 bit geometry; no external research fetches.
+
+Prepared by Zhihao Chen with OpenAI Codex assistance, Apache-2.0.
+Uses the E8 root data and port-reflection construction credited to PR #370.
+"""
+import argparse, gzip, hashlib, json, time
+from pathlib import Path
+import sympy as S
+
+def dump(p, x): p.write_text(json.dumps(x,indent=2,default=str)+'\n')
+def digest(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def factor(a):
+    """Exact elementary factorization, reconstructed from the identity."""
+    n=a.rows; z=a.copy(); ops=[]
+    for j in range(n):
+        p=next(i for i in range(j,n) if z[i,j])
+        if p!=j: z.row_swap(p,j); ops.append(['swap',p,j,None])
+        if z[j,j]!=1:
+            c=1/z[j,j]; z[j,:]=c*z[j,:]; ops.append(['scale',j,None,c])
+        for i in range(n):
+            if i!=j and z[i,j]:
+                c=-z[i,j]; z[i,:]=z[i,:]+c*z[j,:]; ops.append(['add',i,j,c])
+    assert z==S.eye(n)
+    def replay(skip=-1):
+        z=S.eye(n)
+        for k in reversed(range(len(ops))):
+            if k==skip: continue
+            typ,i,j,c=ops[k]
+            if typ=='swap': z.row_swap(i,j)
+            elif typ=='scale': z[i,:]=z[i,:]/c
+            else: z[i,:]=z[i,:]-c*z[j,:]
+        return z
+    assert replay()==a
+    assert ops and replay(0)!=a
+    return [[t,i,j,None if c is None else str(c)] for t,i,j,c in ops]
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--source',type=Path,required=True)
+    ap.add_argument('--out',type=Path,required=True); a=ap.parse_args(); t0=time.monotonic()
+    a.out.mkdir(parents=True,exist_ok=True)
+    p=a.source/'data/bit/bitE8-r865.json.gz'; w=json.loads(gzip.decompress(p.read_bytes()))
+    assert (w['h'],w['v'],w['R'],w['form'])==(8,120,865,'<x,y>/2')
+    lines=[S.Matrix(x) for x in w['lines']]; I=S.eye(8); Z=S.zeros(8)
+    assert lines[0]==S.Matrix([2,0,0,0,0,0,0,0])
+    ip=lambda u,v:(u.T*v)[0]/2
+    gs={0:I}; todo=[0]
+    while todo:
+        more=[]
+        for i in todo:
+            for j in range(120):
+                if j in gs or abs(ip(lines[i],lines[j]))!=1: continue
+                d=lines[i]-lines[j] if ip(lines[i],lines[j])==1 else lines[i]+lines[j]
+                r=I-d*d.T/(d.T*d)[0]*2
+                gs[j]=r*gs[i]; more.append(j)
+        todo=more
+    assert len(gs)==120
+    recipes=[]; denoms=set(); max_factors=0
+    for t,q in enumerate(lines):
+        g=gs[t]; assert g.T*g==I and g*lines[0] in (q,-q)
+        P=q*q.T/4; K=I-P; A=g[:,1:]
+        assert A.T*A==S.eye(7) and A*A.T==K and P*A==S.zeros(8,7)
+        rho=P.row_join(A).col_join(A.T.row_join(S.zeros(7)))
+        assert rho.T==rho and rho*rho==S.eye(15)
+        expected={'P':S.diag(I,S.zeros(7)), 'H':S.eye(15),
+                  '0':S.diag(K,S.zeros(7)), 'K':S.diag(K,S.eye(7))}
+        for name,U in [('P',P),('H',I),('0',Z),('K',K)]:
+            assert rho*S.diag(U,S.eye(7))*rho==expected[name]
+        # Exact bit address operators D_U: head/tail exchange on U.
+        # Unlike complex C_U, they carry no omitted scalar/translation phase.
+        def D(U): return (I-U).row_join(U).col_join(U.row_join(I-U))
+        assert D(I)*D(P)==D(K) and D(P)*D(P)==S.eye(16)
+        ops=factor(rho); max_factors=max(max_factors,len(ops))
+        for typ,i,j,c in ops:
+            if c is not None: denoms.add(int(S.Rational(c).q))
+        # Compact exact global matrices: these 15 axes are the first eight
+        # local coordinates and exterior block s. All other axes are fixed.
+        routes=[dict(stage=0,axes=list(range(8)),identity=True)]
+        for s in range(1,9):
+            axes=list(range(8))+list(range(8+7*(s-1),8+7*s))
+            assert len(set(axes))==15 and max(axes)<64
+            routes.append(dict(stage=s,axes=axes,elementary_inverse_replay=ops))
+        recipes.append(dict(port=t,q=list(map(int,q)),complement_columns=[[str(x) for x in row] for row in A.tolist()],
+                            rho15=[[str(x) for x in row] for row in rho.tolist()],routes=routes))
+        if t%30==0: print('compressed geometry',t+1,flush=True)
+    # Exact nested data levels: local I (or K_q) plus s exterior rank-7
+    # blocks. Width 64=8+8*7; each bridge sees identical complete operators.
+    idle=[]
+    for j in range(1,4):
+        idle += [dict(pair=j,source_level=-1,target_level=2*j-1,rank=14*j,phase='before_positive_bridge'),
+                 dict(pair=j,source_level=2*j-1,target_level=2*j,rank=7,phase='before_negative_bridge')]
+    for j in range(4):
+        idle.append(dict(pair=j,source_level=2*j+2,target_level=8,rank=14*(3-j),phase='terminal'))
+    assert sum(z['rank'] for z in idle)==189
+    # Whole h=8 residual blocks are mutually perpendicular and fill Q^64.
+    slots=[list(range(8*s,8*(s+1))) for s in range(8)]
+    assert sorted(sum(slots,[]))==list(range(64))
+    perms=[]
+    for s in range(8):
+        perm=list(range(64))
+        if s:
+            for j in range(8): perm[j],perm[8*s+j]=perm[8*s+j],perm[j]
+        assert [perm[perm[j]] for j in range(64)]==list(range(64))
+        assert sorted(perm)==list(range(64)) and [perm[j] for j in range(8)]==slots[s]
+        perms.append(perm)
+    assert len({tuple(p) for p in perms})==8
+    assert set(sum(slots[:7]+[slots[6]],[]))!=set(range(64))
+    out=dict(status='PASS_COMPRESSED_NINE_BIT_GEOMETRY_AND_BANK_BLOCKS',h=8,m=64,stages=9,
+             word_sha256=digest(p),ports=recipes,idle_per_port_and_data_member=idle,
+             local_window='U direct_sum E_s, with E_s the first s exterior coordinate 7-blocks',
+             ambient_form='I_64/2',bank_slots=slots,bank_permutations=perms,
+             route_checks=1080,exact_bit_endpoint_operator_checks=240,
+             max_route_factors=max_factors,route_denominators=sorted(denoms),
+             bad_prime_factors=sorted({int(q) for d in denoms for q in S.factorint(d)}),
+             missing_route_factor_controls=120,duplicate_bank_slot_rejected=True,
+             scope='All port isometries, stage boundary identities, nested idle ranks, exact bit endpoint operators and bank coordinate slots. Full local-word scalar and chronological lowering are checked separately.',
+             seconds=time.monotonic()-t0)
+    dump(a.out/'GEOMETRY.json',out)
+    print(json.dumps({k:v for k,v in out.items() if k not in ('ports','bank_permutations','idle_per_port_and_data_member')}),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/global_word_g.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/global_word_g.py
new file mode 100644
index 0000000000..10eab502de
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/global_word_g.py
@@ -0,0 +1,243 @@
+"""Source-bound compressed nine-stage bit template and exact scalar audits, for any bitE8/1 word whose helpers start at
+frame 0 and end at the full frame.
+
+Port of PR #386's global_word.py (Zhihao Chen, with OpenAI Codex assistance; Apache-2.0); generalisation by eumemic
+with Anthropic Claude assistance (Apache-2.0). Every check of the original is kept, in the same order. The literals
+that belong to PR #370's word are replaced by the values of the given word, each bound to an independent receipt:
+  R, 2v + R local columns           <- the word, PR249 states (n), the five-stage formal-columns receipt (4v + R)
+  14,603 local additions            <- the official legality receipt (common_frame_ADDs) = columns local_scalar_additions
+  the literal local histogram       <- the columns receipt's local_raw_H
+  the literal paid profile          <- 72 x local + 48v{7} + 32v{14, 28, 42} (PR #386's PROOF.txt), computed separately
+  865 banks per stage, 62,280 bank assignments, 15,465 live families  <- R, 9 x 8 x R, 64v + 9R
+The geometry (PR #386's geometry.py, unchanged) depends only on the 120 labels; it is computed on PR #370's word and is
+bound here to the given word by the exact equality of the 120 label vectors.
+With --regression the original literals of PR #386 are asserted as well (PR #370's word must give #386's receipt).
+usage: global_word_g.py --word WORD.json.gz --local-check DIR --out DIR [--regression]
+  DIR (local check) holds records/{249-records.bin,249-states.json,frames.json} and cout/{legality.json,columns.json}."""
+import argparse, gzip, hashlib, json, struct, time
+from collections import Counter
+from pathlib import Path
+
+H,L,K,T,M=8,9,4,8,64
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+def write(p,x): p.write_text(json.dumps(x,indent=2)+'\n')
+
+def recipe():
+    out=[dict(kind='local',stage=0,pair=0,reverse=False)]; stage=1
+    for j in range(K):
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=True)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=1))
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=False)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=-1))
+    for j in reversed(range(K-1)): out.append(dict(kind='bridge',dst=j+1,src=j,coefficient=1))
+    out.append(dict(kind='exchange'))
+    return out
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--word',type=Path,required=True)
+    ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    ap.add_argument('--regression',action='store_true')
+    a=ap.parse_args(); start=time.monotonic(); out=a.out; out.mkdir(parents=True,exist_ok=True)
+    wp=a.word; w=json.loads(gzip.decompress(wp.read_bytes()))
+    V,R=w['v'],w['R']; LOCAL=2*V+R; DATA=2*K*V*T; LIVE=DATA+L*R
+    assert (w['h'],V,w['form'])==(8,120,'<x,y>/2')
+    geo=json.loads((out/'GEOMETRY.json').read_text())
+    assert geo['status']=='PASS_COMPRESSED_NINE_BIT_GEOMETRY_AND_BANK_BLOCKS'
+    # the port routes depend only on the labels: same 120 label vectors, in the same order
+    assert len(geo['ports'])==V and all(p['port']==t and p['q']==w['lines'][t] for t,p in enumerate(geo['ports']))
+    if a.regression: assert geo['word_sha256']==sha(wp)
+    rp=a.local_check/'records/249-records.bin'; raw=rp.read_bytes(); rec=list(struct.iter_unpack('<6i',raw))
+    state=json.loads((a.local_check/'records/249-states.json').read_text())
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    dims={int(f):z['dim'] for f,z in fs.items()}
+    lg=json.loads((a.local_check/'cout/legality.json').read_text())
+    cc=json.loads((a.local_check/'cout/columns.json').read_text())
+    assert lg['status'].startswith('PASS') and cc['status'].startswith('PASS')
+    assert (state['v'],state['n'])==(V,LOCAL) and lg['copies']==lg['erasures']==9
+    ADDS=lg['common_frame_ADDs']
+    assert cc['formal_columns_checked']==4*V+R and cc['local_scalar_additions']==ADDS
+    if a.regression: assert cc['formal_columns_checked']==1345 and ADDS==14603
+    initial=[state['initial'][str(i)] for i in range(LOCAL)]
+    final=[state['final'][str(i)] for i in range(LOCAL)]
+    assert all(dims[initial[i]]==0 and dims[final[i]]==H for i in range(2*V,LOCAL))
+    streams={}; checks={}; localH=None
+    for reverse in (False,True):
+        cur=(final if reverse else initial)[:]+[-1]; val=[1<<i for i in range(LOCAL)]+[0]
+        norm=[1]*LOCAL+[0]; maxnorm=1; center=None; hist=Counter(); events=[]; copies=0; adds=0
+        dim=lambda f:H-dims[f] if reverse else dims[f]
+        for op,x,y,c,f,z in (reversed(rec) if reverse else rec):
+            if op==0:
+                oldf,newf=(c,y) if reverse else (y,c)
+                assert cur[x]==oldf and dim(newf)-dim(oldf)==f>=0
+                cur[x]=newf
+                if f: hist[f]+=1
+                events.append([0,x,oldf,newf,f,int(reverse)])
+            elif op==1:
+                assert cur[x]==cur[y]==f and x!=y and x<LOCAL
+                if center is not None: assert x!=center
+                if y==LOCAL: assert center is not None
+                if c&1: val[x]^=val[y]
+                norm[x]+=abs(c)*norm[y]; maxnorm=max(maxnorm,norm[x]); adds+=1
+                events.append([1,x,y,-c if reverse else c,f,int(reverse)])
+            elif op==(3 if reverse else 2):
+                assert center is None and y==LOCAL and cur[x]==c and val[LOCAL]==0
+                copy_rank=abs(dim(c)-dim(f)); assert copy_rank==8
+                assert z==(0 if reverse else copy_rank)
+                center=x; cur[LOCAL]=f; val[LOCAL]=val[x]; norm[LOCAL]=norm[x]
+                hist[copy_rank]+=1; copies+=1; events.append([2,x,LOCAL,c,f,copy_rank,int(reverse)])
+            else:
+                assert op==(2 if reverse else 3)
+                assert center==x and y==LOCAL and cur[x]==c and cur[LOCAL]==f
+                assert val[LOCAL]==val[x]
+                val[LOCAL]=0; norm[LOCAL]=0; cur[LOCAL]=-1; center=None
+                events.append([3,x,LOCAL,c,f,z,int(reverse)])
+        assert center is None and copies==9 and adds==ADDS
+        assert cur[:LOCAL]==(initial if reverse else final)
+        for i in range(LOCAL):
+            want=(1<<i) ^ ((1<<(i-V)) if V<=i<2*V else 0)
+            assert val[i]==want
+        assert val[LOCAL]==0
+        if localH is None: localH=hist
+        else: assert localH==hist
+        key='reverse' if reverse else 'forward'; streams[key]=events
+        checks[key]=dict(copies=copies,adds=adds,records=len(events),all_columns=LOCAL,
+                         cancellation_free_row_l1=maxnorm,profile=dict(sorted(hist.items())),
+                         sha256=hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest())
+    assert sum(r*n for r,n in localH.items())==H*R+72+2*V*(H-1)
+    assert localH==Counter({int(r):n for r,n in cc['local_raw_H']})
+    if a.regression: assert localH==Counter({1:2076,2:942,3:448,4:418,5:308,6:2,8:18}) and H*R+72+2*V*(H-1)==8672
+
+    events=recipe(); levels=[-1]*K; schedule=[]; bridge_controls=[]
+    # Full scalar replay on separate dirty helpers for all nine stages.
+    # Physical banking then uses the separately checked injective cover owners.
+    n=2*K*V+L*R; vals=[1<<i for i in range(n)]+[0]; temp=n
+    stages=[]
+    for e in events:
+        if e['kind']=='local':
+            s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1
+            def mapper(i):
+                if i==LOCAL: return temp
+                if i<2*V:
+                    side=i//V; side=1-side if rev else side
+                    return (2*p+side)*V+i%V
+                return 2*K*V+s*R+i-2*V
+            before=vals[:]; opened=False
+            for z in streams['reverse' if rev else 'forward']:
+                if z[0]==0: continue
+                x,y=mapper(z[1]),mapper(z[2])
+                if z[0]==1:
+                    if z[3]&1: vals[x]^=vals[y]
+                elif z[0]==2:
+                    assert not opened; vals[temp]=vals[x]; opened=True
+                else:
+                    assert opened and vals[temp]==vals[x]; vals[temp]=0; opened=False
+            assert not opened
+            d=(2*p+(0 if rev else 1))*V; src=(2*p+(1 if rev else 0))*V
+            for t in range(V): before[d+t]^=before[src+t]
+            assert vals==before
+            levels[p]=s; schedule.append(dict(kind='local_cover_sweep',**{k:v for k,v in e.items() if k!='kind'}))
+            if s in (1,3,5):
+                j=(s+1)//2; assert levels[j]==-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7*(s+1),source_level=-1,target_level=s))
+            elif s in (2,4,6):
+                j=s//2; assert levels[j]==s-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7,source_level=s-1,target_level=s))
+            elif s==8:
+                for j in range(4):
+                    oldlevel=levels[j]; assert oldlevel==2*j+2
+                    schedule.append(dict(kind='idle',pair=j,rank=7*(8-oldlevel),source_level=oldlevel,target_level=8))
+                    levels[j]=8
+            stages.append(dict(stage=s,all_columns=n,helper_columns=L*R,reverse=rev))
+        elif e['kind']=='bridge':
+            d,s=e['dst'],e['src']; assert levels[d]==levels[s]
+            for t in range(V): vals[2*d*V+t]^=vals[2*s*V+t]; vals[(2*s+1)*V+t]^=vals[(2*d+1)*V+t]
+            schedule.append(e)
+        else:
+            assert levels==[8]*4
+            for j in range(K):
+                for t in range(V):
+                    x=2*j*V+t; y=(2*j+1)*V+t; vals[x],vals[y]=vals[y],vals[x]
+            schedule.append(e)
+    assert vals==[1<<i for i in range(n)]+[0]
+    # Integer scalar eight-bank matrix, with each individual bridge shear omitted.
+    def small(skip=-1):
+        z=[[int(i==j) for j in range(8)] for i in range(8)]; count=0
+        def add(d,s,c): z[d]=[x+c*y for x,y in zip(z[d],z[s])]
+        for e in events:
+            if e['kind']=='local':
+                p=e['pair']; add(2*p,2*p+1,-1) if e['reverse'] else add(2*p+1,2*p,1)
+            elif e['kind']=='bridge':
+                d,s,c=e['dst'],e['src'],e['coefficient']
+                for x,y,sgn in [(2*d,2*s,c),(2*s+1,2*d+1,-c)]:
+                    if count!=skip: add(x,y,sgn)
+                    count+=1
+            else:
+                for j in range(4): z[2*j],z[2*j+1]=z[2*j+1],[-x for x in z[2*j]]
+        return z,count
+    ident=[[int(i==j) for j in range(8)] for i in range(8)]
+    z,nb=small(); assert z==ident and nb==18
+    for skip in range(nb): assert small(skip)[0]!=ident; bridge_controls.append(skip)
+
+    paid=Counter(); calls=[]; assignment=set(); expanded=hashlib.sha256(); full_event_count=0
+    for e in events:
+        if e['kind']!='local': continue
+        s,p,rev=e['stage'],e['pair'],e['reverse']; ori='reverse' if rev else 'forward'
+        for rep in range(T):
+            owners=[]
+            for i in range(2*V):
+                side=i//V; side=1-side if rev else side
+                owners.append([rep*(2*K*V)+(2*p+side)*V+i%V, ['data',s,i%V]])
+            for r in range(R):
+                bank,slot=divmod(rep*R+r,8)
+                owners.append([DATA+s*R+bank,['bank',slot]])
+                assignment.add((s,rep,r,bank,slot))
+            assert len({(f,tuple(route)) for f,route in owners})==LOCAL
+            assert all(0<=f<LIVE for f,route in owners)
+            # Stream one full renamed instruction program into a source-bound
+            # digest, including exact owner route descriptors and reflection.
+            for z in streams[ori]:
+                op=z[0]
+                if op==0: paid[z[4]]+=bool(z[4]); mapped=[op,owners[z[1]],*z[2:]]
+                else:
+                    ox=owners[z[1]]; oy=owners[z[2]] if z[2]<LOCAL else [LIVE,['private',0]]
+                    mapped=[op,ox,oy,*z[3:]]
+                    if op==2: paid[z[5]]+=1
+                expanded.update((json.dumps(mapped,separators=(',',':'))+'\n').encode()); full_event_count+=1
+            calls.append(dict(stage=s,replica=rep,pair=p,orientation=ori,owners=owners,local_hash=checks[ori]['sha256']))
+    paid.pop(0,None)
+    assert len(assignment)==L*T*R and len(calls)==72
+    if a.regression: assert len(assignment)==62280
+    for e in schedule:
+        if e['kind']=='idle' and e['rank']: paid[e['rank']]+=2*V*T
+    mass=sum(r*c for r,c in paid.items()); assert M*LIVE-mass==2496
+    want=Counter({r:72*c for r,c in localH.items()})
+    for r,c in ((7,48*V),(14,32*V),(28,32*V),(42,32*V)): want[r]+=c
+    assert dict(sorted(paid.items()))==dict(sorted(want.items()))
+    if a.regression: assert dict(sorted(paid.items()))=={1:149472,2:67824,3:32256,4:30096,5:22176,6:144,7:5760,8:1296,14:3840,28:3840,42:3840}
+    cf=checks['forward']['cancellation_free_row_l1']; cb=checks['reverse']['cancellation_free_row_l1']
+    prefix=(1<<nb)*cf**5*cb**4; assert prefix<1<<192
+    template=dict(version='compressed-nine-e8-bit-v1',m=M,h=H,stages=L,replicas=T,live=LIVE,private_centre_reserve=9,
+                  cover='O(I_64/2,F_q) for admitted odd address primes q',loop_order='Each recipe phase: replicas then all cover classes; finish every local invocation before the next.',
+                  schedule=schedule,local_programs=streams,calls=calls,bank_padding=None,
+                  helper_route='owner (DATA + stage*%d + floor((%d*replica+helper)/8), d*Pi_slot^-1)'%(R,R),
+                  data_route='owner (replica*960 + (2*pair+side)*120+port, d*rho_stage,port)',
+                  bit_operator='D_U exchanges the two address halves on projector U; D_I D_P = D_(I-P) exactly.',
+                  geometry_sha256=sha(out/'GEOMETRY.json'),source_record_sha256=sha(rp))
+    blob=json.dumps(template,separators=(',',':'),sort_keys=True).encode(); (out/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+    result=dict(status='PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE',h=H,m=M,v=V,R=R,replicas=T,live=LIVE,physical=LIVE+9,
+                word_sha256=sha(wp),source_records_sha256=sha(rp),local_checks=checks,scalar_stages=stages,
+                independent_unbanked_scalar_columns=n,all_scalar_columns_restored=True,
+                geometry_sha256=sha(out/'GEOMETRY.json'),template_sha256=hashlib.sha256(blob).hexdigest(),
+                emitted_program_sha256=expanded.hexdigest(),emitted_events=full_event_count,local_invocations=len(calls),
+                bank_assignments=len(assignment),banks_per_stage=R,whole_rank8_slots_per_bank=8,padding_calls=0,
+                profile=dict(sorted(paid.items())),paid_calls=sum(paid.values()),rank_mass=mass,deficit=2496,
+                maxchild=max(paid),halving_depth=2,halving_integer_inequality=[64**2,2*42**2],
+                local_additions=ADDS,bridge_additions=18*V*T,copy_erase_episodes=9*72,
+                global_prefix_bound=str(prefix),global_prefix_bits=prefix.bit_length(),charged_prefix_bits=192,
+                omitted_bridge_shears_rejected=bridge_controls,
+                scope='Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.',
+                seconds=time.monotonic()-start)
+    write(out/'GLOBAL.json',result)
+    print(json.dumps({k:v for k,v in result.items() if k not in ('local_checks','scalar_stages','global_prefix_bound')}),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/regress386.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/regress386.py
new file mode 100644
index 0000000000..8cbca55668
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/nine/regress386.py
@@ -0,0 +1,36 @@
+"""Regression of the generalised compressed nine-stage scripts against PR #386's own receipts.
+
+Run on PR #370's word, global_word_g.py, audit_g.py and certify_g.py must reproduce PR #386's GLOBAL.json, AUDIT.json
+and the bit fields of COMBINED.json (vendored byte-identical from #386's validation directory) field for field. The only
+fields not compared are wall-clock seconds and the two hashes that cover GEOMETRY.json, whose 'seconds' field differs
+on every run (geometry_sha256 and template_sha256).
+usage: regress386.py OUR_OUT_DIR PR386_RECEIPT_DIR
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import json
+import sys
+from pathlib import Path
+
+ours, ref = Path(sys.argv[1]), Path(sys.argv[2])
+skip = {"seconds", "geometry_sha256", "template_sha256"}
+g, G = json.loads((ours / "GLOBAL.json").read_text()), json.loads((ref / "GLOBAL.json").read_text())
+assert set(g) == set(G), set(g) ^ set(G)
+bad = [k for k in G if k not in skip and g[k] != G[k]]
+assert not bad, bad
+a, A = json.loads((ours / "AUDIT.json").read_text()), json.loads((ref / "AUDIT.json").read_text())
+assert set(a) == set(A), set(a) ^ set(A)
+bad = [k for k in A if k not in skip and a[k] != A[k]]
+assert not bad, bad
+c, C = json.loads((ours / "BIT-NINE.json").read_text()), json.loads((ref / "COMBINED.json").read_text())
+for k in ("bit_coarse", "bit_moment_interval", "composed_moment_upper", "halving_depth"):
+    assert c[k] == C[k], k
+for k in ("unit_additions", "route_items", "selector_calls", "coefficient", "coefficient_bits", "two_level_coefficient",
+          "two_level_coefficient_bits", "charged_bound_bits", "payload_prefix_bits", "charged_payload_prefix_bits",
+          "row_coefficient", "retained_row_coefficient"):
+    assert c["finite"][k] == C["finite"][k], k
+k386 = c["kappa_with_cited_complex"]["pr386"]
+for k in ("complex_coarse", "selected_bit_coarse", "kappa", "bootstrap_chain", "strict_constraints"):
+    assert k386[k] == C[k], k
+assert k386["cutoff"] == C["finite"]["cutoff"]
+print("   regression: on PR #370's word the generalised scripts reproduce PR #386's GLOBAL.json (%d fields), AUDIT.json"
+      " (%d fields) and COMBINED.json's bit, finite and kappa fields (c = %s, kappa = %s), except wall-clock seconds and"
+      " the two GEOMETRY.json hashes" % (len(G) - 3, len(A) - 2, C["bit_coarse"], C["kappa"]))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/pricing/base_two_moment.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/pricing/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/pricing/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/pricing/moment.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/pricing/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/pricing/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/pricing/outer.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/pricing/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/pricing/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/pricing/prime_witnesses.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/pricing/prime_witnesses.py
new file mode 100644
index 0000000000..7f16d93030
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/pricing/prime_witnesses.py
@@ -0,0 +1,99 @@
+"""Exact finite prime exclusions for the selected new rational bit frames.
+
+For integer basis B and G=I-J/9, det(9 B G B^t) is a nonzero integer.
+Excluding its prime divisors and 2,3,5 makes the reduced frame nondegenerate
+over every odd local ring Z/q^w. Projector denominators divide this determinant
+times fixed powers of 3. Retained frames retain their old exclusion witnesses.
+The selected q is an arbitrarily large fixed prime chosen after this finite
+set; this is not verification at a preselected numeric q.
+"""
+from pathlib import Path
+import argparse,gzip,hashlib,json,sys
+
+HERE=Path(__file__).resolve().parent
+
+def det(A):
+    A=[list(r) for r in A];n=len(A)
+    if not n:return 1
+    sign=1;previous=1
+    for k in range(n-1):
+        pivot=next((i for i in range(k,n) if A[i][k]),None)
+        if pivot is None:return 0
+        if pivot!=k:A[k],A[pivot]=A[pivot],A[k];sign=-sign
+        p=A[k][k]
+        for i in range(k+1,n):
+            for j in range(k+1,n):
+                v=A[i][j]*p-A[i][k]*A[k][j]
+                assert v%previous==0
+                A[i][j]=v//previous
+            A[i][k]=0
+        previous=p
+    return sign*A[-1][-1]
+
+PRIMES=(2,3,5,7,11,13,17,19,23,29,31)
+
+def factor_witness(determinant):
+    assert type(determinant) is int and determinant != 0
+    residual=abs(determinant);powers={}
+    for prime in PRIMES:
+        power=0
+        while residual%prime==0:residual//=prime;power+=1
+        powers[str(prime)]=power
+    validate_factor(determinant,powers,residual)
+    return powers,residual
+
+def validate_factor(determinant,powers,residual):
+    assert type(determinant) is int and determinant != 0
+    assert set(powers)==set(map(str,PRIMES))
+    assert all(type(x) is int and x>=0 for x in powers.values())
+    assert type(residual) is int and 0<residual<2**80
+    reconstructed=residual
+    for p in PRIMES:reconstructed*=p**powers[str(p)]
+    assert reconstructed==abs(determinant)
+
+def certificate(word=None):
+    if word is None:
+        from word import Candidate
+        word=Candidate()
+    C=word.C;h=word.h
+    used=set(word.opframe)|set(word.w['source_frame'])|set(word.w['root_frame'])|{word.w['full_frame']}
+    used.update(z['frame'] for z in word.w['gauges'])
+    for e in word.k['entries']:used.update((e['mix_frame'],e['deliver_frame']))
+    groups={}
+    for frame in sorted(used):
+        B=C.B[frame]
+        key=json.dumps(B,separators=(',',':'));groups.setdefault(key,[]).append(frame)
+    records=[]
+    for key,frames in sorted(groups.items()):
+        B=json.loads(key);s=list(map(sum,B))
+        gram=[[9*sum(a*b for a,b in zip(x,y))-s[i]*s[j] for j,y in enumerate(B)] for i,x in enumerate(B)]
+        determinant=det(gram);powers,residual=factor_witness(determinant)
+        records.append(dict(basis_sha256=hashlib.sha256(key.encode()).hexdigest(),
+            frame_ids=frames,dimension=len(B),cleared_gram_determinant=determinant,
+            small_prime_powers=powers,remaining_factor=residual,gram_denominator_power_of_9=len(B)))
+    controls=[];zeros={str(p):0 for p in PRIMES}
+    for name,args in (('zero determinant',(0,zeros,1)),('incorrect factor identity',(15,zeros,1)),
+        ('residual above retained prime lower bound',(2**80+7,zeros,2**80+7))):
+        try:validate_factor(*args)
+        except AssertionError:controls.append(name)
+        else:raise ValueError('Invalid prime witness accepted: '+name)
+    return dict(status='PASS exact prime witnesses for every used physical frame',h=h,
+        source_commit='4a3c769e5c5430e7114c4d3e099ff34664677f17',
+        input_sha256={str(p.relative_to(HERE.parents[2])):hashlib.sha256(p.read_bytes()).hexdigest() for p in word.input_paths},
+        script_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(),
+        stripped_primes=list(PRIMES),frame_witnesses=records,unique_used_bases=len(records),
+        total_used_frames=len(used),total_operation_frames=len(word.changed_frames),
+        maximum_determinant_bits=max(abs(z['cleared_gram_determinant']).bit_length() for z in records),
+        all_remaining_factors_below_retained_prime_lower_bound=True,adverse_controls=controls,
+        rule='Every q>2^80 avoids every nonzero used-frame determinant, so the original prime range is unchanged.',
+        scope='Exact integer cleared-Gram factors for all physical frames including every changed operation, gauge, source, root, partner-mix, delivery and ambient frame. Uniform split-rank and fallback arguments remain the retained local-ring interface.')
+
+def main():
+    assert not sys.flags.optimize
+    ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');args=ap.parse_args()
+    record=certificate();target=HERE/'prime-witnesses.json.gz'
+    if args.write:target.write_bytes(gzip.compress((json.dumps(record,sort_keys=True,separators=(',',':'))+'\n').encode(),mtime=0))
+    else:assert record==json.loads(gzip.decompress(target.read_bytes())),'Exact prime witnesses changed'
+    print(json.dumps({k:v for k,v in record.items() if k!='frame_witnesses'}))
+
+if __name__=='__main__':main()
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/provenance.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/provenance.py
new file mode 100644
index 0000000000..9bfcb10623
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/provenance.py
@@ -0,0 +1,28 @@
+"""Check that every vendored file listed in a SOURCE-pr*.json has the git blob id recorded there, i.e. that it is
+byte-identical to the file at source_path in the cited PR's commit (compare with git ls-tree -r <commit>).
+Adapted from PR #381's code/provenance.py (DaysSky). Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import glob
+import hashlib
+import json
+import os
+import sys
+
+HERE = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
+
+
+def blob(rel):
+    b = open(os.path.join(HERE, rel), "rb").read()
+    return hashlib.sha1(b"blob %d\0" % len(b) + b).hexdigest()
+
+
+seen = set()
+for name in sorted(glob.glob(os.path.join(HERE, "SOURCE-pr*.json"))):
+    src = json.load(open(name))
+    bad = [rel for rel, x in src["identical"].items() if blob(rel) != x["blob"]]
+    if bad:
+        sys.exit("files differ from %s at %s: %s" % (src["source"], src["commit"][:7], bad))
+    seen |= set(src["identical"])
+    print("   %2d files byte-identical to %s at %s (git blob ids)"
+          % (len(src["identical"]), src["source"].replace("https://github.com/CrocSwap/integer-mult-bounds/pull/", "PR #"),
+             src["commit"][:7]))
+print("   %d vendored files in all (some pinned to two PRs); every other file is new in this package" % len(seen))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/controls.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/controls.py
new file mode 100644
index 0000000000..ceb15852b7
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/controls.py
@@ -0,0 +1,71 @@
+"""Negative controls for the elimination reuse: every mutant of the final word must be rejected by PR #370's
+independent all-column checker (code/bit/independent/checkword.py, run unchanged in a subprocess, as PR #370's
+mutate.py does). The mutated gates are the inserted elimination gates listed in the reuse ledger written by regen.py.
+usage: controls.py WORD.json.gz LEDGER.json PRICING_DIR
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import copy
+import gzip
+import json
+import os
+import subprocess
+import sys
+import tempfile
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+CHECK = os.path.join(HERE, "..", "bit", "independent", "checkword.py")
+word, ledger, pricing = sys.argv[1:4]
+w = json.load(gzip.open(word, "rt"))
+led = json.load(open(ledger))
+v = w["v"]
+elim = [(ph, i) for ph, i, kind in led["eliminations"] if kind == "helper"]
+undo = [(ph, i) for ph, i, kind in led["eliminations"] if kind == "total"]
+assert len(elim) == led["helpers"] and len(undo) == led["totals"]
+for ph, i in elim + undo:     # each ledger entry is an elimination into a helper slot
+    assert w[ph][i][1] >= 2 * v and w[ph][i][2]
+lines = [frozenset(f) for f in w["frames"]]   # frames are closed: frame a lies inside frame b iff lines[a] <= lines[b]
+
+
+def prev_frame(c, ph, i, r):
+    """frame id of register r just before gate (ph, i) (its last earlier gate in D, A, ... or its start frame)"""
+    f = c["start"][r]
+    for p in ("D", "A", "B", "C"):
+        for k, g in enumerate(c[p]):
+            if (p, k) == (ph, i):
+                return f
+            if r == g[1] or r in g[2]:
+                f = g[0]
+    raise AssertionError("gate not found")
+
+
+muts = []
+c = copy.deepcopy(w); ph, i = elim[0]; del c[ph][i]
+muts.append(("omit the first helper elimination gate (the reused slot keeps a leftover x-content)", c))
+c = copy.deepcopy(w); ph, i = next((p, k) for p, k in elim if len(w[p][k][2]) >= 2); c[ph][i][2].pop()
+muts.append(("omit one eliminator of a helper elimination with two or more eliminators", c))
+c = copy.deepcopy(w); ph, i = undo[0]; c[ph][i][2].pop()
+muts.append(("omit one x-line read of a retained-total undo gate", c))
+c = copy.deepcopy(w)
+for ph, i in elim:
+    f, d, srcs = c[ph][i]
+    low = prev_frame(c, ph, i, d)
+    if lines[low] < lines[f] and any(not lines[prev_frame(c, ph, i, s)] <= lines[low] for s in srcs):
+        c[ph][i][0] = low
+        break
+else:
+    raise AssertionError("no elimination gate above its slot's own frame")
+muts.append(("an elimination gate lowered to the reused slot's own frame (below an eliminator's frame)", c))
+c = copy.deepcopy(w)
+for ph, i in sorted(elim + undo, key=lambda z: (z[0], -z[1])):
+    del c[ph][i]
+muts.append(("reuse without elimination: all %d elimination and undo gates removed" % (len(elim) + len(undo)), c))
+c = copy.deepcopy(w); ph, i = undo[0]; c[ph][i][0] = w["start"][v]
+muts.append(("a retained-total undo gate moved from the full frame to frame 0", c))
+tmpd = tempfile.mkdtemp()
+for k, (name, c) in enumerate(muts):
+    p = os.path.join(tmpd, "mut%d.json.gz" % k)
+    with gzip.open(p, "wt") as fh:
+        json.dump(c, fh)
+    r = subprocess.run([sys.executable, "-I", "-B", CHECK, p, pricing], capture_output=True, text=True)
+    assert r.returncode != 0, "mutant accepted: " + name
+    print("   REJECTED %s :: %s" % (name, (r.stderr.strip().splitlines() or ["?"])[-1][:90]))
+print("PASS all %d elimination-reuse negative controls rejected by PR #370's independent checker" % len(muts))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/ecost.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/ecost.py
new file mode 100644
index 0000000000..4ec2a959b1
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/ecost.py
@@ -0,0 +1,20 @@
+"""Integer step-cost tables for the search heuristics of reuse.py and retime.py.
+
+cost(r) = r ln(m / r) (the per-child term of the linearised moment equation), scaled by 10^12 and rounded half-even
+with Python's decimal module (correctly rounded natural logarithm), so every comparison made by the two stages is an
+integer comparison and gives the same word on every platform.  The tables only steer the deterministic choices of the
+stages; the word they produce is checked and priced exactly elsewhere.
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+from decimal import Decimal, localcontext, ROUND_HALF_EVEN
+
+SCALE = 10 ** 12
+
+
+def table(m, rmax):
+    out = [0] * (rmax + 1)
+    with localcontext() as ctx:
+        ctx.prec = 60
+        for r in range(1, rmax + 1):
+            x = Decimal(r) * (Decimal(m) / Decimal(r)).ln() * SCALE
+            out[r] = int(x.to_integral_value(rounding=ROUND_HALF_EVEN))
+    return out
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/regen.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/regen.py
new file mode 100644
index 0000000000..529de1b8b3
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/regen.py
@@ -0,0 +1,49 @@
+"""Regenerate the word from pinned inputs.
+
+  1. PR #370's producer, unchanged (ham2.build -> compile2 -> fullword.build), with our producer parameters
+     (data/params/params-r740.json, found by discovery/search_params.py)            -> raw word (R = 863)
+  2. reuse.reuse: helper-slot reuse by elimination of dead registers               -> reused word
+  3. retime.retime: single-gate frame retiming (6 sweeps, M = 64)                  -> final word
+Each word is written as PR #370's fullword.save does (sorted keys, compact JSON, gzip mtime 0).
+usage: regen.py PARAMS.json OUT_RAW.json.gz OUT_REUSED.json.gz OUT_FINAL.json.gz OUT_LEDGER.json
+OUT_LEDGER lists the inserted elimination gates (phase, index, kind) of the final word, for the negative controls.
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import ast
+import json
+import os
+import sys
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+os.environ["E8COORD"] = "ham"
+sys.path.insert(0, os.path.join(HERE, "..", "bit", "producer"))
+sys.path.insert(0, HERE)
+import compile2 as C2  # noqa: E402  (PR #370 producer)
+import fullword  # noqa: E402  (PR #370 producer)
+import ham2  # noqa: E402  (PR #370 producer)
+import reuse as RU  # noqa: E402
+import retime as RT  # noqa: E402
+
+params, out_raw, out_reused, out_final, out_ledger = sys.argv[1:6]
+Pd = {ast.literal_eval(k): v for k, v in json.load(open(params))}
+ham2.P.clear()
+ham2.P.update(Pd)
+h = ham2.build(0, True)
+W = C2.compile2(h)
+raw = fullword.build(W)
+fullword.save(raw, out_raw)
+print("   1. PR #370 producer with our parameters: R %d, gates D/A/B/C %d/%d/%d/%d, frames %d"
+      % (raw["R"], len(raw["D"]), len(raw["A"]), len(raw["B"]), len(raw["C"]), len(raw["frames"])), flush=True)
+reused, nre = RU.reuse(raw)
+fullword.save(reused, out_reused)
+print("   2. elimination reuse: %d dead slots reused by later helpers, %d by the retained totals: R %d -> %d"
+      % (nre["helpers"], nre["totals"], raw["R"], reused["R"]), flush=True)
+final, moved = RT.retime(reused, sweeps=6, M=64)
+fullword.save(final, out_final)
+for ph, i, kind in nre["eliminations"]:      # retiming moves frames only: the ledger positions are unchanged
+    assert final[ph][i][1:] == reused[ph][i][1:]
+with open(out_ledger, "w") as fh:
+    json.dump(dict(helpers=nre["helpers"], totals=nre["totals"], eliminations=nre["eliminations"]), fh)
+    fh.write("\n")
+print("   3. retiming: %d gate moves; final R %d, gates D/A/B/C %d/%d/%d/%d, frames %d"
+      % (moved, final["R"], len(final["D"]), len(final["A"]), len(final["B"]), len(final["C"]), len(final["frames"])),
+      flush=True)
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/retime.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/retime.py
new file mode 100644
index 0000000000..9c3e94b800
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/retime.py
@@ -0,0 +1,112 @@
+"""Single-gate frame retiming of a bitE8/1 word (our implementation of the idea of PR #389, ai-nanachi).
+
+Every A, B and C gate may move to the join of its registers' previous frames (the lowest legal frame) or to the
+root-spanned meet of their next frames (the highest legal frame), whichever lowers the integer step cost
+sum over its registers of cost(rank in) + cost(rank out), cost(r) = r ln(M/r) (ecost.py; M = 64 by default, the
+width of the compressed nine-stage layout). Sweeps alternate direction until no gate moves. D gates (frame 0), the
+targets at frame 0 at the scatter, the retained totals at the full frame, start and final frames are pinned.
+Requires the PR #370 producer modules on sys.path with E8COORD=ham (see regen.py).
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import os
+from collections import defaultdict
+
+assert os.environ.get("E8COORD") == "ham", "set E8COORD=ham before importing (see regen.py)"
+import frames as Fm  # noqa: E402  (PR #370 producer: exact root-spanned closure over Q)
+from ecost import table  # noqa: E402
+
+
+def _bits(mask):
+    out = []
+    while mask:
+        b = mask & -mask
+        out.append(b.bit_length() - 1)
+        mask ^= b
+    return out
+
+
+def retime(w, sweeps=6, M=64):
+    v = w["v"]
+    rc = table(M, M)
+    frames = [sum(1 << s for s in f) for f in w["frames"]]
+    FULL = (1 << v) - 1
+    dcache = {}
+
+    def dim(mask):
+        if mask not in dcache:
+            dcache[mask] = Fm.closure(mask)[1] if mask else 0
+        return dcache[mask]
+
+    nodes = []   # dict(mask, regs, fixed, phase, gate)
+    for ph in ("D", "A"):
+        for g in w[ph]:
+            nodes.append(dict(mask=frames[g[0]], regs=[g[1]] + g[2], fixed=(ph == "D"), phase=ph, gate=g))
+    for q in w["ret"]:
+        nodes.append(dict(mask=FULL, regs=[q], fixed=True, phase="pin", gate=None))
+    for t in range(v):
+        nodes.append(dict(mask=0, regs=[v + t], fixed=True, phase="pin", gate=None))
+    for ph in ("B", "C"):
+        for g in w[ph]:
+            nodes.append(dict(mask=frames[g[0]], regs=[g[1]] + g[2], fixed=False, phase=ph, gate=g))
+    byreg = defaultdict(list)
+    for i, n in enumerate(nodes):
+        for r in n["regs"]:
+            byreg[r].append(i)
+    prev, nxt = {}, {}
+    for r, ids in byreg.items():
+        for p, i in enumerate(ids):
+            prev[i, r] = ids[p - 1] if p else ("start", r)
+            nxt[i, r] = ids[p + 1] if p + 1 < len(ids) else ("final", r)
+
+    def frame_of(key):
+        if isinstance(key, int):
+            return nodes[key]["mask"]
+        kind, r = key
+        return frames[w[kind][r]]
+
+    def node_cost(i, mask):
+        c = 0
+        dm = dim(mask)
+        for r in nodes[i]["regs"]:
+            c += rc[dm - dim(frame_of(prev[i, r]))] + rc[dim(frame_of(nxt[i, r])) - dm]
+        return c
+
+    moved_total = 0
+    for sweep in range(sweeps):
+        moved = 0
+        order = [i for i, n in enumerate(nodes) if not n["fixed"]]
+        if sweep % 2:
+            order.reverse()
+        for i in order:
+            lo, hi = 0, FULL
+            for r in nodes[i]["regs"]:
+                lo |= frame_of(prev[i, r])
+                hi &= frame_of(nxt[i, r])
+            lo = Fm.closure(lo)[0] if lo else 0
+            hi = Fm.closure(hi)[0] if hi else 0
+            if lo & ~hi:
+                continue
+            old = nodes[i]["mask"]
+            best = min([old, lo, hi], key=lambda m_: node_cost(i, m_))   # ties keep the old frame
+            if node_cost(i, best) < node_cost(i, old):
+                nodes[i]["mask"] = best
+                moved += 1
+        moved_total += moved
+        if not moved:
+            break
+    fid = {m: i for i, m in enumerate(frames)}
+
+    def frame_id(mask):
+        if mask not in fid:
+            fid[mask] = len(frames)
+            frames.append(mask)
+        return fid[mask]
+
+    out = {ph: [] for ph in "DABC"}
+    for n in nodes:
+        if n["phase"] == "pin":
+            continue
+        g = n["gate"]
+        out[n["phase"]].append([frame_id(n["mask"]), g[1], list(g[2])])
+    cert = dict(w)
+    cert.update(frames=[_bits(m) for m in frames], D=out["D"], A=out["A"], B=out["B"], C=out["C"])
+    return cert, moved_total
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/reuse.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/reuse.py
new file mode 100644
index 0000000000..df455a0b37
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/reuse/reuse.py
@@ -0,0 +1,258 @@
+"""Helper-slot reuse by elimination of dead registers (bitE8/1 words).
+
+A helper is dead after its last phase-A/B gate. It still holds a leftover x-content (an F2 combination of source
+lines) at its death frame. Before the birth gate of a later helper whose first frame is fb, look among the dead slots
+whose current frame lies inside fb for a linear relation of their x-contents over F2:
+    content(r0) = XOR_{q in S} content(q).
+Emit the gate  r0 += S  at G = the join of the current frames of r0 and S (G lies inside fb). Afterwards r0 holds no
+x-content (only helper dirt, which the rebuilt compensation D and cleanup C account for), so r0 hosts the new helper.
+The eliminators S move to G and stay dead there. The relation is chosen by Gaussian elimination over F2 on the
+candidates sorted by frame dimension, then replaced by the cheapest relation with |S| <= 3 under the integer step costs
+of ecost.py (extra climbing of r0 and of the eliminators), when one exists.
+The 9 retained totals (born at the full frame) also take dead slots: the leftover x-lines of the chosen slot are read
+from the sources at the full frame, which zeroes its x-content.
+D (dirt compensation at frame 0) and C (cleanup at the full frame) are rebuilt exactly as PR #370's fullword.py does.
+Same idea as PR #376's helper-lifetime reuse (applecrusher), generalised from aliasing to linear relations.
+Requires the PR #370 producer modules on sys.path with E8COORD=ham (see regen.py).
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import os
+
+assert os.environ.get("E8COORD") == "ham", "set E8COORD=ham before importing (see regen.py)"
+import e8lib as E  # noqa: E402  (PR #370 producer, unchanged)
+import frames as Fm  # noqa: E402  (PR #370 producer: exact root-spanned closure over Q)
+from ecost import table  # noqa: E402
+
+RC = table(40, 8)          # step cost r ln(40/r) of the five-stage ledger, as integers
+MAXS_PAIRS = 60            # pair/triple relations are searched when at most this many dead slots fit
+
+
+def _step(a, b):
+    return RC[b - a] if b > a else 0
+
+
+def _dim(mask):
+    return Fm.closure(mask)[1] if mask else 0
+
+
+def _bits(mask):
+    out = []
+    while mask:
+        b = mask & -mask
+        out.append(b.bit_length() - 1)
+        mask ^= b
+    return out
+
+
+def sparse_relation(cands, dead, fb):
+    """cheapest (r0, S) with content(r0) = XOR content(S), |S| <= 3, scored by the extra climbing of the
+    eliminators (death frame -> G -> full instead of death frame -> full) and of r0 (death frame -> G -> birth
+    frame instead of 0 -> birth frame and death frame -> full); None if no such relation fits inside fb"""
+    best = None
+    single = {}
+    for q in cands:
+        single.setdefault(dead[q][0], []).append(q)
+    pairs = {}
+    if len(cands) <= MAXS_PAIRS:
+        for i, a in enumerate(cands):
+            for b in cands[i + 1:]:
+                pairs.setdefault(dead[a][0] ^ dead[b][0], []).append((a, b))
+    dfb = _dim(fb)
+
+    def score(r0, S):
+        G = dead[r0][1]
+        for q in S:
+            G |= dead[q][1]
+        G, dg = Fm.closure(G) if G else (0, 0)
+        if G & ~fb:
+            return None
+        d0 = _dim(dead[r0][1])
+        c = _step(d0, dg) + _step(dg, dfb) - _step(d0, 8) - _step(0, dfb)
+        for q in S:
+            if dead[q][1] != G:
+                dq = _dim(dead[q][1])
+                c += _step(dq, dg) + _step(dg, 8) - _step(dq, 8)
+        return c
+
+    for r0 in cands:
+        x = dead[r0][0]
+        opts = []
+        if x == 0:
+            opts.append([])
+        for q in single.get(x, []):
+            if q != r0:
+                opts.append([q])
+        for a, b in pairs.get(x, []):
+            if r0 not in (a, b):
+                opts.append([a, b])
+        if len(cands) <= MAXS_PAIRS:
+            for a in cands:
+                if a == r0:
+                    continue
+                for b, c_ in pairs.get(x ^ dead[a][0], []):
+                    if r0 not in (b, c_) and a not in (b, c_):
+                        opts.append([a, b, c_])
+                        break
+        for S in opts:
+            sc = score(r0, S)
+            if sc is not None and (best is None or sc < best[0]):
+                best = (sc, r0, S)
+    return None if best is None else (best[1], best[2])
+
+
+def reuse(w, maxr=10 ** 9):
+    """returns (new word, dict(helpers=..., totals=...) reuse counts); w is a bitE8/1 word from PR #370's fullword.build (helpers start at
+    frame 0 and end at the full frame)"""
+    v, R = w["v"], w["R"]
+    assert w["format"] == "bitE8/1" and w["coords"] == "ham" and w["lines"] == [list(r) for r in E.LINES]
+    assert all(not w["frames"][w["start"][r]] for r in range(2 * v, 2 * v + R))
+    frames = [sum(1 << s for s in f) for f in w["frames"]]
+    fid = {m: i for i, m in enumerate(frames)}
+    XM = (1 << v) - 1
+
+    def frame_id(mask):
+        if mask not in fid:
+            fid[mask] = len(frames)
+            frames.append(mask)
+        return fid[mask]
+
+    nA = len(w["A"])
+    gates = [list(g) for g in w["A"]] + [list(g) for g in w["B"]]
+    first, last = {}, {}
+    for k, (f, d, srcs) in enumerate(gates):
+        for r in [d] + srcs:
+            if r >= 2 * v:
+                first.setdefault(r, k)
+                last[r] = k
+    ret = set(w["ret"])
+    val = [1 << s for s in range(v)] + [0] * (v + R)    # x-content only (helpers never read targets)
+    cont_at = {}
+    for k, (f, d, srcs) in enumerate(gates):
+        for s in srcs:
+            val[d] ^= val[s]
+        for r in [d] + srcs:
+            if r >= 2 * v and last.get(r) == k:
+                cont_at[r] = (val[r] & XM, frames[f])
+    births = sorted((first[r], r) for r in range(2 * v, 2 * v + R) if r in first and r not in ret)
+    deaths = sorted((last[r], r) for r in cont_at if r not in ret)
+    dead = {}          # physical slot -> [x-content, current frame mask, death gate index]
+    rename = {}        # logical register born later -> physical slot it reuses
+    insert_before = {}
+    di = 0
+    nre = 0
+
+    def bury(upto):
+        nonlocal di
+        while di < len(deaths) and deaths[di][0] < upto:
+            k, r = deaths[di]
+            di += 1
+            x, f = cont_at[r]
+            dead[rename.get(r, r)] = [x, f, k]
+
+    for kb, rb in births:
+        bury(kb)
+        if nre >= maxr:
+            continue
+        fb = frames[gates[kb][0]]
+        cands = sorted((_dim(fm), p) for p, (x, fm, k) in dead.items() if (fm & ~fb) == 0)
+        if not cands:
+            continue
+        basis = []     # (vector, set of slots) with distinct leading bits
+        found = None
+        for dm, p in cands:
+            y, comb = dead[p][0], {p}
+            for bv, bs in basis:
+                if y >> (bv.bit_length() - 1) & 1:
+                    y ^= bv
+                    comb ^= bs
+            if y == 0:
+                found = (p, sorted(q for q in comb if q != p))
+                break
+            basis.append((y, comb))
+            basis.sort(key=lambda z: -z[0])
+        if found is None:
+            continue
+        found = sparse_relation([p for _, p in cands], dead, fb) or found
+        r0, S = found
+        G = dead[r0][1]
+        for q in S:
+            G |= dead[q][1]
+        G = Fm.closure(G)[0] if G else 0
+        assert G & ~fb == 0
+        x = dead[r0][0]
+        for q in S:
+            x ^= dead[q][0]
+        assert x == 0, "not a relation"
+        if S:
+            insert_before.setdefault(kb, []).append([frame_id(G), r0, list(S), "helper"])
+        for q in S:
+            dead[q][1] = G
+        assert dead[r0][2] < kb
+        del dead[r0]
+        rename[rb] = r0
+        nre += 1
+    # retained totals (born at the full frame) reuse dead slots: undo by reading the slot's x-lines at the full frame
+    FULLM = (1 << v) - 1
+    ntot = 0
+    for q in w["ret"]:
+        kq = first[q]
+        bury(kq)
+        free = [p for p in dead if dead[p][2] < kq]      # only slots already dead at the total's birth
+        if not free:
+            continue
+        r0 = min(free, key=lambda p: (bin(dead[p][0]).count("1"), p))
+        xs = _bits(dead[r0][0])
+        if xs:
+            insert_before.setdefault(kq, []).append([frame_id(FULLM), r0, xs, "total"])
+        del dead[r0]
+        rename[q] = r0
+        ntot += 1
+    out, kinds = [], []
+    for k, g in enumerate(gates):
+        for f, d, srcs, kind in insert_before.get(k, []):
+            out.append([f, d, srcs])
+            kinds.append(kind)
+        f, d, srcs = g
+        out.append([f, rename.get(d, d), [rename.get(s, s) for s in srcs]])
+        kinds.append(None)
+    nA2 = nA + sum(len(insert_before.get(k, [])) for k in range(nA))
+    A2, B2 = out[:nA2], out[nA2:]
+    # ledger of the inserted elimination gates: (phase, index in that phase, kind); retime.py keeps gate positions
+    ledger = [["A", i, kd] if i < nA2 else ["B", i - nA2, kd] for i, kd in enumerate(kinds) if kd]
+    alive = sorted(set(range(2 * v, 2 * v + R)) - set(rename))
+    newid = {r: 2 * v + i for i, r in enumerate(alive)}
+    for i in range(2 * v):
+        newid[i] = i
+    R2 = len(alive)
+
+    def ren(gl):
+        return [[f, newid[d], [newid[s] for s in srcs]] for f, d, srcs in gl]
+
+    A2, B2 = ren(A2), ren(B2)
+    ret2 = [newid[rename.get(q, q)] for q in w["ret"]]
+    # dirt compensation and cleanup, rebuilt as in PR #370's fullword.build
+    nreg = 2 * v + R2
+    dv = [0] * nreg
+    for r in range(2 * v, nreg):
+        dv[r] = 1 << (r - 2 * v)
+    for f, d, srcs in A2:
+        for s in srcs:
+            dv[d] ^= dv[s]
+    cdirt = [dv[q] for q in ret2]
+    for t in range(v):
+        for k in w["scatter"][t]:
+            dv[v + t] ^= cdirt[k]
+    for f, d, srcs in B2:
+        for s in srcs:
+            dv[d] ^= dv[s]
+    zero, full = frame_id(0), frame_id(FULLM)
+    D = []
+    for t in range(v):
+        srcs = [2 * v + b for b in _bits(dv[v + t])]
+        if srcs:
+            D.append([zero, v + t, srcs])
+    Cl = [[full, d, srcs] for f, d, srcs in reversed(A2 + B2) if d >= 2 * v]
+    start = w["start"][:2 * v] + [w["start"][2 * v]] * R2
+    final = w["final"][:2 * v] + [w["final"][2 * v]] * R2
+    cert = dict(w)
+    cert.update(R=R2, frames=[_bits(m) for m in frames], start=start, final=final, ret=ret2, D=D, A=A2, B=B2, C=Cl)
+    return cert, dict(helpers=nre, totals=ntot, eliminations=ledger)
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/apply376.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/apply376.py
new file mode 100644
index 0000000000..c401a84d8f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/apply376.py
@@ -0,0 +1,60 @@
+"""Our own re-implementation (from the data semantics in PR376's PROOF.md) of applying PR376's frozen frame witness
+and helper-reuse witness to PR370's E8 bit word. Does not import or run PR376 code.
+usage: apply376.py SRC370.json.gz FRAMESEL.json REUSESEL.json OUT.json.gz"""
+import sys, os, json, gzip, hashlib
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+from e8core import save_word
+
+def canon(c): return json.dumps(c, sort_keys=True, separators=(',', ':')).encode()
+
+def apply_frames(c, sel):
+    w = json.loads(json.dumps(c)); pos = []
+    for ph in ('D', 'A', 'B', 'C'):
+        w[ph] = [[f, d, [s]] for f, d, ss in c[ph] for s in ss]
+        pos += [(ph, i) for i in range(len(w[ph]))]
+    for e in sel['entries']:
+        ph, i = pos[e['scalar_index']]
+        assert ph == e['phase'] != 'D' and w[ph][i] == [e['old_frame'], e['dst'], [e['src']]]
+        w[ph][i][0] = e['new_frame']
+    return w
+
+def apply_reuse(c, sel):
+    v = c['v']; n = 2 * v + c['R']; nA = len(c['A']); ops = c['A'] + c['B']
+    pairs = {p['at']: p for p in sel['pairs']}
+    alias = {p['new']: p['old'] for p in sel['pairs']}
+    for p in sel['pairs']:
+        assert ops[p['at']][0] == p['frame'] and ops[p['at']][1] == p['new'] and p['at'] < nA
+    keep = [r for r in range(n) if r not in alias]; idx = {r: i for i, r in enumerate(keep)}
+    rm = lambda r: idx[alias.get(r, r)]
+    new = []; split = None
+    for i, (f, d, ss) in enumerate(ops):
+        if i == nA: split = len(new)
+        if i in pairs:
+            p = pairs[i]; new.append([f, rm(p['old']), [rm(s) for s in p['sources']]])
+        new.append([f, rm(d), [rm(s) for s in ss]])
+    o = json.loads(json.dumps(c)); o['A'], o['B'] = new[:split], new[split:]
+    o['R'] = c['R'] - len(alias)
+    o['start'] = [c['start'][r] for r in keep]; o['final'] = [c['final'][r] for r in keep]
+    o['ret'] = [rm(q) for q in c['ret']]
+    full, zero = c['final'][0], c['start'][v]
+    o['C'] = [[full, d, list(ss)] for _, d, ss in reversed(new) if d >= 2 * v]
+    # target compensation from helper dirt (F2 symbolic over helper initial values)
+    R = o['R']; dirt = [0] * (2 * v + R)
+    for r in range(2 * v, 2 * v + R): dirt[r] = 1 << (r - 2 * v)
+    for _, d, ss in o['A']:
+        for s in ss: dirt[d] ^= dirt[s]
+    cp = [dirt[q] for q in o['ret']]
+    for t, row in enumerate(o['scatter']):
+        for k in row: dirt[v + t] ^= cp[k]
+    for _, d, ss in o['B']:
+        for s in ss: dirt[d] ^= dirt[s]
+    o['D'] = [[zero, v + t, [2 * v + j for j in range(R) if dirt[v + t] >> j & 1]] for t in range(v) if dirt[v + t]]
+    return o
+
+if __name__ == '__main__':
+    raw = open(sys.argv[1], 'rb').read(); c = json.loads(gzip.decompress(raw))
+    fs = json.load(open(sys.argv[2])); rs = json.load(open(sys.argv[3]))
+    assert hashlib.sha256(raw).hexdigest() == fs['input_sha256']
+    w1 = apply_frames(c, fs); assert hashlib.sha256(canon(w1)).hexdigest() == rs['retimed_input_sha256']
+    w2 = apply_reuse(w1, rs); h = hashlib.sha256(canon(w2)).hexdigest(); assert h == rs['output_sha256'], h
+    save_word(w2, sys.argv[4]); print('PASS our reconstruction of the PR376 word, sha', h)
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/bootstrap.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/bootstrap.py
new file mode 100644
index 0000000000..1bc17e7682
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/bootstrap.py
@@ -0,0 +1,44 @@
+"""Own reimplementation of PR #392's (rohanarun) exact pricing tail, as used by PR #395:
+  certify24: complex coarse root to 24 decimals by both PR #315 engines with the 10^-16 fallback;
+  refine:    six fixed ordinary-bootstrap levels (beta = eta = 10^-18, saving backoff 10^-24), PR #315 outer assembly,
+             47 strict constraints, next grid point and invalid parameters rejected.
+Standard library only; engines are the unchanged PR #315 files (same git blobs as #392's)."""
+from fractions import Fraction as Q
+from e8core import moment, other, outer
+
+def certify24(H, m, W):
+    H = {int(k): v for k, v in H.items()}
+    root = moment.certify(H, m, W, True); lo = Q(root['lower']); hi = Q(root['upper']); assert hi - lo == Q(1, 10**24)
+    assert moment.moment(H, m, W, lo, True)[1] < 1 < moment.moment(H, m, W, hi, True)[0]
+    fb = 32 * m * m * sum(H.values()); dens = Q(1, 10**16)
+    _, up = other.moment(m, W, list(H.items()), lo); _, bad = other.moment(m, W, [(1, fb)], lo)
+    low, _ = other.moment(m, W, list(H.items()), hi); badl, _ = other.moment(m, W, [(1, fb)], hi)
+    assert up + dens * bad < 1 < low + dens * badl
+    return lo, hi
+
+BRIDGE = dict(proof='PROOF.md', representation='Unchanged PR390 inherited finite envelope; fixed-depth PR185 ordinary wrappers restore internal rows',
+              semantic=dict(G=dict(base=2, exponent=30000), E=dict(base=2, exponent=100000), B_upper=dict(base=2, exponent=100001),
+                            C0=dict(base=2, exponent=210000), C1=1, strict_literal_gap=1, induction_gap_lower=1),
+              rows=dict(coefficient=20161, degree=10**6, suffix_slope=4 * 10**6, degree_gap=Q(10**6) - Q(51 * 20161, 25)))
+
+def refine(b, c, depth=6):
+    grid = Q(1, 10**18); eta = beta = Q(1, 10**18); backoff = Q(1, 10**24)
+    s = (1 - beta) * b - backoff
+    assert Q(0) < s < min(c, (1 - beta) * b) < b < Q(1, 32)
+    x0 = Q(384599, 10**10); chain = [x0]
+    for j in range(depth):
+        old = chain[-1]; a = (1 - s) * s + s * old
+        assert old < a < s < 1 - a and a == s - s**(j + 1) * (s - x0)
+        assert min(s - a, 1 - a - s, 1 - a - s * (1 - old), 1 - s) > 0
+        chain.append(a)
+    a = chain[-1]; q = a * (1 - 2 * eta); mn = (1 - eta) * q / (1 + q); t = mn / grid; k = grid * ((t.numerator - 1) // t.denominator)
+    asm = outer.assembly(a, b, BRIDGE, k, eta=eta, beta=beta)
+    assert len(asm['strict_constraints']) == 47 and all(x > 0 for x in asm['strict_constraints'].values()) and asm['minimum_margin'] == mn
+    rej = []
+    for name, kk, e, be in [('next_grid', k + grid, eta, beta), ('zero_eta', k, Q(0), beta), ('zero_beta', k, eta, Q(0)), ('unit_beta', k, eta, Q(1))]:
+        try: outer.assembly(a, b, BRIDGE, kk, eta=e, beta=be)
+        except AssertionError: rej.append(name)
+        else: raise AssertionError('accepted invalid witness ' + name)
+    assert k < mn < b / (1 + b) < k + grid
+    a5 = chain[-2]; q5 = a5 * (1 - 2 * eta); assert (1 - eta) * q5 / (1 + q5) < k
+    return k, rej
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/e8core.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/e8core.py
new file mode 100644
index 0000000000..78983b3687
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/e8core.py
@@ -0,0 +1,203 @@
+"""Our own engine for bitE8/1 words (E8 root-line labels, h = 8): frame algebra over Q via root-line masks,
+legality/F2 replay, five-stage histogram, exact bit coarse saving and PR #315 outer assembly (our engine copies).
+Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0."""
+import gzip, json, os, importlib.util
+from fractions import Fraction as Q
+from collections import Counter
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+def _load(n):
+    s = importlib.util.spec_from_file_location('e8_' + n, os.path.join(HERE, "engines", n + ".py"))
+    m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+moment = _load('moment'); other = _load('base_two_moment'); outer = _load('outer')
+
+B2 = Q(876248285600677, 10**18)   # Sussman E8 five-stage (PR #352)
+B3 = Q(932783231884153, 10**18)   # DaysSky seven-stage B_3 (PR #363; no Lean proof)
+
+
+def load_word(p):
+    with (gzip.open(p, 'rt') if p.endswith('.gz') else open(p)) as f:
+        return json.load(f)
+
+
+def save_word(c, p):
+    with gzip.open(p, 'wt') as f:
+        json.dump(c, f, separators=(',', ':'))
+
+
+def rank(vecs):
+    rows = [[Q(x) for x in r] for r in vecs]; rk = 0
+    n = len(rows[0]) if rows else 0
+    for col in range(n):
+        p = next((i for i in range(rk, len(rows)) if rows[i][col] != 0), None)
+        if p is None: continue
+        rows[rk], rows[p] = rows[p], rows[rk]
+        for i in range(len(rows)):
+            if i != rk and rows[i][col] != 0:
+                f = rows[i][col] / rows[rk][col]; rows[i] = [a - f * b for a, b in zip(rows[i], rows[rk])]
+        rk += 1
+    return rk
+
+
+class Lat:
+    """Root-spanned subspaces of Q^8 represented by the mask of root lines they contain."""
+    def __init__(self, lines):
+        self.lines = [tuple(x) for x in lines]; self.v = len(lines)
+        self._dim = {0: 0}; self._close = {}
+        # Gram (form <x,y>/2) for orthogonality
+        self.ip = [[sum(a * b for a, b in zip(x, y)) // 2 for y in self.lines] for x in self.lines]
+
+    def close(self, mask):
+        """mask of all root lines in span(roots of mask)"""
+        if mask in self._close: return self._close[mask]
+        idx = [i for i in range(self.v) if mask >> i & 1]
+        basis = []
+        for i in idx:
+            if rank([self.lines[j] for j in basis] + [self.lines[i]]) > len(basis): basis.append(i)
+        d = len(basis); out = 0
+        if d == 8: out = (1 << self.v) - 1
+        elif d:
+            B = [self.lines[j] for j in basis]
+            for i in range(self.v):
+                if rank(B + [self.lines[i]]) == d: out |= 1 << i
+        self._close[mask] = out; self._close[out] = out; self._dim[out] = d
+        return out
+
+    def dim(self, mask):
+        if mask not in self._dim: self.close(mask)
+        return self._dim[mask]
+
+    def basis(self, mask):
+        b = []
+        for i in range(self.v):
+            if mask >> i & 1 and rank([self.lines[j] for j in b] + [self.lines[i]]) > len(b): b.append(i)
+        return b
+
+    def perp(self, t):
+        return self.close(sum(1 << j for j in range(self.v) if self.ip[t][j] == 0))
+
+
+def to_masks(c, L):
+    return [L.close(sum(1 << i for i in fr)) for fr in c['frames']]
+
+
+PHASES = ('D', 'A', 'B', 'C')
+
+
+def replay(c, L=None, masks=None, check_f2=True, span=True, span_mode='z'):
+    """Exact legality + F2 replay + histogram of a bitE8/1 word. Returns dict(H_local, steps, ...).
+    Legality: each register's frames nested (mask inclusion = exact Q-subspace inclusion for root-spanned frames) and
+    strictly increasing at each move; every gate at one common frame; D compensation at frame 0; y at frame 0 at the
+    scatter; COPY of retained totals; final frames (x, helpers FULL; y_t at its cap t-perp).
+    Source-span: every non-target operand's x-support lies in the gate frame."""
+    L = L or Lat(c['lines']); masks = masks or to_masks(c, L)
+    v, R, h = c['v'], c['R'], c['h']; n = 2 * v + R; FULL = (1 << v) - 1
+    cur = [masks[f] for f in c['start']]
+    for r in range(v): assert cur[r] == L.close(1 << r), 'x start'
+    for r in range(v, 2 * v): assert cur[r] == 0, 'y start at 0'
+    sig = [L.dim(cur[r]) for r in range(n)]
+    H = Counter(); steps = 0; viol = []
+    val = [1 << i for i in range(n)]
+    zsupp = [{i: 1} if i < v else {} for i in range(n)]  # integer support of each register over the x columns (all ADDs are +1)
+    def climb(r, m):
+        nonlocal steps
+        if cur[r] == m: return
+        assert cur[r] & ~m == 0 and cur[r] != m, ('not nested', r)
+        H[L.dim(m) - L.dim(cur[r])] += 1; steps += 1; cur[r] = m
+    def run(gates, ph):
+        for k, (f, d, srcs) in enumerate(gates):
+            m = masks[f]
+            assert d >= v and d not in srcs and len(set(srcs)) == len(srcs), (ph, k)
+            for x in [d] + srcs: climb(x, m)
+            for s in srcs:
+                val[d] ^= val[s]
+                if span:
+                    if s < v or s >= 2 * v:
+                        ms = sum(1 << i for i in zsupp[s])
+                        if ms & ~m: viol.append((ph, k, s))
+                    zd = zsupp[d]
+                    for i, a in zsupp[s].items():
+                        w = zd.get(i, 0) + a
+                        if w: zd[i] = w
+                        else: zd.pop(i, None)
+                    if span_mode == 'f2':
+                        zsupp[d] = {i: 1 for i in range(v) if val[d] >> i & 1}
+            if span and d >= 2 * v:
+                md = sum(1 << i for i in zsupp[d])
+                if md & ~m: viol.append((ph, k, d))
+    run(c['D'], 'D')
+    for r in range(v, n): assert cur[r] == masks[c['start'][r]], 'D compensation at frame 0 (helpers untouched otherwise)'
+    run(c['A'], 'A')
+    for t in range(v): assert cur[v + t] == 0, 'y at frame 0 at the scatter'
+    copies = [val[q] for q in c['ret']]
+    for q in c['ret']:
+        assert q >= 2 * v; H[L.dim(cur[q])] += 1
+    for t, row in enumerate(c['scatter']):
+        for k in row: val[v + t] ^= copies[k]
+    run(c['B'], 'B'); run(c['C'], 'C')
+    for r in range(n): climb(r, masks[c['final'][r]])
+    for r in range(v): assert cur[r] == FULL
+    for r in range(2 * v, n): assert cur[r] == FULL
+    for t in range(v): assert cur[v + t] == L.perp(t), 'y final at cap'
+    if check_f2:
+        for s in range(v): assert val[s] == 1 << s
+        for t in range(v): assert val[v + t] == (1 << (v + t)) | (1 << t), ('target', t)
+        for r in range(2 * v, n): assert val[r] == 1 << r, ('helper', r)
+    return dict(sig=sig, viol=viol, H=H, steps=steps, n=n, v=v, R=R, h=h, L=L, masks=masks, ncopy=len(c['ret']))
+
+
+def profile(H_local, v, h=8):
+    prof = Counter({j: 5 * c for j, c in H_local.items()})
+    for j in (2 * h - 2, h - 1, 2 * h + 2, 4): prof[j] += 2 * v
+    return prof
+
+
+def coarse(H, m, W):
+    grid = Q(1, 10**18)
+    root = moment.certify(dict(H), m, W, True); c = Q(int(Q(root['lower']) * 10**18), 10**18)
+    assert moment.moment(H, m, W, c, True)[1] < 1 < moment.moment(H, m, W, c + grid, True)[0]
+    fb = 32 * m * m * sum(H.values())
+    _, up = other.moment(m, W, list(H.items()), c); _, bad = other.moment(m, W, [(1, fb)], c)
+    lo, _ = other.moment(m, W, list(H.items()), c + grid); blo, _ = other.moment(m, W, [(1, fb)], c + grid)
+    assert up + Q(1, 10**16) * bad < 1 < lo + Q(1, 10**16) * blo
+    return c
+
+
+def kappa(c, b):
+    grid = Q(1, 10**18); eta = Q(1, 10**12); beta = Q(1, 10**9); cap = (1 - beta) * b
+    sv = min(c, Q(((cap - grid) * 10**18).__floor__(), 10**18)); binding = 'bit' if sv == c else 'complex'
+    chain = [Q(384599, 10**10)]
+    for _ in range(3):
+        a = (1 - sv) * sv + sv * chain[-1]; assert chain[-1] < a < sv < 1 - a; chain.append(a)
+    bit = chain[-1]
+    bridge = dict(proof='PROOF.md', representation='Exact powers with source-bound finite overcharges',
+                  semantic=dict(G=dict(base=2, exponent=30000), E=dict(base=2, exponent=100000), B_upper=dict(base=2, exponent=100001),
+                                C0=dict(base=2, exponent=210000), C1=1, strict_literal_gap=1, induction_gap_lower=1),
+                  rows=dict(coefficient=20161, degree=10**6, suffix_slope=4 * 10**6, degree_gap=Q(10**6) - Q(51 * 20161, 25)))
+    q = bit * (1 - 2 * eta); mn = (1 - eta) * q / (1 + q); t = mn * 10**18; k = Q((t.numerator - 1) // t.denominator, 10**18)
+    asm = outer.assembly(bit, b, bridge, k, eta=eta, beta=beta)
+    assert len(asm['strict_constraints']) == 47 and min(asm['strict_constraints'].values()) > 0
+    try:
+        outer.assembly(bit, b, bridge, k + grid, eta=eta, beta=beta); raise SystemExit('ADJACENT ADMITTED')
+    except AssertionError: pass
+    return k, binding
+
+
+def price_word(c, **kw):
+    r = replay(c, **kw)
+    v, h, R = r['v'], r['h'], r['R']; m = 5 * h
+    resid = sum(h - r['sig'][x] for x in range(2 * v, 2 * v + R))
+    T = 1 if resid % h == 0 else h
+    W = (4 * v * h + resid) * T // h; assert (4 * v * h + resid) * T % h == 0
+    prof = Counter({j: T * k for j, k in profile(r['H'], v, h).items()}); mass = sum(a * b for a, b in prof.items())
+    L_copy = h * r['ncopy']
+    assert m * W - mass == T * (4 * v - 5 * L_copy), ('deficit', m * W - mass)
+    assert 2 * max(prof) < m
+    cc = coarse(prof, m, W)
+    return dict(c=cc, H=r['H'], prof=prof, W=W, T=T, resid=resid, m=m, deficit=m * W - mass, replay=r)
+
+
+def phi_fn(m, W, a):
+    """linearized moment term per child of rank r (float), for search scoring"""
+    import math
+    return lambda r: r / (m * W) * math.exp(a * math.log(m / r))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/engines/base_two_moment.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/engines/moment.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/engines/outer.py b/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/code/tail/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/bit/bitE8-r740.json.gz b/research/e8-rank138-idle-hosting/upstream443/parent436/data/bit/bitE8-r740.json.gz
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diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/bit/bitE8-r865.json.gz b/research/e8-rank138-idle-hosting/upstream443/parent436/data/bit/bitE8-r865.json.gz
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diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/bit/reuse-ledger.json b/research/e8-rank138-idle-hosting/upstream443/parent436/data/bit/reuse-ledger.json
new file mode 100644
index 0000000000..51eb63c7d8
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/bit/reuse-ledger.json
@@ -0,0 +1 @@
+{"helpers": 114, "totals": 9, "eliminations": [["A", 973, "helper"], ["A", 975, "helper"], ["A", 986, "helper"], ["A", 993, "helper"], ["A", 995, "helper"], ["A", 1002, "helper"], ["A", 1009, "helper"], ["A", 1011, "helper"], ["A", 1018, "helper"], ["A", 1025, "helper"], ["A", 1027, "helper"], ["A", 1034, "helper"], ["A", 1036, "helper"], ["A", 1043, "helper"], ["A", 1050, "helper"], ["A", 1052, "helper"], ["A", 1059, "helper"], ["A", 1061, "helper"], ["A", 1068, "helper"], ["A", 1075, "helper"], ["A", 1082, "helper"], ["A", 1085, "helper"], ["A", 1088, "helper"], ["A", 1091, "helper"], ["A", 1094, "helper"], ["A", 1097, "helper"], ["A", 1100, "helper"], ["A", 1103, "helper"], ["A", 1106, "helper"], ["A", 1109, "helper"], ["A", 1112, "helper"], ["A", 1115, "helper"], ["A", 1118, "helper"], ["A", 1121, "helper"], ["A", 1124, "helper"], ["A", 1127, "helper"], ["A", 1130, "helper"], ["A", 1133, "helper"], ["A", 1136, "helper"], ["A", 1139, "helper"], ["A", 1142, "helper"], ["A", 1145, "helper"], ["A", 1148, "helper"], ["A", 1151, "helper"], ["A", 1154, "helper"], ["A", 1157, "helper"], ["A", 1160, "helper"], ["A", 1163, "helper"], ["A", 1166, "helper"], ["A", 1169, "helper"], ["A", 1172, "helper"], ["A", 1175, "helper"], ["A", 1178, "helper"], ["A", 1181, "helper"], ["A", 1184, "helper"], ["A", 1187, "helper"], ["A", 1190, "helper"], ["A", 1193, "helper"], ["A", 1196, "helper"], ["A", 1199, "helper"], ["A", 1202, "helper"], ["A", 1205, "helper"], ["A", 1209, "helper"], ["A", 1213, "helper"], ["A", 1216, "helper"], ["A", 1219, "helper"], ["A", 1222, "helper"], ["A", 1225, "helper"], ["A", 1228, "helper"], ["A", 1231, "helper"], ["A", 1234, "helper"], ["A", 1237, "helper"], ["A", 1240, "helper"], ["A", 1243, "helper"], ["A", 1246, "helper"], ["A", 1249, "helper"], ["A", 1252, "helper"], ["A", 1255, "helper"], ["A", 1258, "helper"], ["A", 1261, "helper"], ["A", 1268, "helper"], ["A", 1271, "helper"], ["A", 1274, "helper"], ["A", 1277, "helper"], ["A", 1280, "helper"], ["A", 1283, "helper"], ["A", 1286, "helper"], ["A", 1289, "helper"], ["A", 1294, "helper"], ["A", 1299, "helper"], ["A", 1304, "helper"], ["A", 1308, "helper"], ["A", 1312, "helper"], ["A", 1315, "helper"], ["A", 1318, "helper"], ["A", 1321, "helper"], ["A", 1324, "helper"], ["A", 1329, "helper"], ["A", 1334, "helper"], ["A", 1339, "helper"], ["A", 1344, "helper"], ["A", 1348, "helper"], ["A", 1352, "helper"], ["A", 1355, "helper"], ["A", 1358, "helper"], ["A", 1367, "helper"], ["A", 1370, "helper"], ["A", 1379, "helper"], ["A", 1384, "helper"], ["A", 1409, "helper"], ["A", 1414, "helper"], ["A", 1427, "helper"], ["A", 1823, "helper"], ["A", 1840, "helper"], ["A", 1855, "total"], ["A", 1857, "total"], ["A", 1859, "total"], ["A", 1861, "total"], ["A", 1863, "total"], ["A", 1865, "total"], ["A", 1867, "total"], ["A", 1869, "total"], ["A", 1871, "total"]]}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/complex-b-433.json b/research/e8-rank138-idle-hosting/upstream443/parent436/data/complex-b-433.json
new file mode 100644
index 0000000000..2d1db89159
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/complex-b-433.json
@@ -0,0 +1,10 @@
+{
+ "note": "PR #433's composition (split-centre complex supplier, R560; bit supplier R758 in #386's compressed nine-stage layout), cited by pinned reference. compose433.py reproduces PR #433's bit c from the stated R758 profile and PR #433's kappa from (c, b) with PR #433's tail (c on the 10^-24 grid, eta = beta = 10^-18, seed min(c, (1 - beta) b) - 10^-24, six bootstrap levels, 47 strict inequalities, next grid point and invalid parameters rejected), then composes this word's bit side with the same complex b. Values only: neither PR #433 supplier is rebuilt here.",
+ "name": "pr433",
+ "b": "1183986549206329/1000000000000000000",
+ "kappa": "560432476129139/500000000000000000",
+ "bit_c": "561061350132569610283/500000000000000000000000",
+ "bit_R": 758,
+ "bit_local_profile": {"1": 2367, "2": 875, "3": 475, "4": 321, "5": 164, "7": 14, "8": 9},
+ "source": "icekylinx PR #433 head 6d9244518175caf9e0089f92486959bc2c317273, research/split-centres-global/CERTIFICATE.json (git blob 7e807079): complex_lower, bit_lower, kappa; the R758 local profile is stated in PROOF.md section 3 (git blob 8366a89e) and asserted in code/bit_global.py there"
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/complex-b-b4.json b/research/e8-rank138-idle-hosting/upstream443/parent436/data/complex-b-b4.json
new file mode 100644
index 0000000000..4fd117cd04
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/complex-b-b4.json
@@ -0,0 +1,13 @@
+{
+ "note": "Complex coarse savings b cited for the outer assembly with the bit side in B_4 (#392's refined pricing tail, as reimplemented in PR #417's bootstrap.refine). Values only; no complex construction is re-run here. kappa is the value each PR states; kappa_b4.py must reproduce it.",
+ "suppliers": [
+  {"name": "pr424", "b": "254887067002137341481/250000000000000000000000", "kappa": "1018509848057013/1000000000000000000",
+   "source": "chafreaky PR #424 (PR description: b = 254887067002137341481/2.5e23, kappa = 1.018509848057013e-3)"},
+  {"name": "pr410", "b": "15915603634335785361/15625000000000000000000", "kappa": "508781072593909/500000000000000000",
+   "source": "eumemic PR #410, as cited in PR #417's data/complex-b.json and README"},
+  {"name": "pr409", "b": "101828635323117962043/100000000000000000000000", "kappa": "508625250464133/500000000000000000",
+   "source": "rohanarun PR #409, as cited in PR #417's data/complex-b.json and README"},
+  {"name": "pr407", "b": "508780574407464422817/500000000000000000000000", "kappa": "7941615395831/7812500000000000",
+   "source": "chafreaky PR #407, as cited in PR #417's data/complex-b.json and README"}
+ ]
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/complex-b-nine.json b/research/e8-rank138-idle-hosting/upstream443/parent436/data/complex-b-nine.json
new file mode 100644
index 0000000000..a215ba6188
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/complex-b-nine.json
@@ -0,0 +1,11 @@
+{
+ "note": "Complex coarse savings b cited by pinned reference for the outer assembly in the compressed nine-stage layout (bit side m = 64; #386's three-step bootstrap with eta = 1e-12, beta = 1e-9, seed strictly below (1 - beta) times both suppliers as in #431). Values only: no complex construction is re-run here. kappa_with_pr370_bit is each PR's own kappa, which pairs b with PR #370's bit word in this layout (c = 1057833103534317/10^18); certify_g.py must reproduce it on PR #370's word (verify.sh step 9, regression).",
+ "suppliers": [
+  {"name": "pr386", "b": "999240641319551/1000000000000000000", "kappa_with_pr370_bit": "998243154231047/1000000000000000000",
+   "source": "jacklightChen PR #386 head dd11cf8069554f0333afde398f12a56c3a7c29dd, research/e8-bit-complex-nine-validation/COMBINED.json (git blob 8d6e3f22): complex_coarse, kappa; PR #377's compressed nine-stage complex component"},
+  {"name": "pr425", "b": "52455248902029/50000000000000000", "kappa_with_pr370_bit": "524002754014103/500000000000000000",
+   "source": "jacklightChen PR #425 head e11ccea1d092beb1b01b4ee4ce49da478234254c, research/hamming-mutable-basis-complex-validation/FINAL.json (git blob 1e9c8784): complex_b, kappa; mutable-basis Hamming packets, R = 680"},
+  {"name": "pr431", "b": "529046848168159/500000000000000000", "kappa_with_pr370_bit": "1056715272872389/1000000000000000000",
+   "source": "rohanarun PR #431 (draft) head db4f46579b95bec6e2a0c59e3e1ee2b6584dbab3, research/hamming-frame-retiming/VALIDATION-LOCAL.json (git blob 0f0a8041; the same values as PRICE.json, git blob 365c0fe2): complex_b, kappa; #425's word with 112 common-frame retimings. Bit-bound with the PR #370 bit; complex-bound with this word"}
+ ]
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/LICENSE-pr426 b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/LICENSE-pr426
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/LICENSE-pr426
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
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+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
+      the Work or Derivative Works thereof, You may choose to offer,
+      and charge a fee for, acceptance of support, warranty, indemnity,
+      or other liability obligations and/or rights consistent with this
+      License. However, in accepting such obligations, You may act only
+      on Your own behalf and on Your sole responsibility, not on behalf
+      of any other Contributor, and only if You agree to indemnify,
+      defend, and hold each Contributor harmless for any liability
+      incurred by, or claims asserted against, such Contributor by reason
+      of your accepting any such warranty or additional liability.
+
+   END OF TERMS AND CONDITIONS
+
+   APPENDIX: How to apply the Apache License to your work.
+
+      To apply the Apache License to your work, attach the following
+      boilerplate notice, with the fields enclosed by brackets "[]"
+      replaced with your own identifying information. (Don't include
+      the brackets!)  The text should be enclosed in the appropriate
+      comment syntax for the file format. We also recommend that a
+      file or class name and description of purpose be included on the
+      same "printed page" as the copyright notice for easier
+      identification within third-party archives.
+
+   Copyright [yyyy] [name of copyright owner]
+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
+
+       http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
+   limitations under the License.
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr376/LICENSE-pr376 b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr376/LICENSE-pr376
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr376/LICENSE-pr376
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
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+
+      "Work" shall mean the work of authorship, whether in Source or
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+
+      "Derivative Works" shall mean any work, whether in Source or Object
+      form, that is based on (or derived from) the Work and for which the
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+      any Contribution intentionally submitted for inclusion in the Work
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+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
+      the Work or Derivative Works thereof, You may choose to offer,
+      and charge a fee for, acceptance of support, warranty, indemnity,
+      or other liability obligations and/or rights consistent with this
+      License. However, in accepting such obligations, You may act only
+      on Your own behalf and on Your sole responsibility, not on behalf
+      of any other Contributor, and only if You agree to indemnify,
+      defend, and hold each Contributor harmless for any liability
+      incurred by, or claims asserted against, such Contributor by reason
+      of your accepting any such warranty or additional liability.
+
+   END OF TERMS AND CONDITIONS
+
+   APPENDIX: How to apply the Apache License to your work.
+
+      To apply the Apache License to your work, attach the following
+      boilerplate notice, with the fields enclosed by brackets "[]"
+      replaced with your own identifying information. (Don't include
+      the brackets!)  The text should be enclosed in the appropriate
+      comment syntax for the file format. We also recommend that a
+      file or class name and description of purpose be included on the
+      same "printed page" as the copyright notice for easier
+      identification within third-party archives.
+
+   Copyright [yyyy] [name of copyright owner]
+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
+
+       http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
+   limitations under the License.
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr376/frame-selection.json b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr376/frame-selection.json
new file mode 100644
index 0000000000..647b34368f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr376/frame-selection.json
@@ -0,0 +1,1296 @@
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diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr376/reuse-selection.json b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr376/reuse-selection.json
new file mode 100644
index 0000000000..a6954dc65f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr376/reuse-selection.json
@@ -0,0 +1,395 @@
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+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr386/AUDIT.json b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr386/AUDIT.json
new file mode 100644
index 0000000000..698e827ae8
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr386/AUDIT.json
@@ -0,0 +1,34 @@
+{
+  "status": "PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT",
+  "template_sha256": "dfc59b42be1ed281eada6cbd7fb63de773ef4f65563dfdd9691cc5bfd24fb2a7",
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+  "exact_reflected_pairs": 3289,
+  "orthogonal_lift_argument": "Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.",
+  "exact_bank_families": 7785,
+  "slots_per_bank": 8,
+  "mutations_rejected": [
+    "omit an idle child",
+    "omit a bridge",
+    "omit terminal exchange",
+    "remove a local invocation",
+    "re-use a helper bank slot",
+    "understate live stock",
+    "omit a local paid move",
+    "wrong reflected copy charge"
+  ],
+  "profile": {
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+    "14": 3840,
+    "28": 3840,
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+  },
+  "seconds": 3.2433449580566958
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr386/COMBINED.json b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr386/COMBINED.json
new file mode 100644
index 0000000000..8d6e3f2266
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr386/COMBINED.json
@@ -0,0 +1,115 @@
+{
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+  "local_and_global_bit_sha256": "55af2a11552c04f5a87268bc2d1798246297874e9e87b50e49773e91cc495c2d",
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+    "charged_bound_bits": 512,
+    "payload_prefix_bits": 117,
+    "charged_payload_prefix_bits": 192,
+    "row_coefficient": 18355,
+    "retained_row_coefficient": 20161,
+    "cutoff": [
+      {
+        "gap": "960051162165086088309017855481/1000000000000000000000000000000000000",
+        "cutoff_log2": "39058336745164"
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+        "cutoff_log2": "39117723032087411874"
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+        "cutoff_log2": "39177199612950066624005104"
+      }
+    ]
+  },
+  "retained_obligations": [
+    "PR370 E8 local bit and nine copied-total admission",
+    "All-size weighted bit compiler, prime/tape/precision and analytic transfer interfaces",
+    "PR377 local E8 complex theorem, exact Clifford compiler and common fine-grid/row/analytic interfaces"
+  ],
+  "scope": "Conditional finite construction and exact arithmetic assembly. No Lean proof or priority claim; no enumeration of the entire orthogonal cover."
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr386/GLOBAL.json b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr386/GLOBAL.json
new file mode 100644
index 0000000000..21bc6dcc7b
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr386/GLOBAL.json
@@ -0,0 +1,165 @@
+{
+  "status": "PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE",
+  "h": 8,
+  "m": 64,
+  "v": 120,
+  "R": 865,
+  "replicas": 8,
+  "live": 15465,
+  "physical": 15474,
+  "word_sha256": "1fb726ea3818fe0837cceb0dd22a71a0814f064e5e781628104610d6468e0e55",
+  "source_records_sha256": "58683148e56b76e33705e418df35613ce99934f5e55056dea7abd8474151b3c5",
+  "local_checks": {
+    "forward": {
+      "copies": 9,
+      "adds": 14603,
+      "records": 18824,
+      "all_columns": 1105,
+      "cancellation_free_row_l1": 742,
+      "profile": {
+        "1": 2076,
+        "2": 942,
+        "3": 448,
+        "4": 418,
+        "5": 308,
+        "6": 2,
+        "8": 18
+      },
+      "sha256": "2b3bc12c3789ed22785189e793b293628e7c71b95411208119455a7b828a7f6b"
+    },
+    "reverse": {
+      "copies": 9,
+      "adds": 14603,
+      "records": 18824,
+      "all_columns": 1105,
+      "cancellation_free_row_l1": 6308,
+      "profile": {
+        "1": 2076,
+        "2": 942,
+        "3": 448,
+        "4": 418,
+        "5": 308,
+        "6": 2,
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+      },
+      "sha256": "f7ef54ad05f52c37b01f4d1ba3ca9b2b9a9ffc10e54099e2d3634cdfd0e8614a"
+    }
+  },
+  "scalar_stages": [
+    {
+      "stage": 0,
+      "all_columns": 8745,
+      "helper_columns": 7785,
+      "reverse": false
+    },
+    {
+      "stage": 1,
+      "all_columns": 8745,
+      "helper_columns": 7785,
+      "reverse": true
+    },
+    {
+      "stage": 2,
+      "all_columns": 8745,
+      "helper_columns": 7785,
+      "reverse": false
+    },
+    {
+      "stage": 3,
+      "all_columns": 8745,
+      "helper_columns": 7785,
+      "reverse": true
+    },
+    {
+      "stage": 4,
+      "all_columns": 8745,
+      "helper_columns": 7785,
+      "reverse": false
+    },
+    {
+      "stage": 5,
+      "all_columns": 8745,
+      "helper_columns": 7785,
+      "reverse": true
+    },
+    {
+      "stage": 6,
+      "all_columns": 8745,
+      "helper_columns": 7785,
+      "reverse": false
+    },
+    {
+      "stage": 7,
+      "all_columns": 8745,
+      "helper_columns": 7785,
+      "reverse": true
+    },
+    {
+      "stage": 8,
+      "all_columns": 8745,
+      "helper_columns": 7785,
+      "reverse": false
+    }
+  ],
+  "independent_unbanked_scalar_columns": 8745,
+  "all_scalar_columns_restored": true,
+  "geometry_sha256": "0bcff6cf3e243ad9192a08d0ff4bc14ed28f10d0b7a1ed6fbe378bdcc8da7048",
+  "template_sha256": "dfc59b42be1ed281eada6cbd7fb63de773ef4f65563dfdd9691cc5bfd24fb2a7",
+  "emitted_program_sha256": "65671c2b8addb093c74a89d418d10983016a9c5430d6c8de81844e63396bb285",
+  "emitted_events": 1355328,
+  "local_invocations": 72,
+  "bank_assignments": 62280,
+  "banks_per_stage": 865,
+  "whole_rank8_slots_per_bank": 8,
+  "padding_calls": 0,
+  "profile": {
+    "1": 149472,
+    "2": 67824,
+    "3": 32256,
+    "4": 30096,
+    "5": 22176,
+    "6": 144,
+    "7": 5760,
+    "8": 1296,
+    "14": 3840,
+    "28": 3840,
+    "42": 3840
+  },
+  "paid_calls": 320544,
+  "rank_mass": 987264,
+  "deficit": 2496,
+  "maxchild": 42,
+  "halving_depth": 2,
+  "halving_integer_inequality": [
+    4096,
+    3528
+  ],
+  "local_additions": 14603,
+  "bridge_additions": 17280,
+  "copy_erase_episodes": 648,
+  "global_prefix_bound": "93352550306090768010924318804410368",
+  "global_prefix_bits": 117,
+  "charged_prefix_bits": 192,
+  "omitted_bridge_shears_rejected": [
+    0,
+    1,
+    2,
+    3,
+    4,
+    5,
+    6,
+    7,
+    8,
+    9,
+    10,
+    11,
+    12,
+    13,
+    14,
+    15,
+    16,
+    17
+  ],
+  "scope": "Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.",
+  "seconds": 3.393421999993734
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr417-bitE8-nine-kernel.json.gz b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr417-bitE8-nine-kernel.json.gz
new file mode 100644
index 0000000000..572172b814
Binary files /dev/null and b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr417-bitE8-nine-kernel.json.gz differ
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr425/FINAL.json b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr425/FINAL.json
new file mode 100644
index 0000000000..1e9c8784c3
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr425/FINAL.json
@@ -0,0 +1,101 @@
+{
+  "status": "PASS_FRESH_CONDITIONAL_MUTABLE_BASIS_HAMMING_COMPLEX",
+  "conditional": true,
+  "complex_b": "52455248902029/50000000000000000",
+  "bit_c": "1057833103534317/1000000000000000000",
+  "kappa": "524002754014103/500000000000000000",
+  "decimal": {
+    "complex_b": "0.001049104978040580",
+    "bit_c": "0.001057833103534317",
+    "kappa": "0.001048005508028206",
+    "log2_kappa": -9.898137985359151
+  },
+  "gain_percent": {
+    "complex_vs_retimed": 4.974679784753074,
+    "kappa_vs_retimed": 4.969466276937444,
+    "kappa_vs_published_PR386": 4.984993244004889
+  },
+  "new_structure": {
+    "helper_registers_before": 783,
+    "helper_registers_after": 680,
+    "ports": 120,
+    "copied_centers": 8,
+    "target_pairs": 56,
+    "explicit_dirty_response_additions": 13216,
+    "scalar_interface": "Mutable source bases and target butterflies; frame-zero preconditioner and full-frame inverse cleanup."
+  },
+  "checks": {
+    "all_columns_each_orientation": 920,
+    "arbitrary_dirty_helper_columns": 680,
+    "exact_phases": true,
+    "independent_emitted_IR": true,
+    "fresh_extracted_package": true,
+    "all_47_strict_outer_inequalities": true,
+    "bootstrap_steps": 3,
+    "two_rational_moment_engines": true,
+    "next_b_and_kappa_grid_rejected": true
+  },
+  "local_profile": {
+    "1": 2248,
+    "2": 896,
+    "3": 168,
+    "4": 336,
+    "5": 392,
+    "8": 24,
+    "9": 8
+  },
+  "global_profile": {
+    "1": 167976,
+    "2": 64512,
+    "3": 12096,
+    "4": 24192,
+    "5": 28224,
+    "8": 7488,
+    "9": 576,
+    "16": 3840,
+    "32": 3840,
+    "48": 3840
+  },
+  "finite_invoice": {
+    "local_primitive_bound": 11165872996852,
+    "local_adapters": 430544,
+    "pervertex": 851835276345928,
+    "physical_stock_bits": 2642,
+    "router_bits": 7985,
+    "literal_bits": 35284,
+    "physical_row_coefficient": 15445,
+    "retained_row_coefficient": 20161,
+    "compiler": 25934336,
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000,
+    "required_C0_bits": 200012,
+    "halving_degree": 2,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ]
+  },
+  "package": {
+    "zip_sha256": "c6751251c9b9da4483092a675a0bae06b9c6f016b78ae806f365f9ded23cc6fa",
+    "zip_bytes": 352461,
+    "manifest_sha256": "41c29c8d074fe91d49afe5517a5e53d379b04178c75044ac72d7676223d6a961",
+    "manifest_files": 22,
+    "repository_payload_matches_extracted_package": true
+  },
+  "canonical_artifacts": {
+    "FULL-WORD.json.gz": "e55a0d4a1f1e3daaa082749489c9df2025f6a4fe9576aad2726cf881280f16fb",
+    "CANONICAL-WORD.json.gz": "1f8158a0d050f095fb7bd46f63f63528048737545660ca85410e4873c758ae4a",
+    "CLIFFORD-RECIPES.json": "5b828c91202ee168dc775dab8d658a1f2cd30ef7ebc7fbdcabcff5d4a7939dc0",
+    "GLOBAL-TEMPLATE.json.gz": "bb99d7f49bfcb409ad71b0941d0cb063496b8c2539a5392c8a1a17eac1ca65c1"
+  },
+  "receipt_sha256": {
+    "SCALAR-FRAME-AUDIT.json": "5ad89322566a411808cd9c76ac1d7039d75defadc0faef2f8e30592a3c0e0aef",
+    "CLIFFORD-REVIEW.json": "684bda187e48b7f4fc5947ca104590664e36e0eff03a291eb3be0a979abccded",
+    "INTEGRATION.json": "66db99cbc37980fa9e5dbffa9164e4d07b64b8eb78368ba1939f4bfa87f84f2b",
+    "INDEPENDENT-REPLAY.json": "fd3c1f35c534ff62e25211c273c85bf40fb4f838daea68cd7df082ab0c0f5ba1",
+    "REPLAY.json": "0d5360f6065e552aaa7ad5819d07115b16246f5c61a9c7603ca1db88b1f2d6f5"
+  },
+  "scope": "Finite written scalar-interface extension with exact rational and Gaussian-Clifford checks. Inherited all-size compiler, common-grid, restored-row, tape/prime/precision and analytic-transfer assumptions remain. No new Lean proof or unconditional theorem; 2^-9 is not reached.",
+  "receipt_stages": "INTEGRATION.json records the assembly stage before independent replay; REPLAY.json and this FINAL.json record the successful completed fresh replay."
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr426-bit-candidate.json.gz b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr426-bit-candidate.json.gz
new file mode 100644
index 0000000000..807cea53eb
Binary files /dev/null and b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr426-bit-candidate.json.gz differ
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr431/VALIDATION-LOCAL.json b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr431/VALIDATION-LOCAL.json
new file mode 100644
index 0000000000..0f0a80418d
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr431/VALIDATION-LOCAL.json
@@ -0,0 +1,18 @@
+{
+  "status": "PASS_FULL_HAMMING_FRAME_RETIMING_AND_SOURCE425_REPLAY",
+  "validated_code_head": "935e17bd43a46571d0e781710ee51848dad4d185",
+  "kappa": "1056715272872389/1000000000000000000",
+  "complex_b": "529046848168159/500000000000000000",
+  "bit_c": "1057833103534317/1000000000000000000",
+  "fresh_full_source425": true,
+  "fresh_changed_phases": 3072,
+  "all_columns_each_orientation": 920,
+  "emitted_events_each_orientation": 27425,
+  "strict_outer_inequalities": 47,
+  "retained_failure": "initial-bit-cap-failure.log: unchanged parent integrator requires complex below bit; explicit bounded-both seed fixes this without relaxing either supplier bound.",
+  "pending": [
+    "GitHub Python3.11/3.14 CI (queued)"
+  ],
+  "bit_scope": "Inherited PR425 bit supplier; no fresh standalone bit compiler proof.",
+  "scope": "Conditional PR425 scalar interface and inherited all-size compiler and analytic assumptions. Bit supplier remains inherited from PR425; no new standalone bit proof."
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr433/CERTIFICATE.json b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr433/CERTIFICATE.json
new file mode 100644
index 0000000000..7e807079c1
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/controls/pr433/CERTIFICATE.json
@@ -0,0 +1,119 @@
+{
+  "status": "PASS_CONDITIONAL_SPLIT_CENTRE_ASSEMBLY",
+  "kappa": "560432476129139/500000000000000000",
+  "kappa_decimal": "0.001120864952258278",
+  "bit_lower": "561061350132569610283/500000000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr425_percent": 6.9522005058117555,
+  "bit_invoice": {
+    "prefix_bits": 223,
+    "charged_prefix_bits": 256,
+    "coefficient_bits": 223,
+    "two_level_coefficient_bits": 483,
+    "charged_two_level_coefficient_bits": 512,
+    "row_coefficient": 18355,
+    "live": 14502,
+    "physical": 14511
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+  "strict_outer_constraints": {
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+    "complex_below_one_over32": "30066013450793671/1000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "791857266447229189304455739864091745201339627252022591017013352985113602942786795000164759817249951996149235225861576966507630300630689893816878766552471016817/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+    "lambda_above_sigma": "791857266447229218822654133098884940741856057546919645815673725733091011925773442015051156874463156995984475408611624970358395074769112927309248465921781123000121233447528983183/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
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+      "cutoff_log2": "24346328299693"
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+      "cutoff_log2": "12195269025875323655994833423982"
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+      "cutoff_log2": "9685246734476302780854842486398253310"
+    },
+    {
+      "gap": "27691483569705102945201339627252022591017013352985113602942786795000164759817249951996149235225861576966507630300630689893816878766552471016817/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "7691835588756193183914168151850588989363719"
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+  ],
+  "bit_template_sha256": "c40f89a2ae3c2c5635ddf8f18d74f24567ddf67fc8c8e93a1fc7a1a8098e857e",
+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f",
+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim.",
+  "verification_steps": [
+    "hamming_packets",
+    "complex_construct",
+    "complex_audit",
+    "complex_emit",
+    "complex_phases",
+    "bit_construct",
+    "bit_export",
+    "bit_global",
+    "bit_audit",
+    "bit_price",
+    "complex_integrate",
+    "complex_replay",
+    "combined"
+  ],
+  "phase_mode": "source-bound unchanged evidence"
+}
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/data/params/params-r740.json b/research/e8-rank138-idle-hosting/upstream443/parent436/data/params/params-r740.json
new file mode 100644
index 0000000000..d9bc74d95b
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/data/params/params-r740.json
@@ -0,0 +1 @@
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7), (0, 0, 0, 1, 0, 0, 0, -1))", 0], ["('ls', (2, 3, 6, 7), (0, 0, 0, 1, 0, 0, 0, 1))", 0], ["('ls', (2, 3, 6, 7), (0, 0, 0, 1, 0, 0, 1, 0))", 0], ["('ls', (2, 3, 6, 7), (0, 0, 1, -1, 0, 0, 0, 0))", 0], ["('ls', (2, 3, 6, 7), (0, 0, 1, 0, 0, 0, -1, 0))", 0], ["('ls', (2, 3, 6, 7), (0, 0, 1, 0, 0, 0, 0, -1))", 0], ["('ls', (2, 3, 6, 7), (0, 0, 1, 0, 0, 0, 0, 1))", 0], ["('ls', (2, 3, 6, 7), (0, 0, 1, 0, 0, 0, 1, 0))", 0], ["('ls', (2, 3, 6, 7), (0, 0, 1, 1, 0, 0, 0, 0))", 0], ["('ls', (4, 5, 6, 7), (0, 0, 0, 0, 0, 0, 1, -1))", 0], ["('ls', (4, 5, 6, 7), (0, 0, 0, 0, 0, 0, 1, 1))", 0], ["('ls', (4, 5, 6, 7), (0, 0, 0, 0, 0, 1, -1, 0))", 0], ["('ls', (4, 5, 6, 7), (0, 0, 0, 0, 0, 1, 0, -1))", 0], ["('ls', (4, 5, 6, 7), (0, 0, 0, 0, 0, 1, 0, 1))", 0], ["('ls', (4, 5, 6, 7), (0, 0, 0, 0, 0, 1, 1, 0))", 0], ["('ls', (4, 5, 6, 7), (0, 0, 0, 0, 1, -1, 0, 0))", 0], ["('ls', (4, 5, 6, 7), (0, 0, 0, 0, 1, 0, -1, 0))", 0], ["('ls', (4, 5, 6, 7), (0, 0, 0, 0, 1, 0, 0, -1))", 0], ["('ls', (4, 5, 6, 7), (0, 0, 0, 0, 1, 0, 0, 1))", 0], ["('ls', (4, 5, 6, 7), (0, 0, 0, 0, 1, 0, 1, 0))", 0], ["('ls', (4, 5, 6, 7), (0, 0, 0, 0, 1, 1, 0, 0))", 0], ["('pair', (0, 1, 2, 3), 64)", 0], ["('pair', (0, 1, 2, 3), 65)", 0], ["('pair', (0, 1, 2, 3), 66)", 1], ["('pair', (0, 1, 2, 3), 67)", 1], ["('pair', (0, 1, 2, 3), 68)", 0], ["('pair', (0, 1, 2, 3), 69)", 0], ["('pair', (0, 1, 2, 3), 70)", 1], ["('pair', (0, 1, 2, 3), 71)", 1], ["('pair', (0, 1, 4, 5), 32)", 0], ["('pair', (0, 1, 4, 5), 33)", 0], ["('pair', (0, 1, 4, 5), 34)", 2], ["('pair', (0, 1, 4, 5), 35)", 1], ["('pair', (0, 1, 4, 5), 36)", 1], ["('pair', (0, 1, 4, 5), 37)", 0], ["('pair', (0, 1, 4, 5), 38)", 2], ["('pair', (0, 1, 4, 5), 39)", 1], ["('pair', (0, 1, 6, 7), 24)", 0], ["('pair', (0, 1, 6, 7), 25)", 0], ["('pair', (0, 1, 6, 7), 26)", 2], ["('pair', (0, 1, 6, 7), 27)", 2], ["('pair', (0, 1, 6, 7), 28)", 2], ["('pair', (0, 1, 6, 7), 29)", 2], ["('pair', (0, 1, 6, 7), 30)", 0], ["('pair', (0, 1, 6, 7), 31)", 2], ["('pair', (0, 2, 4, 6), 16)", 0], ["('pair', (0, 2, 4, 6), 17)", 0], ["('pair', (0, 2, 4, 6), 18)", 1], ["('pair', (0, 2, 4, 6), 19)", 0], ["('pair', (0, 2, 4, 6), 20)", 1], ["('pair', (0, 2, 4, 6), 21)", 0], ["('pair', (0, 2, 4, 6), 22)", 1], ["('pair', (0, 2, 4, 6), 23)", 1], ["('pair', (0, 2, 5, 7), 40)", 0], ["('pair', (0, 2, 5, 7), 41)", 0], ["('pair', (0, 2, 5, 7), 42)", 1], ["('pair', (0, 2, 5, 7), 43)", 2], ["('pair', (0, 2, 5, 7), 44)", 1], ["('pair', (0, 2, 5, 7), 45)", 1], ["('pair', (0, 2, 5, 7), 46)", 0], ["('pair', (0, 2, 5, 7), 47)", 2], ["('pair', (0, 3, 4, 7), 72)", 0], ["('pair', (0, 3, 4, 7), 73)", 0], ["('pair', (0, 3, 4, 7), 74)", 2], ["('pair', (0, 3, 4, 7), 75)", 0], ["('pair', (0, 3, 4, 7), 76)", 1], ["('pair', (0, 3, 4, 7), 77)", 1], ["('pair', (0, 3, 4, 7), 78)", 0], ["('pair', (0, 3, 4, 7), 79)", 0], ["('pair', (0, 3, 5, 6), 112)", 0], ["('pair', (0, 3, 5, 6), 113)", 0], ["('pair', (0, 3, 5, 6), 114)", 0], ["('pair', (0, 3, 5, 6), 115)", 2], ["('pair', (0, 3, 5, 6), 116)", 0], ["('pair', (0, 3, 5, 6), 117)", 2], ["('pair', (0, 3, 5, 6), 118)", 1], ["('pair', (0, 3, 5, 6), 119)", 1], ["('pair', (1, 2, 4, 7), 10)", 2], ["('pair', (1, 2, 4, 7), 11)", 0], ["('pair', (1, 2, 4, 7), 12)", 0], ["('pair', (1, 2, 4, 7), 13)", 0], ["('pair', (1, 2, 4, 7), 14)", 1], ["('pair', (1, 2, 4, 7), 15)", 1], ["('pair', (1, 2, 4, 7), 8)", 0], ["('pair', (1, 2, 4, 7), 9)", 0], ["('pair', (1, 2, 5, 6), 48)", 0], ["('pair', (1, 2, 5, 6), 49)", 0], ["('pair', (1, 2, 5, 6), 50)", 2], ["('pair', (1, 2, 5, 6), 51)", 0], ["('pair', (1, 2, 5, 6), 52)", 0], ["('pair', (1, 2, 5, 6), 53)", 0], ["('pair', (1, 2, 5, 6), 54)", 1], ["('pair', (1, 2, 5, 6), 55)", 0], ["('pair', (1, 3, 4, 6), 80)", 0], ["('pair', (1, 3, 4, 6), 81)", 0], ["('pair', (1, 3, 4, 6), 82)", 2], ["('pair', (1, 3, 4, 6), 83)", 2], ["('pair', (1, 3, 4, 6), 84)", 1], ["('pair', (1, 3, 4, 6), 85)", 0], ["('pair', (1, 3, 4, 6), 86)", 0], ["('pair', (1, 3, 4, 6), 87)", 1], ["('pair', (1, 3, 5, 7), 104)", 0], ["('pair', (1, 3, 5, 7), 105)", 0], ["('pair', (1, 3, 5, 7), 106)", 0], ["('pair', (1, 3, 5, 7), 107)", 0], ["('pair', (1, 3, 5, 7), 108)", 2], ["('pair', (1, 3, 5, 7), 109)", 1], ["('pair', (1, 3, 5, 7), 110)", 0], ["('pair', (1, 3, 5, 7), 111)", 1], ["('pair', (2, 3, 4, 5), 100)", 0], ["('pair', (2, 3, 4, 5), 101)", 0], ["('pair', (2, 3, 4, 5), 102)", 2], ["('pair', (2, 3, 4, 5), 103)", 2], ["('pair', (2, 3, 4, 5), 96)", 0], ["('pair', (2, 3, 4, 5), 97)", 0], ["('pair', (2, 3, 4, 5), 98)", 2], ["('pair', (2, 3, 4, 5), 99)", 0], ["('pair', (2, 3, 6, 7), 88)", 0], ["('pair', (2, 3, 6, 7), 89)", 0], ["('pair', (2, 3, 6, 7), 90)", 0], ["('pair', (2, 3, 6, 7), 91)", 2], ["('pair', (2, 3, 6, 7), 92)", 2], ["('pair', (2, 3, 6, 7), 93)", 2], ["('pair', (2, 3, 6, 7), 94)", 1], ["('pair', (2, 3, 6, 7), 95)", 0], ["('pair', (4, 5, 6, 7), 56)", 0], ["('pair', (4, 5, 6, 7), 57)", 0], ["('pair', (4, 5, 6, 7), 58)", 0], ["('pair', (4, 5, 6, 7), 59)", 2], ["('pair', (4, 5, 6, 7), 60)", 1], ["('pair', (4, 5, 6, 7), 61)", 0], ["('pair', (4, 5, 6, 7), 62)", 0], ["('pair', (4, 5, 6, 7), 63)", 2]]
\ No newline at end of file
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/discovery/README.md b/research/e8-rank138-idle-hosting/upstream443/parent436/discovery/README.md
new file mode 100644
index 0000000000..025c3ac932
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/discovery/README.md
@@ -0,0 +1,5 @@
+# Discovery (not run by verify.sh)
+
+`search_params.py SEED ITERS START OUT` is a local search over the parameters of PR #370's producer (`ham2.P`: fold, l5, pair, fc0, fn and L-split choices), with the elimination-reuse pass of `code/reuse/reuse.py` inside the objective. The score is a floating-point estimate of the compressed nine-stage saving of the reused word. It only nominates parameters.
+
+The shipped `data/params/params-r740.json` came from 4 seeds × 6000 iterations of an earlier version of this loop, started from PR #370's `params-r865.json`. It differs from that file in 67 of 520 entries. `verify.sh` takes the parameters as an input and rebuilds the word from them, and checks and prices the result exactly. No search is run during verification.
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/discovery/search_params.py b/research/e8-rank138-idle-hosting/upstream443/parent436/discovery/search_params.py
new file mode 100644
index 0000000000..6e57d290f3
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/discovery/search_params.py
@@ -0,0 +1,106 @@
+"""Local search over the parameters of PR #370's producer (ham2) with the elimination-reuse pass inside the objective.
+Not run by verify.sh: the shipped parameters (data/params/params-r740.json) are an input, and the word is rebuilt and
+checked from them alone. The objective is a floating-point estimate of the compressed nine-stage saving (moment
+equation s with sum n_r (r/m)^(1-s) = W, profile 72 L + 48v{7} + 32v{14, 28, 42}, m = 64, W = 64v + 9R); it only
+nominates. The parameters shipped here came from 4 seeds x 6000 iterations of an earlier version of this loop, started
+from PR #370's params-r865.json.
+usage: python3 -I search_params.py SEED ITERS START_PARAMS.json OUT_PREFIX
+Prepared by eumemic with Anthropic Claude assistance; Apache-2.0."""
+import ast
+import json
+import os
+import random
+import sys
+import time
+from collections import Counter
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+os.environ["E8COORD"] = "ham"
+sys.path.insert(0, os.path.join(HERE, "..", "code", "bit", "producer"))
+sys.path.insert(0, os.path.join(HERE, "..", "code", "reuse"))
+import compile2 as C2  # noqa: E402
+import frames as Fm  # noqa: E402
+import fullword  # noqa: E402
+import ham2  # noqa: E402
+from ham1 import blocks, cw_lines  # noqa: E402
+from reuse import reuse  # noqa: E402
+
+
+def local_hist(w):
+    fd = [Fm.closure(sum(1 << s for s in f))[1] if f else 0 for f in w["frames"]]
+    cur = list(w["start"])
+    H = Counter()
+
+    def climb(r, f):
+        if cur[r] != f:
+            H[fd[f] - fd[cur[r]]] += 1
+            cur[r] = f
+    for ph in ("D", "A"):
+        for f, d, s in w[ph]:
+            for x in [d] + s:
+                climb(x, f)
+    for q in w["ret"]:
+        H[fd[cur[q]]] += 1
+    for ph in ("B", "C"):
+        for f, d, s in w[ph]:
+            for x in [d] + s:
+                climb(x, f)
+    for r in range(len(cur)):
+        climb(r, w["final"][r])
+    return H
+
+
+def nine(w):
+    v, R = w["v"], w["R"]
+    m, W = 64, 64 * v + 9 * R
+    prof = Counter({r: 72 * n for r, n in local_hist(w).items()})
+    for r, n in ((7, 48 * v), (14, 32 * v), (28, 32 * v), (42, 32 * v)):
+        prof[r] += n
+    lo, hi = 0.0, 0.05
+    for _ in range(100):
+        s = (lo + hi) / 2
+        if sum(n * (r / m) ** (1 - s) for r, n in prof.items()) < W:
+            lo = s
+        else:
+            hi = s
+    return lo
+
+
+def evaluate(Pd):
+    ham2.P.clear()
+    ham2.P.update(Pd)
+    w, _ = reuse(fullword.build(C2.compile2(ham2.build(0, True))))
+    return nine(w), w["R"]
+
+
+keys = []
+for c in blocks:
+    for t in cw_lines(c):
+        keys += [(("fold", t), 2), (("l5", t), 2), (("pair", c, t), 3)]
+for m in range(8):
+    keys += [(("fc0", m), 7), (("fn", m), 3)]
+ham2.build(0, True)
+keys += [(k, 3) for k in sorted(ham2.LSKEYS)]
+seed, iters, start, pref = int(sys.argv[1]), int(sys.argv[2]), sys.argv[3], sys.argv[4]
+Pd = {ast.literal_eval(k): v for k, v in json.load(open(start))}
+rng = random.Random(seed)
+t0 = time.time()
+best, R = evaluate(Pd)
+print("start nine %.6e R %d" % (best, R), flush=True)
+for it in range(iters):
+    k, n = rng.choice(keys)
+    old = Pd.get(k, 0)
+    Pd[k] = (old + rng.randrange(1, n)) % n
+    try:
+        s9, R = evaluate(Pd)
+    except AssertionError:
+        Pd[k] = old
+        continue
+    if s9 > best - 1e-12:
+        if s9 > best + 1e-12:
+            print(it, "improved nine %.6e R %d" % (s9, R), k, Pd[k], "%.0fs" % (time.time() - t0), flush=True)
+            json.dump([[repr(a), b] for a, b in Pd.items()], open(pref + "-params.json", "w"))
+        best = s9
+    else:
+        Pd[k] = old
+print("final", best)
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/portable-include/bits/stdc++.h b/research/e8-rank138-idle-hosting/upstream443/parent436/portable-include/bits/stdc++.h
new file mode 100644
index 0000000000..fc5664e929
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/portable-include/bits/stdc++.h
@@ -0,0 +1,38 @@
+#ifndef PORTABLE_BITS_STDCXX_H
+#define PORTABLE_BITS_STDCXX_H
+#include <algorithm>
+#include <array>
+#include <bitset>
+#include <cassert>
+#include <cctype>
+#include <chrono>
+#include <climits>
+#include <cmath>
+#include <cstdint>
+#include <cstdio>
+#include <cstdlib>
+#include <cstring>
+#include <deque>
+#include <exception>
+#include <fstream>
+#include <functional>
+#include <iomanip>
+#include <iostream>
+#include <iterator>
+#include <limits>
+#include <map>
+#include <memory>
+#include <numeric>
+#include <queue>
+#include <random>
+#include <set>
+#include <sstream>
+#include <stdexcept>
+#include <string>
+#include <tuple>
+#include <type_traits>
+#include <unordered_map>
+#include <unordered_set>
+#include <utility>
+#include <vector>
+#endif
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/requirements.txt b/research/e8-rank138-idle-hosting/upstream443/parent436/requirements.txt
new file mode 100644
index 0000000000..1cc9b96f59
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/requirements.txt
@@ -0,0 +1,3 @@
+numpy
+mpmath
+sympy
diff --git a/research/e8-rank138-idle-hosting/upstream443/parent436/verify.sh b/research/e8-rank138-idle-hosting/upstream443/parent436/verify.sh
new file mode 100644
index 0000000000..1f03e02879
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/parent436/verify.sh
@@ -0,0 +1,190 @@
+#!/usr/bin/env bash
+# One-command verification of research/e8-bit-elimination-reuse: an E8 bit word (h = 8, v = 120, 9 retained totals,
+# R = 740 helpers) rebuilt from pinned inputs, checked exactly, and priced in the compressed nine-stage layout of
+# PR #386 (m = 64, as used by #425, #431 and #433) and in DaysSky's nine-stage bridged word B_4 (PR #381's layout,
+# unsplit); composed with PR #433's complex supplier through PR #433's bit engine, finite invoice and tail.
+#   usage: bash verify.sh [--quick] /fresh/output/dir
+#   needs python3 >= 3.11 with numpy, mpmath and sympy (requirements.txt), a C++17 compiler (CXX, default c++) and
+#   Boost headers (BOOST_INCLUDE, default /usr/include).
+#   --quick skips the regressions on PR #370's word (PR #386's receipts and PR #381's K = 2 receipts) and the B_3 rows.
+set -euo pipefail
+QUICK=0; if [ "${1:-}" = "--quick" ]; then QUICK=1; shift; fi
+HERE=$(cd "$(dirname "$0")" && pwd); WD=$(mkdir -p "$1" && cd "$1" && pwd)
+case "$WD" in "$HERE"*) echo "output dir must be outside the package"; exit 2;; esac
+export PYTHONDONTWRITEBYTECODE=1
+PY="${PYTHON:-python3} -I -B"; CXX=${CXX:-c++}; BI=${BOOST_INCLUDE:-/usr/include}
+C=$HERE/code; B=$C/bit; CK=$B/checkers; D=$HERE/data; BIN=$WD/bin; mkdir -p $BIN
+INC="-I$HERE/portable-include -I$CK -I$BI"
+WORD=$D/bit/bitE8-r740.json.gz; W370=$D/bit/bitE8-r865.json.gz; LEDGER=$D/bit/reuse-ledger.json; EXP=$HERE/EXPECTED.json
+
+echo "== 0. manifest and provenance"
+(cd "$HERE" && $PY -c "
+import hashlib,os,sys
+bad=0;listed=set()
+for line in open('MANIFEST.sha256'):
+    h,p=line.rstrip('\n').split('  ',1);listed.add(p)
+    if hashlib.sha256(open(p,'rb').read()).hexdigest()!=h: print('MISMATCH',p);bad+=1
+files={os.path.relpath(os.path.join(r,f)) for r,_,fs in os.walk('.') for f in fs if '__pycache__' not in r}-{'MANIFEST.sha256'}
+if files-listed: print('UNLISTED',sorted(files-listed));bad+=1
+sys.exit(1 if bad else 0)") && echo "   all files match MANIFEST.sha256"
+$PY $C/provenance.py
+
+echo "== 1. the word, rebuilt from pinned inputs"
+$PY -c "
+import os,sys,json,gzip
+os.environ['E8COORD']='ham';sys.path.insert(0,'$B/producer')
+import ast,ham2,compile2,fullword
+Pd={ast.literal_eval(k):v for k,v in json.load(open('$B/producer/params-r865.json'))};ham2.P.clear();ham2.P.update(Pd)
+w=fullword.build(compile2.compile2(ham2.build(0,True)));assert json.loads(json.dumps(w))==json.load(gzip.open('$W370','rt'))
+print('   control: PR #370 producer (unchanged) regenerates PR #370 word bitE8-r865 from its own parameters')"
+$PY $C/reuse/regen.py $D/params/params-r740.json $WD/raw.json.gz $WD/reused.json.gz $WD/final.json.gz $WD/ledger.json
+$PY -c "
+import json,gzip,hashlib
+a=json.load(gzip.open('$WD/final.json.gz','rt'));b=json.load(gzip.open('$WORD','rt'));assert a==b
+assert json.load(open('$WD/ledger.json'))==json.load(open('$LEDGER'))
+e=json.load(open('$EXP'))['word'];h=hashlib.sha256(json.dumps(b,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+assert h==e['content_sha256'] and b['R']==e['R'] and len(b['ret'])==9 and b['h']==8 and b['v']==120
+print('   rebuilt word equals the shipped word (content sha256',h[:16]+'...); reuse ledger equal')"
+echo "   control word: PR #376's R822 word, rebuilt by PR #417's apply376.py from PR #370's word and PR #376's two witnesses"
+$PY $C/tail/apply376.py $W370 $D/controls/pr376/frame-selection.json $D/controls/pr376/reuse-selection.json $WD/w376.json.gz
+
+echo "== 2. one invocation, exact: PR #370's independent all-column checker and the negative controls"
+$PY $B/export_records.py $WORD $WD/records
+$PY $B/independent/checkword.py $WORD $C/pricing | tee $WD/checkword.txt
+$PY $B/independent/mutate.py $WORD $C/pricing
+$PY $C/reuse/controls.py $WORD $LEDGER $C/pricing
+
+echo "== 3. official PR #266 cohort checkers (PR #370's generalisation, NCOPY = 9) and PR #381's B_K formal columns"
+R=$($PY -c "import gzip,json;print(json.load(gzip.open('$WORD','rt'))['R'])")
+$CXX -O2 -std=c++17 -DHDIM=8 -DNCOPY=9 $INC -o $BIN/legality $CK/legality_h.cpp
+$CXX -O2 -std=c++17 -DHDIM=8 $INC -o $BIN/legality_ncopy_h $CK/legality_h.cpp
+$CXX -O2 -std=c++17 -DHDIM=8 -DNCOPY=9 -DVPORTS=120 -DRHELP=$R $INC -o $BIN/columns_h $CK/columns_h.cpp
+$CXX -O2 -std=c++17 -DHDIM=8 -DNCOPY=9 -DVPORTS=120 -DRHELP=$R -DKPAIRS=4 $INC -o $BIN/columns_k4 $CK/columns_k.cpp
+$PY $B/regression/stage_cohort.py $WD/records $WD/records $WD/cin $WD/cout
+$BIN/legality $WD/cin $WD/cout $WD/cout/legality.json > /dev/null
+$BIN/columns_h $WD/cout/COHORT249-RECORDS.bin $WD/cout/columns.json > /dev/null 2> $WD/cout/columns.log
+$BIN/columns_k4 $WD/cout/COHORT249-RECORDS.bin $WD/cout/columns_k4.json > /dev/null 2> $WD/cout/columns_k4.log
+$PY -c "
+import json
+l=json.load(open('$WD/cout/legality.json'));c=json.load(open('$WD/cout/columns.json'));k=json.load(open('$WD/cout/columns_k4.json'))
+assert l['status']=='PASS_INDEPENDENT_COHORT_LEGALITY_SOURCE_OWNERS_AND_LIFECYCLE' and l['copies']==l['erasures']==9
+print('   legality PASS:',l['records'],'records,',l['common_frame_ADDs'],'common-frame ADDs, rank mass',l['rank_mass'],', 9 COPY/ERASE at the full frame')
+assert c['status']=='PASS_NEW_COHORT249_ALL_FIVE_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL' and c['formal_columns_checked']==4*120+$R
+print('   five-stage formal columns PASS:',c['formal_columns_checked'],'physical columns over F2; prefix payload',c['payload_prefix_bits'],'bits < 104')
+assert k['status']=='PASS_NEW_COHORT249_ALL_BRIDGED_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL' and k['formal_columns_checked']==8*120+$R and len(k['stages'])==9
+assert k['bridge_additions']==18*120 and len(k['negative_controls'])==18 and all(x['rejected'] for x in k['negative_controls'])
+assert dict(map(tuple,k['local_raw_H']))==dict(map(tuple,c['local_raw_H']))
+print('   B_4 formal columns PASS:',k['formal_columns_checked'],'physical columns over F2 (dirty helpers) through 9 invocations, 18 twin bridges and the terminal exchange; 18 omitted-bridge controls rejected')"
+$PY $B/mutate_records.py $WD/records $WD/cin $WD/cout $BIN/legality $BIN/columns_k4 $BIN/legality_ncopy_h
+
+echo "== 4. exact nondegeneracy (E8 Gram) and prime witnesses on every frame"
+$PY $CK/gram_frames.py $WD/records --gram e8ham --h 8 --positive
+
+echo "== 5. retained totals: 9 at the full frame (PR #370's admission, charged as NCOPY = 9 everywhere)"
+$PY -c "
+import gzip,json,struct;w=json.load(gzip.open('$WORD','rt'));rec=open('$WD/records/249-records.bin','rb').read()
+cp=[struct.unpack_from('<6i',rec,24*i) for i in range(len(rec)//24) if struct.unpack_from('<6i',rec,24*i)[0]==2]
+assert len(cp)==len(w['ret'])==9 and all(e[5]==8 for e in cp) and [e[1] for e in cp]==w['ret']
+print('   retained totals 9, COPY rank 8 (full frame); copy loss 72 per invocation')"
+
+echo "== 6. compressed nine-stage layout (PR #386; used by #425 and #431): geometry, source-bound template, audit, price"
+mkdir -p $WD/nine
+$PY $C/nine/geometry.py --source $HERE --out $WD/nine | tail -1 | cut -c1-160
+$PY $C/nine/global_word_g.py --word $WORD --local-check $WD --out $WD/nine | cut -c1-160
+$PY $C/nine/audit_g.py --local-check $WD --out $WD/nine | cut -c1-160
+echo "   cited complex suppliers, bound to the PRs' own receipts (vendored, pinned by git blob id)"
+$PY $C/nine/cited.py $D/complex-b-nine.json $D/controls
+$PY $C/nine/certify_g.py --pricing $C/pricing --out $WD/nine --complex-b $D/complex-b-nine.json
+echo "   PR #433's bit engine, finite invoice and six-level tail (controls: PR #433's own c and kappa), composed with PR #433's complex b"
+$PY $C/nine/compose433.py --pricing $C/pricing --out $WD/nine --cited $D/complex-b-433.json --receipt $D/controls/pr433/CERTIFICATE.json
+if [ $QUICK = 0 ]; then
+  echo "   regression: the same chain on PR #370's word must reproduce PR #386's receipts and the cited kappa values"
+  $CXX -O2 -std=c++17 -DHDIM=8 -DNCOPY=9 -DVPORTS=120 -DRHELP=865 $INC -o $BIN/columns_h865 $CK/columns_h.cpp
+  mkdir -p $WD/r370/nine && $PY $B/export_records.py $W370 $WD/r370/records > /dev/null
+  $PY $B/regression/stage_cohort.py $WD/r370/records $WD/r370/records $WD/r370/cin $WD/r370/cout
+  $BIN/legality $WD/r370/cin $WD/r370/cout $WD/r370/cout/legality.json > /dev/null
+  $BIN/columns_h865 $WD/r370/cout/COHORT249-RECORDS.bin $WD/r370/cout/columns.json > /dev/null 2>&1
+  cp $WD/nine/GEOMETRY.json $WD/r370/nine/
+  $PY $C/nine/global_word_g.py --word $W370 --local-check $WD/r370 --out $WD/r370/nine --regression > /dev/null
+  $PY $C/nine/audit_g.py --local-check $WD/r370 --out $WD/r370/nine --regression > /dev/null
+  $PY $C/nine/certify_g.py --pricing $C/pricing --out $WD/r370/nine --complex-b $D/complex-b-nine.json --regression | sed 's/^/   [PR #370 word] /'
+  $PY $C/nine/regress386.py $WD/r370/nine $D/controls/pr386
+  echo "   comparison, same chain: PR #376's R822 word and PR #426's R767 word in this layout"
+  for n in pr376:$WD/w376.json.gz pr426:$D/controls/pr426-bit-candidate.json.gz; do
+    w=${n#*:}; d=$WD/n-${n%%:*}; RR=$($PY -c "import gzip,json;print(json.load(gzip.open('$w','rt'))['R'])")
+    $CXX -O2 -std=c++17 -DHDIM=8 -DNCOPY=9 -DVPORTS=120 -DRHELP=$RR $INC -o $BIN/columns_h$RR $CK/columns_h.cpp
+    mkdir -p $d/nine && $PY $B/export_records.py $w $d/records > /dev/null
+    $PY $B/regression/stage_cohort.py $d/records $d/records $d/cin $d/cout
+    $BIN/legality $d/cin $d/cout $d/cout/legality.json > /dev/null
+    $BIN/columns_h$RR $d/cout/COHORT249-RECORDS.bin $d/cout/columns.json > /dev/null 2>&1
+    cp $WD/nine/GEOMETRY.json $d/nine/
+    $PY $C/nine/global_word_g.py --word $w --local-check $d --out $d/nine > /dev/null
+    $PY $C/nine/audit_g.py --local-check $d --out $d/nine > /dev/null
+    $PY $C/nine/certify_g.py --pricing $C/pricing --out $d/nine --complex-b $D/complex-b-nine.json | tail -1 | sed "s/^/   [${n%%:*} word, R $RR] /"
+  done
+fi
+
+echo "== 7. B_4 (PR #381's layout, unsplit): geometry, banks, formal columns (step 3), price, finite bill, kappa"
+$PY $CK/geometry_k.py 4 $WORD unsplit | tail -2
+$PY $CK/tile_k.py $WD/records 4 8 9
+B424=$($PY -c "import json;print([s['b'] for s in json.load(open('$D/complex-b-b4.json'))['suppliers'] if s['name']=='pr424'][0])")
+$PY $CK/certify_bit_k.py $WD/records $B424 4 8 9 $WD/kappa_k4.json unsplit > $WD/certify_k4.log
+for n in pr370:$W370 pr376:$WD/w376.json.gz pr417:$D/controls/pr417-bitE8-nine-kernel.json.gz; do
+  $PY $B/export_records.py ${n#*:} $WD/c-${n%%:*}/records > /dev/null
+  $PY $CK/certify_bit_k.py $WD/c-${n%%:*}/records $B424 4 8 9 $WD/c-${n%%:*}/kappa_k4.json unsplit > /dev/null
+done
+$PY $B/receipts_k.py $WORD $WD/records $WD/cout/legality.json $WD/cout/columns_k4.json $WD/kappa_k4.json $WD/finite-input-k4.json > /dev/null
+$PY $CK/finite_k.py e8 $WD/finite-input-k4.json $WD/finite-k4.json
+B417=$($PY -c "import json;print(json.load(open('$WD/c-pr417/kappa_k4.json'))['bit_coarse'])")
+$PY $C/b4/kappa_b4.py $WD/kappa_k4.json $B417 $D/complex-b-b4.json $WD/kappa_b4.json
+if [ $QUICK = 0 ]; then
+  echo "   regression (PR #381): columns_k at K = 2 gives the five-stage columns_h receipt field for field (except seconds)"
+  $CXX -O2 -std=c++17 -DHDIM=8 -DNCOPY=9 -DVPORTS=120 -DRHELP=$R -DKPAIRS=2 $INC -o $BIN/columns_k2 $CK/columns_k.cpp
+  $BIN/columns_k2 $WD/cout/COHORT249-RECORDS.bin $WD/cout/columns_k2.json > /dev/null 2>&1
+  $PY -c "
+import json;a=json.load(open('$WD/cout/columns.json'));b=json.load(open('$WD/cout/columns_k2.json'))
+for d in (a,b): d.pop('seconds')
+assert a==b;print('   PASS')"
+  echo "== 8. B_3 (seven-stage bridged word, unsplit; informational): banks, formal columns, price with controls"
+  $CXX -O2 -std=c++17 -DHDIM=8 -DNCOPY=9 -DVPORTS=120 -DRHELP=$R -DKPAIRS=3 $INC -o $BIN/columns_k3 $CK/columns_k.cpp
+  $BIN/columns_k3 $WD/cout/COHORT249-RECORDS.bin $WD/cout/columns_k3.json > /dev/null 2>&1
+  $PY -c "
+import json;k=json.load(open('$WD/cout/columns_k3.json'))
+assert k['status']=='PASS_NEW_COHORT249_ALL_BRIDGED_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL' and k['formal_columns_checked']==6*120+$R and all(x['rejected'] for x in k['negative_controls'])
+print('   B_3 formal columns PASS:',k['formal_columns_checked'],'physical columns through 7 invocations;',len(k['negative_controls']),'omitted-bridge controls rejected')"
+  $PY $CK/tile_k.py $WD/records 3 8 7
+  $PY $CK/certify_bit_k.py $WD/records $B424 3 8 7 $WD/kappa_k3.json unsplit > /dev/null
+  for n in pr376:$WD/w376.json.gz pr426:$D/controls/pr426-bit-candidate.json.gz; do
+    $PY $B/export_records.py ${n#*:} $WD/c-${n%%:*}/records > /dev/null
+    $PY $CK/certify_bit_k.py $WD/c-${n%%:*}/records $B424 3 8 7 $WD/c-${n%%:*}/kappa_k3.json unsplit > /dev/null
+  done
+fi
+
+echo "== 9. summary against EXPECTED.json"
+$PY -c "
+import json,os
+from fractions import Fraction as F
+e=json.load(open('$EXP'))
+n=json.load(open('$WD/nine/BIT-NINE.json'));k4=json.load(open('$WD/kappa_k4.json'));kb=json.load(open('$WD/kappa_b4.json'))
+assert n['bit_coarse']==e['nine']['c'] and k4['bit_coarse']==e['b4']['c'] and k4['halving_degree']==2 and k4['maxchild']==50
+assert {str(r):x for r,x in json.load(open('$WD/cout/columns.json'))['local_raw_H']}==e['word']['local_histogram']
+for name,want in e['b4']['controls'].items(): assert json.load(open('$WD/c-'+name+'/kappa_k4.json'))['bit_coarse']==want,(name,want)
+for name,want in e['nine']['kappa'].items(): assert n['kappa_with_cited_complex'][name]['kappa']==want,(name,want)
+for name,want in e['b4']['kappa'].items(): assert kb['kappa'][name]['kappa']==want,(name,want)
+x=json.load(open('$WD/nine/COMPOSED-433.json'));assert x['bit_lower']==e['pr433']['bit_lower'] and x['kappa']==e['pr433']['kappa'] and x['binding_component']=='bit'
+c9=F(n['bit_coarse']);c4=F(k4['bit_coarse'])
+print('PASS kappa =',x['kappa'],'=',x['kappa_decimal'],'(bit-bound): this word in the compressed nine-stage layout with PR #433\'s complex b =',x['complex_lower'])
+print('     bit c (PR #433 engine, 10^-24 grid) =',x['bit_lower'],'=',x['bit_lower_decimal'],'; PR #433 (R758): kappa %s, %+.4f%%'%(json.load(open('$D/complex-b-433.json'))['kappa'],x['gain_over_pr433_percent']))
+print('PASS compressed nine-stage (PR #386 layout, m = 64; 10^-18 grid): c =',n['bit_coarse'],'= %.15e'%float(c9),'(PR #370 word: 1057833103534317/10^18, %+.3f%%)'%(100*float(c9/F(1057833103534317,10**18)-1)))
+k=n['kappa_with_cited_complex']['pr431']
+print('     kappa with PR #431 complex b =',k['complex_coarse'],':',k['kappa'],'= %.15e'%float(F(k['kappa'])),'(%s-bound; PR #431 with the PR #370 bit: %s)'%(k['binding'],k['cited_kappa_with_pr370_bit']))
+print('PASS B_4 (PR #381 layout, unsplit): c =',k4['bit_coarse'],'= %.15e'%float(c4),'(PR #417: 1044063934627389/10^18, %+.3f%%); complex-bound with every cited B_4 complex supplier'%(100*float(c4/F(1044063934627389,10**18)-1)))
+if not $QUICK:
+    for name,want in e['nine']['controls'].items():
+        got=json.load(open('$WD/n-'+name+'/nine/BIT-NINE.json'))
+        assert got['bit_coarse']==want and got['kappa_with_cited_complex']['pr431']['kappa']==e['nine']['kappa']['pr431'],name
+    print('     the same kappa with PR #431 holds for any bit word with c > b: PR #376 word c =',e['nine']['controls']['pr376'],', PR #426 word c =',e['nine']['controls']['pr426'])
+    k3=json.load(open('$WD/kappa_k3.json'));assert k3['bit_coarse']==e['b3']['c']
+    for name,want in e['b3']['controls'].items(): assert json.load(open('$WD/c-'+name+'/kappa_k3.json'))['bit_coarse']==want,(name,want)
+    print('PASS B_3 (unsplit, informational): c =',k3['bit_coarse'],'= %.15e'%float(F(k3['bit_coarse'])),'(PR #426 R767: 104575879789097/10^17, %+.3f%%)'%(100*float(F(k3['bit_coarse'])/F(104575879789097,10**17)-1)))
+"
diff --git a/research/e8-rank138-idle-hosting/upstream443/verify.sh b/research/e8-rank138-idle-hosting/upstream443/verify.sh
new file mode 100644
index 0000000000..6b03a7598f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/upstream443/verify.sh
@@ -0,0 +1,65 @@
+#!/usr/bin/env bash
+set -euo pipefail
+QUICK=0
+if [ "${1:-}" = --quick ]; then QUICK=1; shift; fi
+HERE=$(cd "$(dirname "$0")" && pwd)
+OUT=$(mkdir -p "$1" && cd "$1" && pwd)
+case "$OUT" in "$HERE"*) echo 'Output must be outside this package'; exit 2;; esac
+PY=${PYTHON:-python3}
+export PYTHONDONTWRITEBYTECODE=1
+export PYTHON="$PY"
+
+echo '== Frozen package and complete upstream provenance'
+"$PY" -I -B - "$HERE" <<'PY'
+import hashlib,json,pathlib,sys
+p=pathlib.Path(sys.argv[1])
+manifest=json.loads((p/'MANIFEST.json').read_text())
+actual={str(f.relative_to(p)):hashlib.sha256(f.read_bytes()).hexdigest()
+        for f in p.rglob('*') if f.is_file() and '__pycache__' not in f.parts and f.name!='MANIFEST.json'}
+assert actual==manifest, 'package differs from frozen manifest'
+source=json.loads((p/'SOURCE.json').read_text())
+for rel,expected in source['parent436_blobs'].items():
+    data=(p/'parent436'/rel).read_bytes()
+    assert hashlib.sha1(b'blob %d\0'%len(data)+data).hexdigest()==expected,rel
+for rel,expected in (source['kernel_identical_blobs'] | source['witness_identical_blobs']).items():
+    data=(p/rel).read_bytes()
+    assert hashlib.sha1(b'blob %d\0'%len(data)+data).hexdigest()==expected,rel
+print('PASS package manifest, byte-identical PR436 parent, PR417 code and PR441 witnesses')
+PY
+
+echo '== Reproduce PR436 with its unchanged verification wrapper'
+if [ "$QUICK" = 1 ]; then
+  bash "$HERE/parent436/verify.sh" --quick "$OUT/parent"
+else
+  bash "$HERE/parent436/verify.sh" "$OUT/parent"
+fi
+
+echo '== Rebuild primitive retiming, kernel and 32-replica bank admission'
+"$PY" -B "$HERE/code/rebuild.py" | tee "$OUT/REBUILD.json"
+B=$HERE/parent436/code/bit
+WORD=$HERE/data/word.json.gz
+mkdir -p "$OUT/candidate/nine"
+"$PY" -I -B "$B/export_records.py" "$WORD" "$OUT/candidate/records"
+"$PY" -I -B "$B/regression/stage_cohort.py" "$OUT/candidate/records" "$OUT/candidate/records" "$OUT/candidate/cin" "$OUT/candidate/cout"
+"$OUT/parent/bin/legality" "$OUT/candidate/cin" "$OUT/candidate/cout" "$OUT/candidate/cout/legality.json"
+"$OUT/parent/bin/columns_h" "$OUT/candidate/cout/COHORT249-RECORDS.bin" "$OUT/candidate/cout/columns.json"
+"$OUT/parent/bin/columns_k4" "$OUT/candidate/cout/COHORT249-RECORDS.bin" "$OUT/candidate/cout/columns_k4.json"
+"$PY" -I -B "$B/mutate_records.py" "$OUT/candidate/records" "$OUT/candidate/cin" "$OUT/candidate/cout" "$OUT/parent/bin/legality" "$OUT/parent/bin/columns_k4" "$OUT/parent/bin/legality_ncopy_h"
+"$PY" -I -B "$B/checkers/gram_frames.py" "$OUT/candidate/records" --gram e8ham --h 8 --positive
+
+echo '== Compressed geometry, residual routes, global audit and finite invoice'
+cp "$OUT/parent/nine/GEOMETRY.json" "$OUT/candidate/nine/GEOMETRY.json"
+"$PY" -B "$HERE/code/global_kernel.py" --word "$WORD" --local-check "$OUT/candidate" --out "$OUT/candidate/nine" --isometries "$HERE/data/residual-isometries.json"
+"$PY" -B "$HERE/code/audit_kernel.py" --word "$WORD" --local-check "$OUT/candidate" --out "$OUT/candidate/nine"
+"$PY" -B "$HERE/code/compose_kernel.py" --pricing "$HERE/parent436/code/pricing" --out "$OUT/candidate/nine" --cited "$HERE/parent436/data/complex-b-433.json" --receipt "$HERE/parent436/data/controls/pr433/CERTIFICATE.json"
+"$PY" -I -B - "$HERE" "$OUT" <<'PY'
+import json,pathlib,sys
+p,out=map(pathlib.Path,sys.argv[1:])
+g=json.loads((out/'candidate/nine/GLOBAL.json').read_text())
+r=json.loads((out/'candidate/nine/COMPOSED-433.json').read_text())
+expected=json.loads((p/'EXPECTED.json').read_text())
+for key,value in expected['global'].items(): assert g[key]==value,(key,g[key],value)
+for key,value in expected['result'].items(): assert r[key]==value,(key,r[key],value)
+assert len(r['strict_outer_constraints'])==47 and len(r['outer_controls'])==4
+print('PASS conditional kappa',r['kappa'],'=',r['kappa_decimal'])
+PY
diff --git a/research/e8-rank138-idle-hosting/vendor/pr439/LICENSE b/research/e8-rank138-idle-hosting/vendor/pr439/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/vendor/pr439/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
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+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
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+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
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diff --git a/research/e8-rank138-idle-hosting/vendor/pr439/NOTICE.md b/research/e8-rank138-idle-hosting/vendor/pr439/NOTICE.md
new file mode 100644
index 0000000000..3dfad2ad57
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/vendor/pr439/NOTICE.md
@@ -0,0 +1,26 @@
+# Attribution and scope
+
+New kernel selection, explicit residual route witnesses, integration and audits:
+chafreaky, with substantial OpenAI Codex assistance. Apache-2.0.
+
+- eumemic, PR #436 (`da8ca2025472553ac9b36f4400138ed48a6a0e3b`): R740 bit word,
+  reconstruction, elimination/reuse, independent checkers and #433 composition.
+  The entire parent package is byte-identical, including its notices, licenses,
+  source pins and Anthropic Claude disclosure.
+- chafreaky, PR #417: shared-donor kernel, exact local replay and tiling code;
+  the earlier implementation had substantial Anthropic Claude assistance.
+- rohanarun, PR #435 (`2c9c833ac8709402c37fc88a6a23393fb0d397fb`): prior mixed-width
+  residual-bank composition on #433. The new implementation derives from the
+  pinned #436 global/audit code and adds explicit residual isometries and controls.
+- icekylinx, PR #433: split-centre complex supplier, bit finite invoice and tail,
+  with OpenAI Codex assistance; the complex result is cited, not rebuilt here.
+- jacklightChen, PRs #386 and #425: compressed nine-stage geometry and the
+  mutable-basis complex interface, with OpenAI Codex assistance.
+- utcorvusvolat-dotcom / Dylan Crow, PR #370: E8 bit format, producer and
+  independent checker lineage, with Anthropic Claude assistance.
+- applecrusher (#376), ai-nanachi (#389/#426), DaysSky (#363/#375/#381),
+  DreamingOfClouds (#315), Jacob Sussman, and all earlier credited contributors:
+  see the unchanged `parent436/NOTICE.md` and source-specific notices.
+
+Do not infer an unconditional theorem or a new Lean proof from the finite
+certificates. No inherited author or AI-assistance disclosure has been removed.
diff --git a/research/e8-rank138-idle-hosting/vendor/pr439/bank_routes.py b/research/e8-rank138-idle-hosting/vendor/pr439/bank_routes.py
new file mode 100644
index 0000000000..919fe32f7e
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/vendor/pr439/bank_routes.py
@@ -0,0 +1,64 @@
+"""Exact residual bank routes for the kernel word; chafreaky with OpenAI Codex.
+
+The stored integer rows divided by two are an orthonormal basis. Entrance
+rows span E; the remaining rows span E-perp. A coordinate permutation sends
+the latter to the assigned contiguous block in a width-64 bank. This gives
+an explicit rational isometry, with only powers of two in denominators.
+"""
+from collections import Counter, deque
+from tile_m import tile
+
+
+def placement(widths):
+    by_width = {}
+    for rep in range(8):
+        for helper, width in enumerate(widths):
+            assert 0 < width <= 8
+            by_width.setdefault(width, deque()).append((rep, helper))
+    patterns = tile({w: len(q) for w, q in by_width.items()}, 64)
+    result = {}
+    bank = 0
+    for widths_in_bank, count in patterns:
+        for _ in range(count):
+            offset = 0
+            for width in widths_in_bank:
+                key = by_width[width].popleft()
+                result[key] = (bank, offset, width)
+                offset += width
+            assert offset == 64
+            bank += 1
+    assert all(not q for q in by_width.values())
+    assert len(result) == 8 * len(widths)
+    return result, bank
+
+
+def validate_isometries(rows, frames, roots, dimensions):
+    seen = set()
+    dot = lambda a, b: sum(x*y for x, y in zip(a, b))
+    for record in rows:
+        f = record['frame']
+        assert f not in seen
+        seen.add(f)
+        e = record['entrance_rank']
+        assert e == dimensions[f] and record['denominator'] == 2
+        basis = record['entrance_basis'] + record['residual_basis']
+        matrix = record['orthogonal_rows_numerator']
+        assert len(basis) == len(matrix) == 8
+        assert matrix == [roots[i] for i in basis]
+        assert all(len(r) == 8 and all(type(x) is int for x in r) for r in matrix)
+        assert all(dot(a,b) == 4*(i==j) for i,a in enumerate(matrix) for j,b in enumerate(matrix))
+        # The first e rows span precisely the frame, not only its dimension.
+        for i in frames[f]:
+            assert sum(dot(roots[i], q)**2 for q in matrix[:e]) == 4*dot(roots[i], roots[i])
+        assert len(record['entrance_basis']) == e
+        # This selected family needs coordinate permutations only. Checking the
+        # elementary reduction also bounds the literal route cost and primes.
+        reduced = [[x // 2 for x in row] for row in matrix]
+        assert all(x % 2 == 0 for row in matrix for x in row)
+        operations = record['gaussian_reduction']
+        assert len(operations) <= 7
+        for kind, i, j, scalar in operations:
+            assert kind == 'swap' and scalar is None and 0 <= i < 8 and 0 <= j < 8
+            reduced[i], reduced[j] = reduced[j], reduced[i]
+        assert reduced == [[int(i == j) for j in range(8)] for i in range(8)]
+    return seen
diff --git a/research/e8-rank138-idle-hosting/vendor/pr439/e8core.py b/research/e8-rank138-idle-hosting/vendor/pr439/e8core.py
new file mode 100644
index 0000000000..78983b3687
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/vendor/pr439/e8core.py
@@ -0,0 +1,203 @@
+"""Our own engine for bitE8/1 words (E8 root-line labels, h = 8): frame algebra over Q via root-line masks,
+legality/F2 replay, five-stage histogram, exact bit coarse saving and PR #315 outer assembly (our engine copies).
+Chafik Boukhalfa (chafreaky) with Anthropic Claude assistance; Apache-2.0."""
+import gzip, json, os, importlib.util
+from fractions import Fraction as Q
+from collections import Counter
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+def _load(n):
+    s = importlib.util.spec_from_file_location('e8_' + n, os.path.join(HERE, "engines", n + ".py"))
+    m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+moment = _load('moment'); other = _load('base_two_moment'); outer = _load('outer')
+
+B2 = Q(876248285600677, 10**18)   # Sussman E8 five-stage (PR #352)
+B3 = Q(932783231884153, 10**18)   # DaysSky seven-stage B_3 (PR #363; no Lean proof)
+
+
+def load_word(p):
+    with (gzip.open(p, 'rt') if p.endswith('.gz') else open(p)) as f:
+        return json.load(f)
+
+
+def save_word(c, p):
+    with gzip.open(p, 'wt') as f:
+        json.dump(c, f, separators=(',', ':'))
+
+
+def rank(vecs):
+    rows = [[Q(x) for x in r] for r in vecs]; rk = 0
+    n = len(rows[0]) if rows else 0
+    for col in range(n):
+        p = next((i for i in range(rk, len(rows)) if rows[i][col] != 0), None)
+        if p is None: continue
+        rows[rk], rows[p] = rows[p], rows[rk]
+        for i in range(len(rows)):
+            if i != rk and rows[i][col] != 0:
+                f = rows[i][col] / rows[rk][col]; rows[i] = [a - f * b for a, b in zip(rows[i], rows[rk])]
+        rk += 1
+    return rk
+
+
+class Lat:
+    """Root-spanned subspaces of Q^8 represented by the mask of root lines they contain."""
+    def __init__(self, lines):
+        self.lines = [tuple(x) for x in lines]; self.v = len(lines)
+        self._dim = {0: 0}; self._close = {}
+        # Gram (form <x,y>/2) for orthogonality
+        self.ip = [[sum(a * b for a, b in zip(x, y)) // 2 for y in self.lines] for x in self.lines]
+
+    def close(self, mask):
+        """mask of all root lines in span(roots of mask)"""
+        if mask in self._close: return self._close[mask]
+        idx = [i for i in range(self.v) if mask >> i & 1]
+        basis = []
+        for i in idx:
+            if rank([self.lines[j] for j in basis] + [self.lines[i]]) > len(basis): basis.append(i)
+        d = len(basis); out = 0
+        if d == 8: out = (1 << self.v) - 1
+        elif d:
+            B = [self.lines[j] for j in basis]
+            for i in range(self.v):
+                if rank(B + [self.lines[i]]) == d: out |= 1 << i
+        self._close[mask] = out; self._close[out] = out; self._dim[out] = d
+        return out
+
+    def dim(self, mask):
+        if mask not in self._dim: self.close(mask)
+        return self._dim[mask]
+
+    def basis(self, mask):
+        b = []
+        for i in range(self.v):
+            if mask >> i & 1 and rank([self.lines[j] for j in b] + [self.lines[i]]) > len(b): b.append(i)
+        return b
+
+    def perp(self, t):
+        return self.close(sum(1 << j for j in range(self.v) if self.ip[t][j] == 0))
+
+
+def to_masks(c, L):
+    return [L.close(sum(1 << i for i in fr)) for fr in c['frames']]
+
+
+PHASES = ('D', 'A', 'B', 'C')
+
+
+def replay(c, L=None, masks=None, check_f2=True, span=True, span_mode='z'):
+    """Exact legality + F2 replay + histogram of a bitE8/1 word. Returns dict(H_local, steps, ...).
+    Legality: each register's frames nested (mask inclusion = exact Q-subspace inclusion for root-spanned frames) and
+    strictly increasing at each move; every gate at one common frame; D compensation at frame 0; y at frame 0 at the
+    scatter; COPY of retained totals; final frames (x, helpers FULL; y_t at its cap t-perp).
+    Source-span: every non-target operand's x-support lies in the gate frame."""
+    L = L or Lat(c['lines']); masks = masks or to_masks(c, L)
+    v, R, h = c['v'], c['R'], c['h']; n = 2 * v + R; FULL = (1 << v) - 1
+    cur = [masks[f] for f in c['start']]
+    for r in range(v): assert cur[r] == L.close(1 << r), 'x start'
+    for r in range(v, 2 * v): assert cur[r] == 0, 'y start at 0'
+    sig = [L.dim(cur[r]) for r in range(n)]
+    H = Counter(); steps = 0; viol = []
+    val = [1 << i for i in range(n)]
+    zsupp = [{i: 1} if i < v else {} for i in range(n)]  # integer support of each register over the x columns (all ADDs are +1)
+    def climb(r, m):
+        nonlocal steps
+        if cur[r] == m: return
+        assert cur[r] & ~m == 0 and cur[r] != m, ('not nested', r)
+        H[L.dim(m) - L.dim(cur[r])] += 1; steps += 1; cur[r] = m
+    def run(gates, ph):
+        for k, (f, d, srcs) in enumerate(gates):
+            m = masks[f]
+            assert d >= v and d not in srcs and len(set(srcs)) == len(srcs), (ph, k)
+            for x in [d] + srcs: climb(x, m)
+            for s in srcs:
+                val[d] ^= val[s]
+                if span:
+                    if s < v or s >= 2 * v:
+                        ms = sum(1 << i for i in zsupp[s])
+                        if ms & ~m: viol.append((ph, k, s))
+                    zd = zsupp[d]
+                    for i, a in zsupp[s].items():
+                        w = zd.get(i, 0) + a
+                        if w: zd[i] = w
+                        else: zd.pop(i, None)
+                    if span_mode == 'f2':
+                        zsupp[d] = {i: 1 for i in range(v) if val[d] >> i & 1}
+            if span and d >= 2 * v:
+                md = sum(1 << i for i in zsupp[d])
+                if md & ~m: viol.append((ph, k, d))
+    run(c['D'], 'D')
+    for r in range(v, n): assert cur[r] == masks[c['start'][r]], 'D compensation at frame 0 (helpers untouched otherwise)'
+    run(c['A'], 'A')
+    for t in range(v): assert cur[v + t] == 0, 'y at frame 0 at the scatter'
+    copies = [val[q] for q in c['ret']]
+    for q in c['ret']:
+        assert q >= 2 * v; H[L.dim(cur[q])] += 1
+    for t, row in enumerate(c['scatter']):
+        for k in row: val[v + t] ^= copies[k]
+    run(c['B'], 'B'); run(c['C'], 'C')
+    for r in range(n): climb(r, masks[c['final'][r]])
+    for r in range(v): assert cur[r] == FULL
+    for r in range(2 * v, n): assert cur[r] == FULL
+    for t in range(v): assert cur[v + t] == L.perp(t), 'y final at cap'
+    if check_f2:
+        for s in range(v): assert val[s] == 1 << s
+        for t in range(v): assert val[v + t] == (1 << (v + t)) | (1 << t), ('target', t)
+        for r in range(2 * v, n): assert val[r] == 1 << r, ('helper', r)
+    return dict(sig=sig, viol=viol, H=H, steps=steps, n=n, v=v, R=R, h=h, L=L, masks=masks, ncopy=len(c['ret']))
+
+
+def profile(H_local, v, h=8):
+    prof = Counter({j: 5 * c for j, c in H_local.items()})
+    for j in (2 * h - 2, h - 1, 2 * h + 2, 4): prof[j] += 2 * v
+    return prof
+
+
+def coarse(H, m, W):
+    grid = Q(1, 10**18)
+    root = moment.certify(dict(H), m, W, True); c = Q(int(Q(root['lower']) * 10**18), 10**18)
+    assert moment.moment(H, m, W, c, True)[1] < 1 < moment.moment(H, m, W, c + grid, True)[0]
+    fb = 32 * m * m * sum(H.values())
+    _, up = other.moment(m, W, list(H.items()), c); _, bad = other.moment(m, W, [(1, fb)], c)
+    lo, _ = other.moment(m, W, list(H.items()), c + grid); blo, _ = other.moment(m, W, [(1, fb)], c + grid)
+    assert up + Q(1, 10**16) * bad < 1 < lo + Q(1, 10**16) * blo
+    return c
+
+
+def kappa(c, b):
+    grid = Q(1, 10**18); eta = Q(1, 10**12); beta = Q(1, 10**9); cap = (1 - beta) * b
+    sv = min(c, Q(((cap - grid) * 10**18).__floor__(), 10**18)); binding = 'bit' if sv == c else 'complex'
+    chain = [Q(384599, 10**10)]
+    for _ in range(3):
+        a = (1 - sv) * sv + sv * chain[-1]; assert chain[-1] < a < sv < 1 - a; chain.append(a)
+    bit = chain[-1]
+    bridge = dict(proof='PROOF.md', representation='Exact powers with source-bound finite overcharges',
+                  semantic=dict(G=dict(base=2, exponent=30000), E=dict(base=2, exponent=100000), B_upper=dict(base=2, exponent=100001),
+                                C0=dict(base=2, exponent=210000), C1=1, strict_literal_gap=1, induction_gap_lower=1),
+                  rows=dict(coefficient=20161, degree=10**6, suffix_slope=4 * 10**6, degree_gap=Q(10**6) - Q(51 * 20161, 25)))
+    q = bit * (1 - 2 * eta); mn = (1 - eta) * q / (1 + q); t = mn * 10**18; k = Q((t.numerator - 1) // t.denominator, 10**18)
+    asm = outer.assembly(bit, b, bridge, k, eta=eta, beta=beta)
+    assert len(asm['strict_constraints']) == 47 and min(asm['strict_constraints'].values()) > 0
+    try:
+        outer.assembly(bit, b, bridge, k + grid, eta=eta, beta=beta); raise SystemExit('ADJACENT ADMITTED')
+    except AssertionError: pass
+    return k, binding
+
+
+def price_word(c, **kw):
+    r = replay(c, **kw)
+    v, h, R = r['v'], r['h'], r['R']; m = 5 * h
+    resid = sum(h - r['sig'][x] for x in range(2 * v, 2 * v + R))
+    T = 1 if resid % h == 0 else h
+    W = (4 * v * h + resid) * T // h; assert (4 * v * h + resid) * T % h == 0
+    prof = Counter({j: T * k for j, k in profile(r['H'], v, h).items()}); mass = sum(a * b for a, b in prof.items())
+    L_copy = h * r['ncopy']
+    assert m * W - mass == T * (4 * v - 5 * L_copy), ('deficit', m * W - mass)
+    assert 2 * max(prof) < m
+    cc = coarse(prof, m, W)
+    return dict(c=cc, H=r['H'], prof=prof, W=W, T=T, resid=resid, m=m, deficit=m * W - mass, replay=r)
+
+
+def phi_fn(m, W, a):
+    """linearized moment term per child of rank r (float), for search scoring"""
+    import math
+    return lambda r: r / (m * W) * math.exp(a * math.log(m / r))
diff --git a/research/e8-rank138-idle-hosting/vendor/pr439/engines/base_two_moment.py b/research/e8-rank138-idle-hosting/vendor/pr439/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/vendor/pr439/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/e8-rank138-idle-hosting/vendor/pr439/engines/moment.py b/research/e8-rank138-idle-hosting/vendor/pr439/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/vendor/pr439/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/e8-rank138-idle-hosting/vendor/pr439/engines/outer.py b/research/e8-rank138-idle-hosting/vendor/pr439/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/vendor/pr439/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/e8-rank138-idle-hosting/vendor/pr439/tile_m.py b/research/e8-rank138-idle-hosting/vendor/pr439/tile_m.py
new file mode 100644
index 0000000000..cd5fd9b539
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/vendor/pr439/tile_m.py
@@ -0,0 +1,93 @@
+"""Residual census (8 - sigma per helper) and an exact zero-padding bank tiling of width m = (2K+1)h with T replicas:
+tile() and economy_tile() verbatim from our PR #329 bank_template.py (via code/tile.py of our dtst3 package).
+usage: tile_m.py WORD.json.gz M [replicas]  (replicas default: the least T with T x residual sum = 0 mod M that tiles)"""
+import sys,os,collections
+from collections import Counter
+sys.path.insert(0,os.path.dirname(os.path.abspath(__file__)))
+from e8core import *
+def economy_tile(blocks, m):
+    """Exact zero-padding tiling used when the filler search of tile() runs out of filler blocks (the kernel pivots
+    and early restorations of the stage stack add many residual widths that do not divide m; the PR #299 analogue at
+    p = 12 was the (r^4, 24, 4^(24-r)) re-tiling). The fillers are the two most numerous widths dividing m (here the
+    full helper width h and the rank-4 entrance residual). Each other width w, in decreasing order, gets the bank
+    w^a F^c f^b (w*a + F*c + f*b = m) that spends the fewest narrow fillers f per w block (then the largest a), plus
+    at most one bank w^r F^c' f^b' for the remainder r = n mod a. The leftover fillers fill pure banks F^(m/F),
+    f^(m/f) and y residue banks F^j f^k. Every bank sums to m and every block is used exactly once (no padding)."""
+    from fractions import Fraction
+    blocks = {w: n for w, n in blocks.items() if n}
+    div = sorted((w for w in blocks if m % w == 0), key=lambda w: (-blocks[w], w))
+    assert len(div) >= 2, ('economy tiling needs two filler widths', blocks)
+    F, f = sorted(div[:2], reverse=True)
+
+    def fill(rest):
+        """(c, b) with F*c + f*b = rest, c maximal (fewest narrow fillers); None if impossible."""
+        return next(((c, (rest - F*c)//f) for c in range(rest//F, -1, -1) if (rest - F*c) % f == 0), None)
+
+    left = {F: blocks[F], f: blocks[f]}; out = []
+    for w in sorted((x for x in blocks if x not in (F, f)), reverse=True):
+        n = blocks[w]
+        opts = [(Fraction(cb[1], a), -a, a, cb) for a in range(m//w, 0, -1) for cb in [fill(m - w*a)] if cb]
+        assert opts, ('no bank for width', w)
+        _, _, a, (c, b) = min(opts); q, r = divmod(n, a)
+        if q: out.append(((w,)*a + (F,)*c + (f,)*b, q)); left[F] -= q*c; left[f] -= q*b
+        if r:
+            cb = fill(m - w*r); assert cb, ('no remainder bank', w, r)
+            out.append(((w,)*r + (F,)*cb[0] + (f,)*cb[1], 1)); left[F] -= cb[0]; left[f] -= cb[1]
+    assert left[F] >= 0 and left[f] >= 0, ('fillers exhausted', left)
+    pF, pf = m//F, m//f
+    for y in range((pF*pf) + 1):
+        for j in range(1 if y else 0, pF if y else 1):
+            if (m - F*j) % f: continue
+            k = (m - F*j)//f; aF, af = left[F] - y*j, left[f] - y*k
+            if aF >= 0 and af >= 0 and aF % pF == 0 and af % pf == 0:
+                out += ([((F,)*j + (f,)*k, y)] if y else []) + ([((F,)*pF, aF//pF)] if aF else []) + ([((f,)*pf, af//pf)] if af else [])
+                return out
+    raise AssertionError(('no exact zero-padding tiling', blocks, m))
+
+
+def tile(blocks, m):
+    """Exact tiling of {width: number of blocks} into banks of total width m, as ((widths, banks), ...).
+
+    A width dividing m fills pure banks. A width w not dividing m is mixed with a filler width f dividing m:
+    banks w^a f^b with a maximal (w*a + f*b = m), then at most one bank w^r f^t for the remainder r. Fillers
+    are tried in a fixed order (most blocks first) with backtracking until every pure width also divides out.
+    Fails (AssertionError) unless every block is used and every bank is full; there is no padding."""
+    blocks = {w: n for w, n in blocks.items() if n}
+    assert all(0 < w <= m for w in blocks)
+    mixed = sorted(x for x in blocks if m % x)
+
+    def search(i, left, out):
+        if i == len(mixed):
+            if any(left[w] % (m // w) for w in left): return None
+            return out + [(tuple([w]*(m // w)), left[w]//(m // w)) for w in sorted(left) if left[w]]
+        w = mixed[i]; n = blocks[w]
+        for f in sorted(left, key=lambda x: (-left[x], x)):
+            a = next((a for a in range(m // w, 0, -1) if (m - w*a) % f == 0), None)
+            if a is None: continue
+            b = (m - w*a)//f; q, r = divmod(n, a)
+            if r and (m - w*r) % f: continue
+            t = (m - w*r)//f if r else 0
+            if q*b + t > left[f]: continue
+            rest = dict(left); rest[f] -= q*b + t
+            found = search(i + 1, rest, out + ([(tuple([w]*a + [f]*b), q)] if q else []) + ([(tuple([w]*r + [f]*t), 1)] if r else []))
+            if found is not None: return found
+        return None
+    out = search(0, {w: n for w, n in blocks.items() if not m % w}, [])
+    if out is None: out = economy_tile(blocks, m)
+    assert all(sum(widths) == m and count > 0 for widths, count in out)
+    used = Counter()
+    for widths, count in out:
+        for x in widths: used[x] += count
+    assert used == Counter(blocks), 'every block used exactly once'
+    return tuple(out)
+if __name__ == '__main__':
+    c = load_word(sys.argv[1]); m = int(sys.argv[2])
+    L = Lat(c['lines']); M = to_masks(c, L); v = c['v']; n = 2 * v + c['R']
+    res = Counter(8 - L.dim(M[c['start'][r]]) for r in range(2 * v, n)); tot = sum(k * x for k, x in res.items())
+    reps = [int(sys.argv[3])] if len(sys.argv) > 3 else [t for t in range(1, 200) if t * tot % m == 0]
+    for T in reps:
+        try: pat = tile({r: T * k for r, k in res.items() if r > 0}, m); break
+        except AssertionError: pat = None
+    assert pat, 'no tiling'
+    print('   residual census', dict(sorted(res.items())), 'sum', tot)
+    print('   PASS exact width-%d tiling with %d replicas: %d banks' % (m, T, sum(k for _, k in pat)), pat)
diff --git a/research/e8-rank138-idle-hosting/verify.py b/research/e8-rank138-idle-hosting/verify.py
new file mode 100644
index 0000000000..ee88a6e2db
--- /dev/null
+++ b/research/e8-rank138-idle-hosting/verify.py
@@ -0,0 +1,57 @@
+"""Full rank-138 / idle-hosting composition; Python 3.11+, standard library.
+Rebuild the full R740/complex parent, reconstruct pinned PR443, emit and audit
+32 bit replicas, then host both suppliers. Complex replication remains eight.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+import gzip, hashlib, json, os, subprocess, sys, time
+assert __debug__
+ROOT=Path(__file__).resolve().parent
+PARENT=ROOT.parent/'e8-joint-frame-retiming'
+OUT=Path(sys.argv[1]).resolve()
+assert not OUT.exists() and not OUT.is_relative_to(ROOT.parent)
+sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+read=lambda p:json.loads(p.read_text())
+def integrity():
+    m=read(ROOT/'MANIFEST.json')
+    actual={p.relative_to(ROOT).as_posix():sha(p) for p in ROOT.rglob('*') if p.is_file() and p!=ROOT/'MANIFEST.json' and '__pycache__' not in p.parts}
+    assert actual==m['files']
+    assert sha(PARENT/'MANIFEST.json')==m['parent_manifest_sha256']
+    up=ROOT/'upstream443'; expected=read(up/'MANIFEST.json')
+    assert {p.relative_to(up).as_posix():sha(p) for p in up.rglob('*') if p.is_file() and p.name!='MANIFEST.json' and '__pycache__' not in p.parts}==expected
+integrity();OUT.mkdir(parents=True)
+env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONINTMAXSTRDIGITS='0');env.pop('PYTHONOPTIMIZE',None)
+steps=[]
+def run(name,file,*args,cwd=None):
+    log=OUT/(name+'.log');start=time.monotonic();print('RUN',name,flush=True)
+    with log.open('w') as f:q=subprocess.run([sys.executable,'-B',str(file),*map(str,args)],cwd=cwd,env=env,stdout=f,stderr=subprocess.STDOUT)
+    assert q.returncode==0,(name,log.read_text()[-3000:])
+    steps.append(dict(name=name,seconds=round(time.monotonic()-start,2),log_sha256=sha(log)))
+    print('PASS',name,flush=True)
+try:
+    run('parent-full',PARENT/'verify.py',OUT/'parent','--replay-phases')
+    run('rank138-rebuild',ROOT/'upstream443/code/rebuild.py')
+    changed=OUT/'changed';changed.mkdir()
+    for d in ('work','inherited','split-centres'):
+        (changed/d).symlink_to(OUT/'parent'/d,target_is_directory=True)
+    b=changed/'bit426-source-centres';b.mkdir()
+    w=json.loads(gzip.decompress((ROOT/'upstream443/data/word.json.gz').read_bytes()))
+    old=read(OUT/'parent/bit426-source-centres/bit-source-centres.json')
+    assert {tuple(sorted(x)) for x in w['frames']}=={tuple(sorted(x)) for x in old['frames']}
+    raw=json.dumps(w,sort_keys=True,separators=(',',':')).encode()
+    (b/'bit-source-centres.json').write_bytes(raw)
+    (b/'bit-kernel-receipt.json').write_text(json.dumps(dict(output_sha256=hashlib.sha256(raw).hexdigest(),new_frames=0))+'\n')
+    run('export-records',PARENT/'vendor/export_records.py',b/'bit-source-centres.json',b/'records')
+    run('bit-global-32',ROOT/'code/bit_global.py','--source',b,'--local-check',b,'--out',b/'global',cwd=changed)
+    run('bit-global-audit',ROOT/'code/bit_audit.py','--local-check',b,'--out',b/'global',cwd=changed)
+    run('bit-hosting',ROOT/'code/bit_hosted.py',b/'global',b,OUT/'bit',cwd=changed)
+    run('complex-hosting',ROOT/'code/complex_hosted.py',changed/'split-centres',OUT/'complex',cwd=changed)
+    run('independent-hosting-audit',ROOT/'code/audit.py',changed,OUT/'bit',OUT/'complex',OUT/'AUDIT.json')
+    run('exact-assembly',ROOT/'code/assemble.py',changed,OUT/'bit',OUT/'complex',OUT/'AUDIT.json',OUT/'RESULT.json')
+    actual=read(OUT/'RESULT.json')
+    for k,v in read(ROOT/'EXPECTED.json').items():assert actual[k]==v,(k,actual[k],v)
+    integrity()
+    receipt=dict(status='PASS_FULL_RANK138_IDLE_HOSTING',python=sys.version.split()[0],kappa=actual['kappa'],kappa_decimal=actual['kappa_decimal'],manifest_sha256=sha(ROOT/'MANIFEST.json'),checks=steps)
+    (OUT/'RECEIPT.json').write_text(json.dumps(receipt,indent=2)+'\n');print(json.dumps(receipt,indent=2))
+except BaseException as e:
+    (OUT/'FAILURE.json').write_text(json.dumps(dict(error=repr(e),completed=steps),indent=2)+'\n');raise
diff --git a/research/split-centres-global/.gitattributes b/research/split-centres-global/.gitattributes
new file mode 100644
index 0000000000..a251e913f2
--- /dev/null
+++ b/research/split-centres-global/.gitattributes
@@ -0,0 +1,6 @@
+# Hashes bind exact imported and generated bytes.
+* -text
+vendor/** -whitespace
+inputs/** -whitespace
+notices/** -whitespace
+proofs/** -whitespace
diff --git a/research/split-centres-global/CERTIFICATE.json b/research/split-centres-global/CERTIFICATE.json
new file mode 100644
index 0000000000..7e807079c1
--- /dev/null
+++ b/research/split-centres-global/CERTIFICATE.json
@@ -0,0 +1,119 @@
+{
+  "status": "PASS_CONDITIONAL_SPLIT_CENTRE_ASSEMBLY",
+  "kappa": "560432476129139/500000000000000000",
+  "kappa_decimal": "0.001120864952258278",
+  "bit_lower": "561061350132569610283/500000000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "gain_over_pr425_percent": 6.9522005058117555,
+  "bit_invoice": {
+    "prefix_bits": 223,
+    "charged_prefix_bits": 256,
+    "coefficient_bits": 223,
+    "two_level_coefficient_bits": 483,
+    "charged_two_level_coefficient_bits": 512,
+    "row_coefficient": 18355,
+    "live": 14502,
+    "physical": 14511
+  },
+  "strict_outer_constraints": {
+    "bit_positive": "14363170563393781995540516430294897054798660372747977408982986647014886397057213204999835240182750048003850764774138423033492369699369310106183121233447528983183/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "791857266447229204459483569705102945201339627252022591017013352985113602942786795000164759817249951996149235225861576966507630300630689893816878766552471016817/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "30066013450793671/1000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "791857266447229189304455739864091745201339627252022591017013352985113602942786795000164759817249951996149235225861576966507630300630689893816878766552471016817/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_positive": "7181585281696890983407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_internal": "14363170563393781995540516430294897054798660372747977408982986647014886397057213204999835240182750048003850764774138423033492369699369310106183121233447528983183/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_leaf": "395928633223614609015398433325827868141186243920908350307167049240534210454380044514968776965838180997909857795680836487104579924453767980400809082645545614591621233447528983183/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_positive": "7181585281696892583407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "c_below_one": "6392818414718303107416592912348246333468141186243920908350307167049240534210454380044514968776965838180997909857795680836487104579924453767980400809082645545614591621233447528983183/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_reservations": "1/4000000000000000000",
+    "lambda_above_tau": "14363170563393781995540516430294897054798660372747977408982986647014886397057213204999835240182750048003850764774138423033492369699369310106183121233447528983183/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_sigma": "791857266447229218822654133098884940741856057546919645815673725733091011925773442015051156874463156995984475408611624970358395074769112927309248465921781123000121233447528983183/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_internal": "14363170563393781995540516430294897054798660372747977408982986647014886397057213204999835240182750048003850764774138423033492369699369310106183121233447528983183/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_prime_above_lambda": "14363170563393781995540516430294897054798660372747977408982986647014886397057213204999835240182750048003850764774138423033492369699369310106183121233447528983183/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_leaf": "395928633223614609015398433325827868141186243920908350307167049240534210454380044514968776965838180997909857795680836487104579924453767980400809082645545614591621233447528983183/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_reservations": "1/4000000000000000000",
+    "lambda_prime_below_one": "7181585281696890983407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "epsilon_positive": "6399999999999999993600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000/6407181585281696890983407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817",
+    "epsilon_below_one": "7181585281696897383407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817/6407181585281696890983407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817",
+    "guard_width": "7181585281696897383407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817/6407181585281696890983407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817",
+    "K_geometry": "4807181585281696892583407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817/6407181585281696890983407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817000000000000000000",
+    "K_dominates_log": "231664041345061050845983947421186256401668584010497584446258683699366907737186677571792433338340060113453513521617978855187267028104098984087218414251878140832554446748323117142213588175726741393/206683276944570867451077647988766247307479316572776744891925575256476111799662761934047904233001101994161357746522719973016545013550824072000632231965075950141464786411824273258607000000000000000000",
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+    "phase_local": "57452682253575172660075115932332441271463422396879066665683849849996634666672126693120783994727674596531689914600391489101073218400050692643898107263289403063667839215065313749127621233447528983183/51257452682253575127867256701214029332254870510048632733197542663606075726316364959643880249784273294552016721137634553308103163360604369856156793527338835635083267030132419768134536000000000000000000",
+    "phase_boundary": "11490536450715029406269754961108975467567014357972880107649718965136053613580158978016584167309038954918313004492748842618542529916554807718463285392220894997054215109129499241498821233447528983183/10251490536450715025573451340242805866450974102009726546639508532721215145263272991928776049956854658910403344227526910661620632672120873971231358705467767127016653406026483953626907200000000000000000",
+    "gamma_sublinear": "1/2000000000000000000",
+    "cell_above_band": "12799999999999999980792818414718303109016592912348246333468141186243920908350307167049240534210454380044514968776965838180997909857795680836487104579924453767980400809082645545614591621233447528983183/25628726341126787563933628350607014666127435255024316366598771331803037863158182479821940124892136647276008360568817276654051581680302184928078396763669417817541633515066209884067268000000000000000000",
+    "prime_interval_packing": "7181585281696897383407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817/6407181585281696890983407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817",
+    "alpha_positive": "14363170563393788359632590021810442080310539860404516767526852145439839929398406960210596656522703682519149061374476508023700697946773300526302961759162676751217566615750487648225621233447528983183/12814363170563393781966814175303507333063717627512158183299385665901518931579091239910970062446068323638004180284408638327025790840151092464039198381834708908770816757533104942033634000000000000000000",
+    "alpha_below_one": "12799999999999999993607181585281696890983407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817/12814363170563393781966814175303507333063717627512158183299385665901518931579091239910970062446068323638004180284408638327025790840151092464039198381834708908770816757533104942033634000000000000000000",
+    "alpha_below_one_fourth": "3189227622077454657132070953804066391185618867017635029057319564329939892965374403017531918954994377226981896009727683073732747012090999815483496633699514550441486622767525747860182878766552471016817/12814363170563393781966814175303507333063717627512158183299385665901518931579091239910970062446068323638004180284408638327025790840151092464039198381834708908770816757533104942033634000000000000000000",
+    "delta_positive": "1/8000000000000000000",
+    "delta_below_one_eighth": "999999999999999999/8000000000000000000",
+    "short_record_fallback": "81827972558059963142482295831039750365059753405165839859500887157900070163784215146039541956047009515286378723945407637791323146319740145866082020356197908534083134290654194352838948148633280800174595114507063924980758679362172726895650066012032777455278212210736064133662717611940569491044304210260992667579958374711353997952140066809896811489/82011924291605720204587610721942446931607792816077812373116068261769721162106183935430208399654837271283226753820215285292965061376966991769850869643742137016133227248211871629015257600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "small_field_exposure": "1/1000000000000000000",
+    "artificial_boundary": "358859621458028601093359598365557325330989185343344322865175917750116843085479998176003320395642823216282588862770178911921831577311447916339793034478937323776724933813811421508232513136299657413050451/51257452682253575127867256701214029332254870510048632733197542663606075726316364959643880249784273294552016721137634553308103163360604369856156793527338835635083267030132419768134536000000000000000000",
+    "literal_scalar_guard": "1",
+    "row_product_gap": "23971789/25",
+    "balanced_prefix_above_kappa": "5122866517862023505724960619093421545844111701898553134698525509504383311993872387184513125657251444712150871805627114225726283245038727038504547469670408073428467093191496467269437/3203590792640848445491703543825876833265929406878039545824846416475379732894772809977742515611517080909501045071102159581756447710037773116009799595458677227192704189383276235508408500000000000000000",
+    "coordinate_movement_above_kappa": "16099174487823595540516430294897054798660372747977408982986647014886397057213204999835240182750048003850764774138423033492369699369310106183121233447528983183/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_phase_layer_above_kappa": "3838551450442350120466514150535089425156364590041027177747358186058007158198199154413541220091468727605299653469049909287939671070001907844989495748423461692471525807616440463522057/6407181585281696890983407087651753666531858813756079091649692832950759465789545619955485031223034161819002090142204319163512895420075546232019599190917354454385408378766552471016817000000000000000000",
+    "bulk_exposure_above_kappa": "16099174487823595540516430294897054798660372747977408982986647014886397057213204999835240182750048003850764774138423033492369699369310106183121233447528983183/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "Gaussian_arithmetic_above_kappa": "49929956359383891636682334467235976400846493161596454696927943987316335662954230095174784854400852306299403498179012231794056054820241901455974763560139756902928431597231181121226907/51257452682253575127867256701214029332254870510048632733197542663606075726316364959643880249784273294552016721137634553308103163360604369856156793527338835635083267030132419768134536000000000000000000",
+    "scalar_work_above_kappa": "3022347308020427168024638512713719642678957136664830842541068612764774941044496502999868999171719558143016474349913180337924305460021763455362126412952366988818802604491895640211767/2050298107290143005114690268048561173290194820401945309327901706544243029052654598385755209991370931782080668845505382132324126534424174794246271741093553425403330681205296790725381440000000000000000",
+    "dimension_above_kappa": "3196409207359151553231162974036146672459031212215382000019265285423173401803752699526640796382355306275012080586149285130394424095589341109716483649580049811311843280287131837920058593191496467269437/3203590792640848445491703543825876833265929406878039545824846416475379732894772809977742515611517080909501045071102159581756447710037773116009799595458677227192704189383276235508408500000000000000000"
+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "48640105104416009930955104551272628756769/40000000000000000000000000000000000000000000000",
+      "cutoff_log2": "24346328299693"
+    },
+    {
+      "gap": "10916033216189494908506938862091413300675156484737667525550897/8000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "19335382939135799529"
+    },
+    {
+      "gap": "2449825733746901655394438404809502019511708753179325050819248403056515410563319361/1600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "15355787073969246541017124"
+    },
+    {
+      "gap": "549801013506219857550281901936704203615404924098069138182437287931091972275689180385852832590942771793/320000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "12195269025875323655994833423982"
+    },
+    {
+      "gap": "123388839576821941106964776874551364767558290306753584545234931806617408234472738882773008179061080923160999418343337504609/64000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "9685246734476302780854842486398253310"
+    },
+    {
+      "gap": "27691483569705102945201339627252022591017013352985113602942786795000164759817249951996149235225861576966507630300630689893816878766552471016817/12800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "7691835588756193183914168151850588989363719"
+    }
+  ],
+  "bit_template_sha256": "c40f89a2ae3c2c5635ddf8f18d74f24567ddf67fc8c8e93a1fc7a1a8098e857e",
+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f",
+  "scope": "Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim.",
+  "verification_steps": [
+    "hamming_packets",
+    "complex_construct",
+    "complex_audit",
+    "complex_emit",
+    "complex_phases",
+    "bit_construct",
+    "bit_export",
+    "bit_global",
+    "bit_audit",
+    "bit_price",
+    "complex_integrate",
+    "complex_replay",
+    "combined"
+  ],
+  "phase_mode": "source-bound unchanged evidence"
+}
diff --git a/research/split-centres-global/EXPECTED.json b/research/split-centres-global/EXPECTED.json
new file mode 100644
index 0000000000..de7c122419
--- /dev/null
+++ b/research/split-centres-global/EXPECTED.json
@@ -0,0 +1,9 @@
+{
+  "kappa": "560432476129139/500000000000000000",
+  "kappa_decimal": "0.001120864952258278",
+  "bit_lower": "561061350132569610283/500000000000000000000000",
+  "complex_lower": "1183986549206329/1000000000000000000",
+  "binding_component": "bit",
+  "bit_template_sha256": "c40f89a2ae3c2c5635ddf8f18d74f24567ddf67fc8c8e93a1fc7a1a8098e857e",
+  "complex_template_sha256": "942d030fa43316c560c88d7d7d904583446e1a96945b3ebd37a91c88a192ab4f"
+}
diff --git a/research/split-centres-global/LICENSE b/research/split-centres-global/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/split-centres-global/LICENSE
@@ -0,0 +1,201 @@
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+   6. Trademarks. This License does not grant permission to use the trade
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diff --git a/research/split-centres-global/MANIFEST.json b/research/split-centres-global/MANIFEST.json
new file mode 100644
index 0000000000..1695125698
--- /dev/null
+++ b/research/split-centres-global/MANIFEST.json
@@ -0,0 +1,51 @@
+{
+  "format": "split-centres-global-manifest/1",
+  "files": {
+    ".gitattributes": "2f9541c7c27f084baad73b4cd50ddaeb264cc3aa8dbf13ec21df5ab3f673ca7e",
+    "CERTIFICATE.json": "f71580f22193726fb582eae604807ff70a7302265e001d9484a718e63bbe14c4",
+    "EXPECTED.json": "9b8e56eee3d5bdabd2e3e6e4ba0d9eba537525fba25a54126f9f0e41d2491a06",
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE.md": "66101a9e74d0ba9c2da4c8802bcb1968534adfa7130b954628eb8bf515fc0389",
+    "PROOF.md": "6983e75f29af6eeaab20a30b08307ec6fab75ccb8b10291df8f9eb04d497f894",
+    "README.md": "b432292594adf2fcba2a8ddd87eda6167c76ff055e85aa5e3e2af7dd7e0f976e",
+    "SOURCES.json": "11aa666d678fed084b01d1e8e47239e1674eaedbc6fe0cee7edb2753477af9be",
+    "VALIDATION.json": "656d9bd7bd66058fdeb60cc90bd887e7ce75c0e0f9a100514e2bd84b95de89b6",
+    "code/bit_audit.py": "7fdbc077b7501a53662769ff2bf2ab44cc2e32dafc34478d7ef2c10e3144503a",
+    "code/bit_construct.py": "a461e6c983531beb5c8ac82ff593f39ce4e056387d1d6061f6e6b294dde4395f",
+    "code/bit_global.py": "3b2cb3ba21e5cf9b4deddb9e606322f33e9d8082020c0ee9092c21f4ebd9ad48",
+    "code/bit_price.py": "36bf15803567a95b139a908461541bf19efe1f5b85fb31c270021833ab1393ee",
+    "code/combined.py": "9c5bc70f2331b7342ceb252adcddb993581c45f80c37bcc58642dbad3b9775c2",
+    "code/complex_audit.py": "adeba5ea113652b60105db2e8719b18ffa292d3cc23730cca614b40272348330",
+    "code/complex_construct.py": "0f7f45b2333ec7daf4291e2bf675b49bc330b97fb5965dd27220ba353c291d6f",
+    "code/complex_emit.py": "f56d5f01f7c121741f175814138dca7190d769920f0a27e2d5b99c21aebed0f1",
+    "code/complex_integrate.py": "3792f41e409383e6989bda22801a4836a646a530f99e99bbd7244a8f3a1a8b4f",
+    "code/complex_phases.py": "13a959c52092776ae217df554b51c0298fa9eb3a350279acff6dece651c3f9cc",
+    "code/complex_phases_full.py": "0f2795aaffafe0c64d77f3748ef2109a3c42c58da867e4cf269a0a8cb6109466",
+    "code/complex_replay.py": "be2dccce2d1ad2c4f5c01a851c9c3896cc88236b5aeae706aad2ab16d6bfdad9",
+    "inputs/bit-geometry.json.gz": "5c980202227859e8bb9b863f94503930c2a59d460c0421356688e2b0d828b4a1",
+    "inputs/bit-r767.json.gz": "bd3b84244528767b85d8d7fe423b155630b5c659e21e51563674b1dcb6305ad7",
+    "inputs/complex-data-phases.json.gz": "c972b5b60649c2a52354f5160f69adc0f4a270fa09d32012beff9888774ab84f",
+    "inputs/complex-phase-receipt.json": "01763fee5017745de982f2ff5ee68004e815d6684097cc88011dfbfb1e789581",
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+    "inputs/complex-ports.json.gz": "77b0c0fa19ef3da1c7316010e13493aa5eea1a50c3506eddc08f7480e659878b",
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+    "inputs/e8-r865.json.gz": "1fb726ea3818fe0837cceb0dd22a71a0814f064e5e781628104610d6468e0e55",
+    "notices/NOTICE-PR352.md": "967e6d7e76e216e4898cf543c75b527e8d397ec1ddba3800cb20701f24c89524",
+    "notices/NOTICE.md": "025773f32fb43667395e64c627a1752877bdc93afbfe01b106703eee438d21d3",
+    "notices/PR386.txt": "ae2241615a23063b18a04f1b7a88a52e62b3d7d42e333fbd21e3668567ab83d1",
+    "notices/PR426-SOURCE-PINS.json": "18ace817f2f9af22511bb303e99656ed114e534b87f3dd95a65ca4ca670baf2f",
+    "notices/PR426.md": "6a5593d0f284a2f0865037f5c5fa9e5f76f9e12cf50ec5284486d3b8137c89da",
+    "notices/SUSSMAN-NOTICE": "9419dd03a2f52cf8bdfc4d18216ce29f263ab583b27f01ced8e420985bcb7c81",
+    "proofs/INHERITED-COMPLEX-GEOMETRY.txt": "c1ff55536594222a8d2a30bc0e0956959774e1be2d5420b7838ad553ee556df2",
+    "proofs/PR386-BIT-GEOMETRY.txt": "c5f077b849e9add9957ab4ee36095dd47bc678dee7e09baa146dac4c0a0d66b2",
+    "proofs/PR425-COMPLEX.txt": "2cda27b9b9a1eb24127c38c2c7a6e085155a2472183e220189a3ea2c2b7720dc",
+    "proofs/PR426.md": "5787738ceb6faf14d3d96e8452592860a6c6a469733a9bcf196e8d1562ba1ffb",
+    "vendor/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+    "vendor/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "vendor/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "vendor/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "vendor/export_records.py": "8a5999601f917dbb492bb9ae9a344611f18cc7cedc53dc3c76496a369e530eb3",
+    "vendor/hamming_packets.py": "daa9301e2767a711cfe66c6bebaad68e1a3bdb97ec9e848c927527ab43b37ae5",
+    "verify.py": "12fcdb20a87f75812b09c4916fbfc86305982cb410247186a123b5c58d517b4c"
+  }
+}
diff --git a/research/split-centres-global/NOTICE.md b/research/split-centres-global/NOTICE.md
new file mode 100644
index 0000000000..b7daf8de49
--- /dev/null
+++ b/research/split-centres-global/NOTICE.md
@@ -0,0 +1,41 @@
+# Attribution
+
+Copyright 2026 icekylinx. New split-centre cancellation, reversible source-centre
+composition, integration and verification changes were prepared by icekylinx
+with substantial OpenAI Codex assistance. Apache-2.0 applies to these changes.
+Earlier private Pro exploration used GPT-6 Astra; the new construction and
+composition in this package were developed with Codex.
+
+## Direct sources
+
+- Zhihao Chen, with OpenAI Codex assistance: PR425's mutable-basis Hamming packet
+  producer, common-frame scalar interface, exact phase lowering and verification;
+  PR386's compressed nine-stage bit geometry, owner template, audit and finite
+  accounting. These supply the immediate complex and geometric baselines.
+- ai-nanachi, with OpenAI Codex assistance: PR426's R767 bit word, including 55
+  clean-reset helper reuses and 54 frame changes. The complete selected word is
+  imported unchanged before the nine source-centre replacements.
+- Dylan Crow (utcorvusvolat-dotcom), with Anthropic Claude assistance: PR370's
+  Hamming E8 bit producer, root table, record exporter and local format.
+- Jacob Sussman: the E8 family, complex unit and underlying interchange framework.
+- applecrusher, Dugongue, eumemic, Rohan Arun, Chafik Boukhalfa, DaysSky,
+  DreamingOfClouds, Henry Grant, Evan McKinney, LJH-217 and other contributors:
+  the source, frame, compiler, rational-pricing and analytic lineage detailed
+  in the preserved original notices.
+
+The current value is computed from the two actual resulting programs.
+Independently published improvements are not added numerically. `SOURCES.json`
+records original commits and file hashes; `notices/` preserves source notices.
+Files under `proofs/` describe their original packages and retain their original
+scope and attribution; the current statement is in `PROOF.md`.
+
+## Earlier contributions by icekylinx
+
+The earlier #10, #18, #24, #32 and #36 contributions developed projector batching,
+partial-swap frames, endpoint gauges and conditional analytic/tape integration.
+The subsequent #104, #115, #130 and #144 contributions covered stopped-product
+integration, partial gauges, three-stage covers and paired-cube/source chronology.
+These provide historical context, not additional savings in this ledger. The
+source-centre idea from the preceding local round is used here on PR426's bit
+word. Unselected research experiments and superseded submission candidates are
+not part of this package.
diff --git a/research/split-centres-global/PROOF.md b/research/split-centres-global/PROOF.md
new file mode 100644
index 0000000000..8366a89e36
--- /dev/null
+++ b/research/split-centres-global/PROOF.md
@@ -0,0 +1,184 @@
+# Split centres and a joint conditional exponent
+
+The finite construction gives
+
+$$
+T(n)=O\!\left(n(\log n)^{1-\kappa}\right),
+\qquad \kappa=0.001120864952258278,
+$$
+
+conditional on the retained all-size compiler, compressed-window, correlated
+bank-dirt, restored-work, fixed-tape/common-grid, precision and analytic
+interfaces. The changes below concern both finite suppliers. Original source
+proofs and notices are retained; they do not replace the changed checks.
+
+## 1. Cancel coordinate terms before lifting the complex decoder
+
+Partition the 120 Hamming E8 root lines into the 112 code lines C and the eight
+coordinate lines F, represented by 2e_i. Write r_s for a root representative and
+G_ts = r_t · r_s / 2. The parent decoder is the rank-eight centre factorization
+G/2 together with its negative off-diagonal entries.
+
+For each code target t, the coordinate-source centre contribution is
+r_ti x_(2e_i)/2. Its side contribution is its negative. Cancel this pair before
+constructing the lifted program. For code targets retain only
+
+$$
+Z_i=\sum_{s\in C}r_{si}x_s,
+\qquad
+\sum_i\frac{r_{ti}}4Z_i
+-\sum_{\substack{s\in C\\s\ne t}}\frac{G_{ts}}2x_s=x_t.
+$$
+
+For coordinate targets, implement the identity x_(2e_i) directly. Thus the
+entire 120-by-120 clean decoder is still the identity, including both cross
+blocks between C and F.
+
+In the parent's binary address realization,
+
+$$
+p_s\cdot p_t=1+G_{st}\pmod2.
+$$
+
+Every code source contributing to Z_i is orthogonal to p_(2e_i), because its
+ith root coordinate is ±1. The already constructed global sum Z_i lies in that
+rank-eight hyperplane. Copy it there, lower the private copy to frame zero with
+one rank-eight child, and scatter into the code targets. The eight coordinate
+identities copy their source lines with one rank-one child each. Each private
+copy has a sequential lifetime, and is erased before the next episode.
+
+The total copied rank is unchanged:
+
+$$
+8\cdot8+8\cdot1=72.
+$$
+
+The 112 coordinate-source helpers and eight dedicated full-centre helpers are
+removed. Own-block corrections use their original source-copy rows directly;
+all remaining signed packets and selected target butterflies are retained.
+The actual helper count is 560. No rank-four recovered row is substituted for
+a rank-three input.
+
+## 2. Arbitrary dirt and heterogeneous copy frames
+
+The explicit main word has block form z' = Uz and y' = Vy + x + Ks, where
+z=(x,s), and U,V are invertible. No target feeds z. At the common initial frame,
+apply V^-1 to the target basis and the literal correction -V^-1 Ks. Recompute K
+from the new word. After all main gates and final climbs, apply the literal
+inverse of the source/helper subword at the common full frame. This restores
+all sources and arbitrary helpers while adding x to y.
+
+The parent common-frame proof applies to each copy separately. A private copy
+created at label L(F) is lowered by the exact operator L(0)L(F)^-1, whether F
+has rank one or eight. Scalar operations occur only at equal labels. Adding
+the common exterior window to both labels cancels it exactly. The proof
+therefore does not require a full-frame centre, or infer an operator from rank
+alone. The inverse-transpose negates/transposes each scalar shear in the same
+order and reverses each private gather/child/scatter operation as emitted.
+
+Both scalar orientations and the serialized private-work programs replay all
+800 input columns. Both restore arbitrary source/helper inputs and erase private
+work. The changed exact Gaussian recipes include the heterogeneous centre
+transitions and their global phases. Of 2,918 selected directed pairs, 248 were
+newly computed; 2,670 were unchanged source-bound exact pairs already checked in
+the local phase run. The release optionally replays all selected pairs.
+
+The local paid profile is
+
+$$
+\{1:1912,\ 2:784,\ 3:168,\ 4:224,\ 5:392,\ 8:24\}.
+$$
+
+The compressed complex geometry uses m=73, eight replicas and nine stages.
+There are 560 banks per stage, each holding eight whole rank-nine residuals and
+one paid rank-one pad. Live width is 12,720; physical stock is 13,298, including
+16 centre slots, the conservative 560-row tableau reserve and two coefficient
+streams. The global rank deficit is 2,496. Explicit owner tables, padding,
+terminal translations and the cover correction are independently decoded.
+The largest child is 48; 73² > 2·48² gives two-level halving.
+
+The fresh invoice fits the retained 2^30000 router, 2^100000 literal and 2^210000
+precision reserves. Two exact rational engines certify
+
+$$
+b=0.001183986549206329.
+$$
+
+## 3. Source-centre bit composition
+
+Start with the exact R767 word from PR426. Its nine retained rows are written
+only by original sources at the full frame and are not read by ordinary A/B
+gates. Their nine independent binary forms have an invertible minor in source
+columns 0,1,2,4,8,9,16,32,64.
+
+Replace those rows of the 120-dimensional identity by the nine retained forms.
+Exact elimination produces an invertible source basis T, emitted as 559 XOR
+additions. Delete the nine retained helper rows and their old-dirt columns.
+After A apply T, perform the same nine sequential copies using the designated
+source rows, and immediately apply T^-1 before B. The copies have unchanged
+rank eight. All scalar operations of T and its inverse use the full frame.
+
+All 998 columns, arbitrary dirt, frame incidences and restoration pass. Omitting
+T^-1 or the remaining old-dirt correction fails. The actual exported record
+stream is reflected in reverse order with complementary frames. A reflected
+ERASE becomes a fresh COPY at that chronological point; the original source
+row remains unchanged within each copy episode. Both reflected programs and
+all nine composed invocations are replayed, rather than assuming that mutable
+source rows meet an old immutability restriction.
+
+Use the unchanged compressed bit windows in dimension 64: a local eight-space
+and eight exterior seven-spaces. The root data, rational frame family, form,
+port isometries and bank slots are source-bound to PR386. Every changed nested
+pair is checked by exact rational spans; positive definiteness gives the
+projector identity and its reflected version. There are 758 banks per stage,
+each filled by eight rank-eight residuals, with no padding. Live width is 14,502
+and physical stock is 14,511. All 54,576 owner assignments are checked. The
+unbanked global replay restores all 7,782 independent columns.
+
+The bit local profile is
+
+$$
+\{1:2367,\ 2:875,\ 3:475,\ 4:321,\ 5:164,\ 7:14,\ 8:9\}.
+$$
+
+Its global deficit is again 2,496. The maximum child is 42 and 64² > 2·42².
+The actual cancellation-free prefix bound needs 223 bits; the new charge is
+256 bits, replacing the parent's 192-bit allowance. The finite two-level
+coefficient needs 483 bits and fits the retained 2^512 allowance. The row
+coefficient is 18,355 < 20,161. These costs, including the basis operations,
+are recomputed from the emitted word. Two exact rational moment engines give
+
+$$
+c=0.001122122700265139220566.
+$$
+
+## 4. Joint strict assembly
+
+Both moments include the inherited 10^-16 bad-branch allowance. The bit supplier
+binds because c < b. Let eta=beta=10^-18 and
+
+$$
+s=\min\{c,(1-\beta)b\}-10^{-24}.
+$$
+
+Starting at a_0=384599/10^10, use six fixed ordinary bootstrap levels
+
+$$
+a_{j+1}=(1-s)s+sa_j.
+$$
+
+All bootstrap cutoff inequalities are checked with the actual charged finite
+coefficient. With q=a_6(1-2eta), choose the greatest 10^-18 grid point strictly
+below (1-eta)q/(1+q). It is
+
+$$
+\kappa=\frac{560432476129139}{500000000000000000}
+       =0.001120864952258278.
+$$
+
+All 47 retained strict outer inequalities pass. The next grid point, zero eta,
+zero beta and unit beta are rejected. The candidate is computed from both
+actual new templates; no independently reported savings are added together.
+
+The source-bound finite claims above do not discharge the inherited all-size
+interfaces or establish unconditional integer-multiplication complexity.
diff --git a/research/split-centres-global/README.md b/research/split-centres-global/README.md
new file mode 100644
index 0000000000..1e31463921
--- /dev/null
+++ b/research/split-centres-global/README.md
@@ -0,0 +1,56 @@
+# Conditional κ = 0.001120864952258278
+
+This package combines a split-centre Hamming complex construction with a
+source-centre bit construction in compressed nine-stage windows. The resulting
+conditional exponent saving is
+
+$$
+\kappa=\frac{560432476129139}{500000000000000000}
+       =0.001120864952258278.
+$$
+
+This is approximately **6.9522% above PR425**. Both components change:
+
+| Component | Helpers | Ambient width | Certified saving |
+|---|---:|---:|---:|
+| Complex | 560 | 73 | 0.001183986549206329 |
+| Bit | 758 | 64 | 0.001122122700265139220566 |
+
+The bit component limits the final assembly. The complex construction removes
+coordinate contributions that cancel in the decoder, replacing eight full
+centres with eight rank-eight and eight rank-one copies. The bit construction
+starts from PR426's R767 word, computes its nine retained forms reversibly in
+source rows, and uses PR386's compressed windows.
+
+## Verification
+
+Python 3.11+ and its standard library suffice. Use a new output directory:
+
+```sh
+python3 -B research/split-centres-global/verify.py /tmp/split-centres-check
+```
+
+The default replays both changed words, reflected/inverse-transpose programs,
+bank ownership, costs, two rational moment engines and 47 strict outer
+inequalities. Exact complex phase evidence is reused only when the regenerated
+canonical word and complete recipe hashes match. To regenerate every selected
+Gaussian phase pair as well:
+
+```sh
+python3 -B research/split-centres-global/verify.py /tmp/split-centres-full-phases --replay-phases
+```
+
+The unchanged historical repository suite and PDF build are not required by
+this package. `EXPECTED.json` binds the result to both emitted global templates;
+`MANIFEST.json` binds the package files; `SOURCES.json` pins imported sources.
+
+## Scope
+
+[PROOF.md](PROOF.md) supplies the changed finite construction. The all-size
+compressed-window and correlated dirty-bank semantics, recursive compiler,
+restored-work/tape/common-grid precision, and analytic transfer interfaces remain
+conditional. This does not claim unchanged legacy gx/gxcore acceptance, a new
+Lean proof, or an unconditional multiplication theorem.
+
+Contributor history and AI assistance are recorded in [NOTICE.md](NOTICE.md).
+Original notices and the inherited proofs are retained separately.
diff --git a/research/split-centres-global/SOURCES.json b/research/split-centres-global/SOURCES.json
new file mode 100644
index 0000000000..215f58a649
--- /dev/null
+++ b/research/split-centres-global/SOURCES.json
@@ -0,0 +1,134 @@
+{
+  "upstream_base": "12a4934d15006e8c10f9b2264f13f8f341be802b",
+  "pr425": "e11ccea1d092beb1b01b4ee4ce49da478234254c",
+  "pr426": "88d552526893cd15325948bb1487e9a4d4bf32f6",
+  "imported_files": [
+    {
+      "path": "vendor/hamming_packets.py",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/complex-network/hamming_packets.py",
+      "sha256": "daa9301e2767a711cfe66c6bebaad68e1a3bdb97ec9e848c927527ab43b37ae5"
+    },
+    {
+      "path": "vendor/clifford_exact.py",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/odd-stages/clifford_exact.py",
+      "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+    },
+    {
+      "path": "inputs/complex-ports.json.gz",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz",
+      "sha256": "77b0c0fa19ef3da1c7316010e13493aa5eea1a50c3506eddc08f7480e659878b"
+    },
+    {
+      "path": "inputs/complex-template.json.gz",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz",
+      "sha256": "1b84904a31a733aab9bfdda3f528c06719f590d2133a43687a8bded955dc991e"
+    },
+    {
+      "path": "inputs/complex-data-phases.json.gz",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/complex-nine-native/DATA-PHASES.json",
+      "sha256": "c972b5b60649c2a52354f5160f69adc0f4a270fa09d32012beff9888774ab84f",
+      "source_sha256": "f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a",
+      "encoding": "gzip; decoded bytes identical to source"
+    },
+    {
+      "path": "inputs/e8-r865.json.gz",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz",
+      "sha256": "1fb726ea3818fe0837cceb0dd22a71a0814f064e5e781628104610d6468e0e55"
+    },
+    {
+      "path": "proofs/PR425-COMPLEX.txt",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/complex-network/hamming/PROOF.txt",
+      "sha256": "2cda27b9b9a1eb24127c38c2c7a6e085155a2472183e220189a3ea2c2b7720dc"
+    },
+    {
+      "path": "proofs/INHERITED-COMPLEX-GEOMETRY.txt",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/complex-nine-native/PROOF.txt",
+      "sha256": "c1ff55536594222a8d2a30bc0e0956959774e1be2d5420b7838ad553ee556df2"
+    },
+    {
+      "path": "vendor/engines/moment.py",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/pr361/code/engines/moment.py",
+      "sha256": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482"
+    },
+    {
+      "path": "vendor/engines/base_two_moment.py",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/pr361/code/engines/base_two_moment.py",
+      "sha256": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098"
+    },
+    {
+      "path": "vendor/engines/outer.py",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/pr361/code/engines/outer.py",
+      "sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+    },
+    {
+      "path": "vendor/export_records.py",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/e8-bit/code/bit/export_records.py",
+      "sha256": "8a5999601f917dbb492bb9ae9a344611f18cc7cedc53dc3c76496a369e530eb3"
+    },
+    {
+      "path": "inputs/bit-geometry.json.gz",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/e8-bit-complex-nine-validation/GEOMETRY.json.gz",
+      "sha256": "5c980202227859e8bb9b863f94503930c2a59d460c0421356688e2b0d828b4a1"
+    },
+    {
+      "path": "proofs/PR386-BIT-GEOMETRY.txt",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/e8-bit-complex-nine/PROOF.txt",
+      "sha256": "c5f077b849e9add9957ab4ee36095dd47bc678dee7e09baa146dac4c0a0d66b2"
+    },
+    {
+      "path": "notices/PR386.txt",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/e8-bit-complex-nine/NOTICE.txt",
+      "sha256": "ae2241615a23063b18a04f1b7a88a52e62b3d7d42e333fbd21e3668567ab83d1"
+    },
+    {
+      "path": "inputs/bit-r767.json.gz",
+      "source": "CrocSwap/integer-mult-bounds@88d552526893cd15325948bb1487e9a4d4bf32f6:research/e8-clean-reuse-extension/data/bit-candidate.json.gz",
+      "sha256": "bd3b84244528767b85d8d7fe423b155630b5c659e21e51563674b1dcb6305ad7"
+    },
+    {
+      "path": "notices/PR426.md",
+      "source": "CrocSwap/integer-mult-bounds@88d552526893cd15325948bb1487e9a4d4bf32f6:research/e8-clean-reuse-extension/NOTICE.md",
+      "sha256": "6a5593d0f284a2f0865037f5c5fa9e5f76f9e12cf50ec5284486d3b8137c89da"
+    },
+    {
+      "path": "proofs/PR426.md",
+      "source": "CrocSwap/integer-mult-bounds@88d552526893cd15325948bb1487e9a4d4bf32f6:research/e8-clean-reuse-extension/PROOF.md",
+      "sha256": "5787738ceb6faf14d3d96e8452592860a6c6a469733a9bcf196e8d1562ba1ffb"
+    },
+    {
+      "path": "notices/PR426-SOURCE-PINS.json",
+      "source": "CrocSwap/integer-mult-bounds@88d552526893cd15325948bb1487e9a4d4bf32f6:research/e8-clean-reuse-extension/SOURCE-PINS.json",
+      "sha256": "18ace817f2f9af22511bb303e99656ed114e534b87f3dd95a65ca4ca670baf2f"
+    },
+    {
+      "path": "notices/NOTICE-PR352.md",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/pr370-source/research/e8-bit/NOTICE-PR352.md",
+      "sha256": "967e6d7e76e216e4898cf543c75b527e8d397ec1ddba3800cb20701f24c89524"
+    },
+    {
+      "path": "notices/NOTICE.md",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/pr370-source/research/e8-bit/NOTICE.md",
+      "sha256": "025773f32fb43667395e64c627a1752877bdc93afbfe01b106703eee438d21d3"
+    },
+    {
+      "path": "LICENSE",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/pr370-source/research/e8-bit/LICENSE",
+      "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4"
+    },
+    {
+      "path": "notices/SUSSMAN-NOTICE",
+      "source": "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/e8-bit/code/complex/inputs/complex/NOTICE",
+      "sha256": "9419dd03a2f52cf8bdfc4d18216ce29f263ab583b27f01ced8e420985bcb7c81"
+    }
+  ],
+  "adapted_sources": {
+    "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/complex-network/hamming_full.py": "613796df039dfc08de708831582533e553316eaf157485531e4df2d897bdb3bb",
+    "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/complex-network/audit_full.py": "fdc1da8fa95716d60076383e691a5be1bf8bec0b229b7582bc056afac28951d0",
+    "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/complex-network/integrate.py": "eb5b427f2095578f28a1fb320b4694047e20abdbe0c8bcdc65b1e9e05ab90d01",
+    "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/complex-network/phase_full.py": "5c2bd267cc3106c9eee8787132c460614fdde8177c0c2653435f8a7b110ebac1",
+    "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/hamming-mutable-basis-complex/work/complex-network/replay_ir.py": "f7a3829118581ee59fdeefc1f91166d8e7bb94686ea92e7743a2ef7d50139dcc",
+    "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/e8-bit-complex-nine/global_word.py": "2c438be46213e014170e607a745185e45e33c7b7240b833efc86a2330de0d1f6",
+    "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/e8-bit-complex-nine/audit.py": "75811327b0d6cbd56aae8e28d72abd42d57c7f3f3630781d045efee2d36446e9",
+    "CrocSwap/integer-mult-bounds@e11ccea1d092beb1b01b4ee4ce49da478234254c:research/e8-bit-complex-nine/certify.py": "550b1408fb3a581dd6b82c90e3f84ad7a9f78746d2be11ffa1cf543d719ae2d4"
+  }
+}
diff --git a/research/split-centres-global/VALIDATION.json b/research/split-centres-global/VALIDATION.json
new file mode 100644
index 0000000000..70b00c0bc7
--- /dev/null
+++ b/research/split-centres-global/VALIDATION.json
@@ -0,0 +1,39 @@
+{
+  "status": "PASS_CLEAN_DIRECTORY_INCREMENTAL_REPLAY",
+  "python": "3.14",
+  "tested_code_vendor_input_digest": "c15599626c4222a95ddb4f0a9da028cfce5c8636c7a737d6869155c2f33301ed",
+  "steps": [
+    "hamming_packets",
+    "complex_construct",
+    "complex_audit",
+    "complex_emit",
+    "complex_phases",
+    "bit_construct",
+    "bit_export",
+    "bit_global",
+    "bit_audit",
+    "bit_price",
+    "complex_integrate",
+    "complex_replay",
+    "combined"
+  ],
+  "phase_mode": "source-bound unchanged evidence",
+  "new_complex_phase_pairs": 248,
+  "reused_verified_complex_phase_pairs": 2670,
+  "source_bound_bit_geometry": "PR386; exact unchanged root/frame/port/slot identities",
+  "historical_full_suite_rerun": false,
+  "pdf_built": false,
+  "ci_status": "Not yet run for this commit",
+  "post_replay_packaging": "Phase JSON gzip round-trip matched the verified decoded bytes; mathematical code and witnesses unchanged.",
+  "portability_validation": {
+    "python": "3.11.17",
+    "status": "PASS_ALL_PACKAGE_STEPS_AND_UNCHANGED_EXPECTED_RESULT",
+    "cause": "gzip OS header differs from Python 3.14; exact decoded canonical bytes agree",
+    "phase_binding": "SHA256 of exact decompressed bytes; current archive hash remains bound in downstream receipts",
+    "negative_control": "A modified canonical witness is rejected",
+    "python314_incremental": "Changed phase-binding step passed against the previously validated output",
+    "historical_full_suite_rerun": false
+  },
+  "portability_code_vendor_input_digest": "a2534c803ecb3afb25662517ad542c1b05869046ced4ac78250625b1707014e4",
+  "portability_digest_format": "SHA256 of compact sorted JSON mapping package-relative code/vendor/inputs paths to file SHA256"
+}
diff --git a/research/split-centres-global/code/bit_audit.py b/research/split-centres-global/code/bit_audit.py
new file mode 100644
index 0000000000..82e1663e58
--- /dev/null
+++ b/research/split-centres-global/code/bit_audit.py
@@ -0,0 +1,126 @@
+# Adapted with exact rational span checks by icekylinx; Codex assistance.
+"""Independent audit of the emitted bit template, including mutation controls.
+Prepared by Zhihao Chen with OpenAI Codex assistance; Apache-2.0.
+"""
+import argparse, copy, gzip, hashlib, json, struct, time
+from collections import Counter, defaultdict
+from pathlib import Path
+from fractions import Fraction as Q
+
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out
+    blob=gzip.decompress((out/'GLOBAL-TEMPLATE.json.gz').read_bytes()); t=json.loads(blob)
+    g=json.loads((out/'GLOBAL.json').read_text()); geo=json.loads((out/'GEOMETRY.json').read_text())
+    assert hashlib.sha256(blob).hexdigest()==g['template_sha256']
+    assert t['geometry_sha256']==sha(out/'GEOMETRY.json') and t['source_record_sha256']==sha(a.local_check/'records/249-records.bin')
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    records=list(struct.iter_unpack('<6i',(a.local_check/'records/249-records.bin').read_bytes()))
+    word=json.loads((a.local_check/'bit-source-centres.json').read_text())
+    assert g['word_sha256']==sha(a.local_check/'bit-source-centres.json')
+    def rank(rows):
+        piv={}
+        for rr in rows:
+            row=list(map(Q,rr))
+            for k,b in sorted(piv.items()):
+                q=row[k]
+                if q:row=[x-q*y for x,y in zip(row,b)]
+            k=next((j for j,x in enumerate(row) if x),None)
+            if k is not None:
+                q=row[k];piv[k]=[x/q for x in row]
+        return len(piv)
+    dimensions={};proj={}
+    for key,f in fs.items():
+        k=int(key);B=f['B'];roots=[word['lines'][j] for j in word['frames'][k]]
+        assert rank(B)==f['dim']==rank(B+roots)==rank(roots)
+        dimensions[k]=f['dim'];proj[k]=B
+    sets=[set(f) for f in word['frames']];pairs={}
+    for op,x,y,c,r,z in records:
+        if op==0:
+            assert sets[y]<=sets[c] and dimensions[c]-dimensions[y]==r
+            pairs[y,c]=r
+    # Positive definite rational form: exact inclusion implies commuting
+    # orthogonal projectors and rank(P_V-P_U)=dim(V)-dim(U), also in reflection.
+    assert len(proj)==944
+    expected={}
+    for rev in (False,True):
+        es=[]
+        for op,x,y,c,f,z in (reversed(records) if rev else records):
+            if op==0: es.append([0,x,c if rev else y,y if rev else c,f,int(rev)])
+            elif op==1: es.append([1,x,y,-c if rev else c,f,int(rev)])
+            elif op==(3 if rev else 2): es.append([2,x,y,c,f,abs(dimensions[c]-dimensions[f]),int(rev)])
+            else: es.append([3,x,y,c,f,z,int(rev)])
+        expected['reverse' if rev else 'forward']=es
+    assert t['local_programs']==expected
+
+    def validate(q,check_profile=True):
+        assert (q['m'],q['live'],q['replicas'],q['stages'])==(64,14502,8,9)
+        assert q['bank_padding'] is None and q['local_programs']==expected
+        hist=Counter(); occupation=defaultdict(set); calls=set()
+        for c in q['calls']:
+            st,rep,p=c['stage'],c['replica'],c['pair']; rev=c['orientation']=='reverse'
+            assert 0<=st<9 and 0<=rep<8 and p==max(0,(st-1)//2)
+            assert rev==(st in (1,3,5,7)) and (st,rep) not in calls; calls.add((st,rep))
+            own=c['owners']; assert len(own)==998
+            assert len({(f,tuple(r)) for f,r in own})==998
+            for i,(family,route) in enumerate(own):
+                assert 0<=family<14502
+                if i<240:
+                    side=i//120; side=1-side if rev else side
+                    assert family==rep*960+(2*p+side)*120+i%120 and route==['data',st,i%120]
+                else:
+                    j=i-240; bank,slot=divmod(rep*758+j,8)
+                    assert family==7680+st*758+bank and route==['bank',slot]
+                    assert slot not in occupation[family]; occupation[family].add(slot)
+            for e in q['local_programs'][c['orientation']]:
+                if e[0]==0 and e[4]: hist[e[4]]+=1
+                if e[0]==2: hist[e[5]]+=1
+        assert calls=={(s,r) for s in range(9) for r in range(8)}
+        assert set(occupation)==set(range(7680,14502)) and all(s==set(range(8)) for s in occupation.values())
+        levels=[-1]*4; scalar=[1<<i for i in range(8)]; seen=[]; br=0; exchanged=False
+        for e in q['schedule']:
+            if e['kind']=='local_cover_sweep':
+                s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1 and not exchanged
+                src,dst=(2*p+1,2*p) if rev else (2*p,2*p+1)
+                scalar[dst]^=scalar[src]; levels[p]=s; seen.append(s)
+            elif e['kind']=='idle':
+                p,src,dst,r=e['pair'],e['source_level'],e['target_level'],e['rank']
+                assert levels[p]==src and src<=dst<=8
+                assert r==7*(dst-src); levels[p]=dst
+                if r: hist[r]+=1920
+            elif e['kind']=='bridge':
+                d,s=e['dst'],e['src']; assert levels[d]==levels[s] and e['coefficient'] in (-1,1)
+                scalar[2*d]^=scalar[2*s]; scalar[2*s+1]^=scalar[2*d+1]; br+=1
+            else:
+                assert e['kind']=='exchange' and levels==[8]*4 and not exchanged
+                for p in range(4): scalar[2*p],scalar[2*p+1]=scalar[2*p+1],scalar[2*p]
+                exchanged=True
+        assert exchanged and scalar==[1<<i for i in range(8)] and seen==list(range(9)) and br==9
+        assert 64*14502-sum(r*n for r,n in hist.items())==2496
+        if check_profile: assert hist==Counter({int(k):v for k,v in g['profile'].items()})
+        return hist
+    hist=validate(t)
+    controls=[]
+    def rejects(name,mutator):
+        q=copy.deepcopy(t); mutator(q)
+        try: validate(q)
+        except (AssertionError,KeyError,IndexError): controls.append(name)
+        else: raise AssertionError('mutation accepted: '+name)
+    rejects('omit an idle child',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='idle')))
+    rejects('omit a bridge',lambda q:q['schedule'].pop(next(i for i,e in enumerate(q['schedule']) if e['kind']=='bridge')))
+    rejects('omit terminal exchange',lambda q:q['schedule'].pop())
+    rejects('remove a local invocation',lambda q:q['calls'].pop())
+    rejects('re-use a helper bank slot',lambda q:q['calls'][0]['owners'].__setitem__(241,q['calls'][0]['owners'][240]))
+    rejects('understate live stock',lambda q:q.__setitem__('live',14501))
+    rejects('omit a local paid move',lambda q:q['local_programs']['forward'].pop(next(i for i,e in enumerate(q['local_programs']['forward']) if e[0]==0)))
+    rejects('wrong reflected copy charge',lambda q:q['local_programs']['reverse'][next(i for i,e in enumerate(q['local_programs']['reverse']) if e[0]==2)].__setitem__(5,0))
+    result=dict(status='PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT',template_sha256=g['template_sha256'],
+                source_frames=len(proj),exact_nested_frame_pairs=len(pairs),exact_reflected_pairs=len(pairs),
+                orthogonal_lift_argument='Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.',
+                exact_bank_families=6822,slots_per_bank=8,mutations_rejected=controls,
+                profile=dict(sorted(hist.items())),seconds=time.monotonic()-start)
+    (out/'AUDIT.json').write_text(json.dumps(result,indent=2)+'\n'); print(json.dumps(result),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/split-centres-global/code/bit_construct.py b/research/split-centres-global/code/bit_construct.py
new file mode 100644
index 0000000000..e43632e95f
--- /dev/null
+++ b/research/split-centres-global/code/bit_construct.py
@@ -0,0 +1,134 @@
+"""Replace independent retained helpers by a reversible source-basis word.
+
+icekylinx, with Codex assistance. Inherited E8 input notices apply. This
+certifies the finite local F2 word and nested incidences, not a new kappa.
+"""
+from pathlib import Path
+from hashlib import sha256
+import copy
+import json
+
+import os
+ROOT = Path(os.environ['E8_OUTPUT']) / 'bit426-source-centres'
+
+
+def replay(c, skip_inverse=False, skip_dirt=False):
+    v, n = c['v'], 2*c['v'] + c['R']
+    x = [1 << i for i in range(n)]
+    def run(gs):
+        for f, d, ss in gs:
+            assert d not in ss
+            for s in ss:
+                x[d] ^= x[s]
+    if not skip_dirt:
+        run(c['D'])
+    run(c['A'])
+    totals = [x[r] for r in c['ret']]
+    for t, ss in enumerate(c['scatter']):
+        for k in ss:
+            x[v+t] ^= totals[k]
+    run(c['B'][c.get('source_basis_gates', 0):] if skip_inverse else c['B'])
+    run(c['C'])
+    expected = [1 << i for i in range(n)]
+    for t in range(v):
+        expected[v+t] ^= 1 << t
+    return x == expected
+
+
+def main():
+    source = ROOT / 'bit-input.json'
+    old = json.loads(source.read_bytes())
+    assert replay(old)
+    v = old['v']
+    retired = set(old['ret'])
+    full = old['final'][0]
+    rows = []
+    for r in old['ret']:
+        row = 0
+        for f, d, ss in old['A']:
+            if d == r:
+                assert f == full and all(s < v for s in ss)
+                for s in ss:
+                    row ^= 1 << s
+        assert row
+        rows.append(row)
+    assert all(not retired.intersection(ss) for f, d, ss in old['A'] + old['B'])
+    assert all(d not in retired for f, d, ss in old['B'])
+    # Find an invertible minor, preserving the original order of centre rows.
+    echelon = {}
+    for row in rows:
+        for p, q in sorted(echelon.items()):
+            if row >> p & 1:
+                row ^= q
+        assert row, 'Retained forms must be independent'
+        p = (row & -row).bit_length() - 1
+        echelon[p] = row
+    pivots = sorted(echelon)
+    matrix = [1 << i for i in range(v)]
+    for p, row in zip(pivots, rows):
+        matrix[p] = row
+    target = matrix[:]
+    elimination = []
+    def add(d, s):
+        matrix[d] ^= matrix[s]
+        elimination.append((d, s))
+    for p in range(v):
+        q = next(i for i in range(p, v) if matrix[i] >> p & 1)
+        if q != p:
+            add(p, q); add(q, p); add(p, q)
+        for i in range(v):
+            if i != p and matrix[i] >> p & 1:
+                add(i, p)
+    assert matrix == [1 << i for i in range(v)]
+    forward = [[full, d, [s]] for d, s in reversed(elimination)]
+    inverse = list(reversed(forward))
+    check = [1 << i for i in range(v)]
+    for f, d, ss in forward:
+        check[d] ^= check[ss[0]]
+    assert check == target
+    out = copy.deepcopy(old)
+    physical = [i for i in range(2*v+old['R']) if i not in retired]
+    index = {r: i for i, r in enumerate(physical)}
+    def remap(gs):
+        return [[f, index[d], [index[s] for s in ss if s not in retired]]
+                for f, d, ss in gs if d not in retired]
+    out['R'] -= len(retired)
+    out['ret'] = pivots
+    out['D'] = remap(old['D'])
+    out['A'] = remap(old['A']) + forward
+    out['B'] = inverse + remap(old['B'])
+    out['C'] = remap(old['C'])
+    out['start'] = [old['start'][i] for i in physical]
+    out['final'] = [old['final'][i] for i in physical]
+    out['source_basis_gates'] = len(forward)
+    assert replay(out), 'All independent source, target and dirty columns'
+    assert not replay(out, skip_inverse=True)
+    assert not replay(out, skip_dirt=True)
+    # Frame incidence inclusion uses the root-closed sets in this bit format.
+    frames = [set(f) for f in out['frames']]
+    cur = out['start'][:]
+    for phase in ['D', 'A', 'B', 'C']:
+        for f, d, ss in out[phase]:
+            for r in [d] + ss:
+                assert frames[cur[r]] <= frames[f], (phase, r, cur[r], f)
+                cur[r] = f
+        if phase == 'A':
+            assert all(cur[r] == full for r in out['ret'])
+    assert all(frames[f] <= frames[g] for f, g in zip(cur, out['final']))
+    raw = json.dumps(out, sort_keys=True, separators=(',', ':')).encode()
+    (ROOT / 'bit-source-centres.json').write_bytes(raw)
+    result = dict(status='PASS_LOCAL_ALL_COLUMNS_AND_NESTED_FRAMES',
+                  original_R=old['R'], new_R=out['R'],
+                  removed_retained_helpers=sorted(retired), retained_source_rows=pivots,
+                  formal_columns=2*v+out['R'], reversible_basis_gates_each_way=len(forward),
+                  source_sha256=sha256(source.read_bytes()).hexdigest(),
+                  output_sha256=sha256(raw).hexdigest(),
+                  controls=['unmodified word passes', 'missing inverse rejected', 'missing dirt rejected'],
+                  kappa_claimed=False,
+                  remaining=['global ordinary-call and reflected integration', 'finite coefficient and tape invoice', 'exact priced component comparison'])
+    (ROOT / 'bit-source-centres-receipt.json').write_text(json.dumps(result, indent=2)+'\n')
+    print(json.dumps(result))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/split-centres-global/code/bit_global.py b/research/split-centres-global/code/bit_global.py
new file mode 100644
index 0000000000..5ccf622825
--- /dev/null
+++ b/research/split-centres-global/code/bit_global.py
@@ -0,0 +1,226 @@
+# Adapted for the PR426/source-centre composition by icekylinx with Codex assistance.
+"""Source-bound compressed nine-stage bit template and exact scalar audits.
+
+Prepared by Zhihao Chen with OpenAI Codex assistance, Apache-2.0.
+The local E8 bit word is Dylan Crow's pinned PR #370 contribution.
+"""
+import argparse, gzip, hashlib, json, struct, time
+from collections import Counter
+from pathlib import Path
+
+H,V,R,L,K,T,M=8,120,758,9,4,8,64
+LOCAL=2*V+R; DATA=2*K*V*T; LIVE=DATA+L*R
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+def write(p,x): p.write_text(json.dumps(x,indent=2)+'\n')
+
+def recipe():
+    out=[dict(kind='local',stage=0,pair=0,reverse=False)]; stage=1
+    for j in range(K):
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=True)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=1))
+        out.append(dict(kind='local',stage=stage,pair=j,reverse=False)); stage+=1
+        if j<K-1: out.append(dict(kind='bridge',dst=j,src=j+1,coefficient=-1))
+    for j in reversed(range(K-1)): out.append(dict(kind='bridge',dst=j+1,src=j,coefficient=1))
+    out.append(dict(kind='exchange'))
+    return out
+
+def main():
+    ap=argparse.ArgumentParser(); ap.add_argument('--source',type=Path,required=True)
+    ap.add_argument('--local-check',type=Path,required=True); ap.add_argument('--out',type=Path,required=True)
+    a=ap.parse_args(); start=time.monotonic(); out=a.out; out.mkdir(parents=True,exist_ok=True)
+    wp=a.source/'bit-source-centres.json'; w=json.loads(wp.read_bytes())
+    inherited=Path('inherited/bit-geometry.json.gz')
+    geo=json.loads(gzip.decompress(inherited.read_bytes()))
+    base=Path('work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz')
+    original=json.loads(gzip.decompress(base.read_bytes()))
+    assert geo['word_sha256']==sha(base)
+    assert w['lines']==original['lines'] and w['frames']==original['frames'] and w['form']==original['form']
+    geo['inherited_geometry_sha256']=sha(inherited);geo['word_sha256']=sha(wp)
+    geo['reuse_scope']='Unchanged ports, rational frames, compressed windows and whole rank-eight bank slots; changed owners are replayed separately.'
+    write(out/'GEOMETRY.json',geo)
+    rp=a.local_check/'records/249-records.bin';raw=rp.read_bytes();rec=list(struct.iter_unpack('<6i',raw))
+    state=json.loads((a.local_check/'records/249-states.json').read_text())
+    fs=json.loads((a.local_check/'records/frames.json').read_text())['frames']
+    dims={int(f):z['dim'] for f,z in fs.items()}
+    assert (state['v'],state['n'])==(V,LOCAL)
+    expected_adds=sum(e[0]==1 for e in rec)
+    initial=[state['initial'][str(i)] for i in range(LOCAL)]
+    final=[state['final'][str(i)] for i in range(LOCAL)]
+    assert all(dims[initial[i]]==0 and dims[final[i]]==H for i in range(2*V,LOCAL))
+    streams={}; checks={}; localH=None
+    for reverse in (False,True):
+        cur=(final if reverse else initial)[:]+[-1]; val=[1<<i for i in range(LOCAL)]+[0]
+        norm=[1]*LOCAL+[0]; maxnorm=1; center=None; hist=Counter(); events=[]; copies=0; adds=0
+        dim=lambda f:H-dims[f] if reverse else dims[f]
+        for op,x,y,c,f,z in (reversed(rec) if reverse else rec):
+            if op==0:
+                oldf,newf=(c,y) if reverse else (y,c)
+                assert cur[x]==oldf and dim(newf)-dim(oldf)==f>=0
+                cur[x]=newf
+                if f: hist[f]+=1
+                events.append([0,x,oldf,newf,f,int(reverse)])
+            elif op==1:
+                assert cur[x]==cur[y]==f and x!=y and x<LOCAL
+                if center is not None: assert x!=center
+                if y==LOCAL: assert center is not None
+                if c&1: val[x]^=val[y]
+                norm[x]+=abs(c)*norm[y]; maxnorm=max(maxnorm,norm[x]); adds+=1
+                events.append([1,x,y,-c if reverse else c,f,int(reverse)])
+            elif op==(3 if reverse else 2):
+                assert center is None and y==LOCAL and cur[x]==c and val[LOCAL]==0
+                copy_rank=abs(dim(c)-dim(f)); assert copy_rank==8
+                assert z==(0 if reverse else copy_rank)
+                center=x; cur[LOCAL]=f; val[LOCAL]=val[x]; norm[LOCAL]=norm[x]
+                hist[copy_rank]+=1; copies+=1; events.append([2,x,LOCAL,c,f,copy_rank,int(reverse)])
+            else:
+                assert op==(2 if reverse else 3)
+                assert center==x and y==LOCAL and cur[x]==c and cur[LOCAL]==f
+                assert val[LOCAL]==val[x]
+                val[LOCAL]=0; norm[LOCAL]=0; cur[LOCAL]=-1; center=None
+                events.append([3,x,LOCAL,c,f,z,int(reverse)])
+        assert center is None and copies==9 and adds==expected_adds
+        assert cur[:LOCAL]==(initial if reverse else final)
+        for i in range(LOCAL):
+            want=(1<<i) ^ ((1<<(i-V)) if V<=i<2*V else 0)
+            assert val[i]==want
+        assert val[LOCAL]==0
+        if localH is None: localH=hist
+        else: assert localH==hist
+        key='reverse' if reverse else 'forward'; streams[key]=events
+        checks[key]=dict(copies=copies,adds=adds,records=len(events),all_columns=LOCAL,
+                         cancellation_free_row_l1=maxnorm,profile=dict(sorted(hist.items())),
+                         sha256=hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest())
+    assert sum(r*n for r,n in localH.items())==H*R+72+2*V*(H-1)==7816
+    assert localH==Counter({1:2367,2:875,3:475,4:321,5:164,7:14,8:9})
+
+    events=recipe(); levels=[-1]*K; schedule=[]; bridge_controls=[]
+    # Full scalar replay on separate dirty helpers for all nine stages.
+    # Physical banking then uses the separately checked injective cover owners.
+    n=2*K*V+L*R; vals=[1<<i for i in range(n)]+[0]; temp=n
+    stages=[]
+    for e in events:
+        if e['kind']=='local':
+            s,p,rev=e['stage'],e['pair'],e['reverse']; assert levels[p]==s-1
+            def mapper(i):
+                if i==LOCAL: return temp
+                if i<2*V:
+                    side=i//V; side=1-side if rev else side
+                    return (2*p+side)*V+i%V
+                return 2*K*V+s*R+i-2*V
+            before=vals[:]; opened=False
+            for z in streams['reverse' if rev else 'forward']:
+                if z[0]==0: continue
+                x,y=mapper(z[1]),mapper(z[2])
+                if z[0]==1:
+                    if z[3]&1: vals[x]^=vals[y]
+                elif z[0]==2:
+                    assert not opened; vals[temp]=vals[x]; opened=True
+                else:
+                    assert opened and vals[temp]==vals[x]; vals[temp]=0; opened=False
+            assert not opened
+            d=(2*p+(0 if rev else 1))*V; src=(2*p+(1 if rev else 0))*V
+            for t in range(V): before[d+t]^=before[src+t]
+            assert vals==before
+            levels[p]=s; schedule.append(dict(kind='local_cover_sweep',**{k:v for k,v in e.items() if k!='kind'}))
+            if s in (1,3,5):
+                j=(s+1)//2; assert levels[j]==-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7*(s+1),source_level=-1,target_level=s))
+            elif s in (2,4,6):
+                j=s//2; assert levels[j]==s-1; levels[j]=s
+                schedule.append(dict(kind='idle',pair=j,rank=7,source_level=s-1,target_level=s))
+            elif s==8:
+                for j in range(4):
+                    oldlevel=levels[j]; assert oldlevel==2*j+2
+                    schedule.append(dict(kind='idle',pair=j,rank=7*(8-oldlevel),source_level=oldlevel,target_level=8))
+                    levels[j]=8
+            stages.append(dict(stage=s,all_columns=n,helper_columns=L*R,reverse=rev))
+        elif e['kind']=='bridge':
+            d,s=e['dst'],e['src']; assert levels[d]==levels[s]
+            for t in range(V): vals[2*d*V+t]^=vals[2*s*V+t]; vals[(2*s+1)*V+t]^=vals[(2*d+1)*V+t]
+            schedule.append(e)
+        else:
+            assert levels==[8]*4
+            for j in range(K):
+                for t in range(V):
+                    x=2*j*V+t; y=(2*j+1)*V+t; vals[x],vals[y]=vals[y],vals[x]
+            schedule.append(e)
+    assert vals==[1<<i for i in range(n)]+[0]
+    # Integer scalar eight-bank matrix, with each individual bridge shear omitted.
+    def small(skip=-1):
+        z=[[int(i==j) for j in range(8)] for i in range(8)]; count=0
+        def add(d,s,c): z[d]=[x+c*y for x,y in zip(z[d],z[s])]
+        for e in events:
+            if e['kind']=='local':
+                p=e['pair']; add(2*p,2*p+1,-1) if e['reverse'] else add(2*p+1,2*p,1)
+            elif e['kind']=='bridge':
+                d,s,c=e['dst'],e['src'],e['coefficient']
+                for x,y,sgn in [(2*d,2*s,c),(2*s+1,2*d+1,-c)]:
+                    if count!=skip: add(x,y,sgn)
+                    count+=1
+            else:
+                for j in range(4): z[2*j],z[2*j+1]=z[2*j+1],[-x for x in z[2*j]]
+        return z,count
+    ident=[[int(i==j) for j in range(8)] for i in range(8)]
+    z,nb=small(); assert z==ident and nb==18
+    for skip in range(nb): assert small(skip)[0]!=ident; bridge_controls.append(skip)
+
+    paid=Counter(); calls=[]; assignment=set(); expanded=hashlib.sha256(); full_event_count=0
+    for e in events:
+        if e['kind']!='local': continue
+        s,p,rev=e['stage'],e['pair'],e['reverse']; ori='reverse' if rev else 'forward'
+        for rep in range(T):
+            owners=[]
+            for i in range(2*V):
+                side=i//V; side=1-side if rev else side
+                owners.append([rep*(2*K*V)+(2*p+side)*V+i%V, ['data',s,i%V]])
+            for r in range(R):
+                bank,slot=divmod(rep*R+r,8)
+                owners.append([DATA+s*R+bank,['bank',slot]])
+                assignment.add((s,rep,r,bank,slot))
+            assert len({(f,tuple(route)) for f,route in owners})==LOCAL
+            assert all(0<=f<LIVE for f,route in owners)
+            # Stream one full renamed instruction program into a source-bound
+            # digest, including exact owner route descriptors and reflection.
+            for z in streams[ori]:
+                op=z[0]
+                if op==0: paid[z[4]]+=bool(z[4]); mapped=[op,owners[z[1]],*z[2:]]
+                else:
+                    ox=owners[z[1]]; oy=owners[z[2]] if z[2]<LOCAL else [LIVE,['private',0]]
+                    mapped=[op,ox,oy,*z[3:]]
+                    if op==2: paid[z[5]]+=1
+                expanded.update((json.dumps(mapped,separators=(',',':'))+'\n').encode()); full_event_count+=1
+            calls.append(dict(stage=s,replica=rep,pair=p,orientation=ori,owners=owners,local_hash=checks[ori]['sha256']))
+    paid.pop(0,None)
+    assert len(assignment)==L*T*R==54576 and len(calls)==72
+    for e in schedule:
+        if e['kind']=='idle' and e['rank']: paid[e['rank']]+=2*V*T
+    mass=sum(r*c for r,c in paid.items()); assert M*LIVE-mass==2496
+    assert dict(sorted(paid.items()))=={1:170424,2:63000,3:34200,4:23112,5:11808,7:6768,8:648,14:3840,28:3840,42:3840}
+    cf=checks['forward']['cancellation_free_row_l1']; cb=checks['reverse']['cancellation_free_row_l1']
+    prefix=(1<<nb)*cf**5*cb**4; charged_prefix=64*((prefix.bit_length()+63)//64);assert prefix<1<<charged_prefix
+    print('Fresh prefix bits',prefix.bit_length(),'charged',charged_prefix,flush=True)
+    template=dict(version='compressed-nine-e8-bit-v1',m=M,h=H,stages=L,replicas=T,live=LIVE,private_centre_reserve=9,
+                  cover='O(I_64/2,F_q) for admitted odd address primes q',loop_order='Each recipe phase: replicas then all cover classes; finish every local invocation before the next.',
+                  schedule=schedule,local_programs=streams,calls=calls,bank_padding=None,
+                  helper_route='owner (DATA + stage*758 + floor((758*replica+helper)/8), d*Pi_slot^-1)',
+                  data_route='owner (replica*960 + (2*pair+side)*120+port, d*rho_stage,port)',
+                  bit_operator='D_U exchanges the two address halves on projector U; D_I D_P = D_(I-P) exactly.',
+                  geometry_sha256=sha(out/'GEOMETRY.json'),source_record_sha256=sha(rp))
+    blob=json.dumps(template,separators=(',',':'),sort_keys=True).encode(); (out/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+    result=dict(status='PASS_SOURCE_BOUND_NINE_STAGE_BIT_TEMPLATE',h=H,m=M,v=V,R=R,replicas=T,live=LIVE,physical=LIVE+9,
+                word_sha256=sha(wp),source_records_sha256=sha(rp),local_checks=checks,scalar_stages=stages,
+                independent_unbanked_scalar_columns=n,all_scalar_columns_restored=True,
+                geometry_sha256=sha(out/'GEOMETRY.json'),template_sha256=hashlib.sha256(blob).hexdigest(),
+                emitted_program_sha256=expanded.hexdigest(),emitted_events=full_event_count,local_invocations=len(calls),
+                bank_assignments=len(assignment),banks_per_stage=R,whole_rank8_slots_per_bank=8,padding_calls=0,
+                profile=dict(sorted(paid.items())),paid_calls=sum(paid.values()),rank_mass=mass,deficit=2496,
+                maxchild=max(paid),halving_depth=2,halving_integer_inequality=[64**2,2*42**2],
+                local_additions=expected_adds,bridge_additions=18*V*T,copy_erase_episodes=9*72,
+                global_prefix_bound=str(prefix),global_prefix_bits=prefix.bit_length(),charged_prefix_bits=charged_prefix,
+                omitted_bridge_shears_rejected=bridge_controls,
+                scope='Complete source-bound finite cover template. Local and unbanked global F2 columns are replayed; arbitrary physical bank dirt follows by injective owner routes and the all-column local theorem. Astronomical cover enumeration and all-size compiler interfaces remain explicit inherited assumptions.',
+                seconds=time.monotonic()-start)
+    write(out/'GLOBAL.json',result)
+    print(json.dumps({k:v for k,v in result.items() if k not in ('local_checks','scalar_stages','global_prefix_bound')}),flush=True)
+
+if __name__=='__main__': main()
diff --git a/research/split-centres-global/code/bit_price.py b/research/split-centres-global/code/bit_price.py
new file mode 100644
index 0000000000..005da012a3
--- /dev/null
+++ b/research/split-centres-global/code/bit_price.py
@@ -0,0 +1,18 @@
+"""Exact price of the emitted bit program; no histogram supplied by discovery."""
+import json,importlib.util
+from fractions import Fraction as Q
+from pathlib import Path
+
+def load(name):
+ p=Path('work/pr361/code/engines')/(name+'.py');sp=importlib.util.spec_from_file_location('price_'+name,p);m=importlib.util.module_from_spec(sp);sp.loader.exec_module(m);return m
+p=Path('bit426-source-centres/global');g=json.loads((p/'GLOBAL.json').read_text());a=json.loads((p/'AUDIT.json').read_text())
+assert a['template_sha256']==g['template_sha256']
+H={int(r):n for r,n in a['profile'].items()};m,W=g['m'],g['live']
+M,B=load('moment'),load('base_two_moment');root=M.certify(H,m,W,True);lo,hi=Q(root['lower']),Q(root['upper'])
+fb=32*m*m*sum(H.values())
+def other(x):
+ l,u=B.moment(m,W,list(H.items()),x);a,b=B.moment(m,W,[(1,fb)],x);return l+a/10**16,u+b/10**16
+assert other(lo)[1]<1<other(hi)[0]
+root.update(source_template_sha256=g['template_sha256'],two_exact_engines=True)
+Path('BIT-PRICE.json').write_text(json.dumps(root,indent=2)+'\n')
+print('PASS two rational bit moments',root['lower'])
diff --git a/research/split-centres-global/code/combined.py b/research/split-centres-global/code/combined.py
new file mode 100644
index 0000000000..4131327bce
--- /dev/null
+++ b/research/split-centres-global/code/combined.py
@@ -0,0 +1,55 @@
+"""Fresh bit finite invoice and joint strict arithmetic for two changed suppliers.
+icekylinx, with Codex assistance. Inherited all-size interfaces remain conditional.
+"""
+import json,hashlib,importlib.util
+from pathlib import Path
+from fractions import Fraction as Q
+import os
+ROOT=Path(os.environ['E8_OUTPUT']);D=ROOT/'bit426-source-centres/global';C=ROOT/'split-centres'
+read=lambda p:json.loads(p.read_text())
+g=read(D/'GLOBAL.json');geo=read(D/'GEOMETRY.json');audit=read(D/'AUDIT.json')
+cx=read(C/'INTEGRATION.json');ca=read(C/'INDEPENDENT-REPLAY.json')
+assert audit['template_sha256']==g['template_sha256'] and ca['template_sha256']==cx['global_template_sha256']
+assert len(audit['mutations_rejected'])==8 and len(ca['mutation_controls_rejected'])==7
+P={int(r):z for r,z in audit['profile'].items()};m,W=64,14502;E=sum(P.values());T,L,R,V,K=8,9,758,120,4
+mass=sum(r*z for r,z in P.items());assert m*W-mass==2496 and g['live']==W
+physical=g['physical'];d=m*m;N=2*m
+unit=L*T*g['local_additions']+g['bridge_additions']
+J=8*T*L*(2*V+R)+8*(2*K*V*T)+2*g['bank_assignments']+2*g['copy_erase_episodes']
+high=16*(d+1)**2;good=8*m*m+8;compiler=128*N**3
+selectors=2*L*T*((W-1)+R*m*(geo['max_route_factors']+(m-1)+m))
+prefix=int(g['global_prefix_bound']);assert prefix<1<<256
+coefficient=unit+J*high+J*physical+E*(good+compiler)+16*m**3+g['copy_erase_episodes']+selectors+prefix+1
+two=(coefficient+1)**2*(E+1)**2
+assert two<1<<512 and 2*max(P)**2<m*m
+row=2*(m*m+1)+9909+252;assert row==18355<20161
+assert geo['bad_prime_factors']==[2] and geo['route_denominators']==[1,2,4]
+def load(name):
+ p=ROOT/'work/pr361/code/engines'/(name+'.py');sp=importlib.util.spec_from_file_location('joint_'+name,p);mod=importlib.util.module_from_spec(sp);sp.loader.exec_module(mod);return mod
+M,Other,Outer=load('moment'),load('base_two_moment'),load('outer')
+root=M.certify(P,m,W,True);c=Q(root['lower']);grid=Q(1,10**18);b=Q(ca['complex_b'])
+fb=32*m*m*E
+lo,hi=Other.moment(m,W,list(P.items()),c);bl,bh=Other.moment(m,W,[(1,fb)],c)
+assert hi+bh/10**16<1
+eta=beta=Q(1,10**18);s=min(c,(1-beta)*b)-Q(1,10**24)
+assert 0<s<c and s<(1-beta)*b
+chain=[Q(384599,10**10)];cutoffs=[]
+def ceil(x):return -((-x.numerator)//x.denominator)
+for j in range(6):
+ old=chain[-1];a=(1-s)*s+s*old
+ gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+ cutoff=max(ceil(36/gap**2),ceil(2*(4+512)/gap))
+ assert cutoff*gap**2>=36 and cutoff*gap>=2*(4+512)
+ cutoffs.append(dict(gap=str(gap),cutoff_log2=str(cutoff)));chain.append(a)
+q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin/grid;k=grid*((ticks.numerator-1)//ticks.denominator)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}
+a=Outer.assembly(chain[-1],b,bridge,k,eta=eta,beta=beta)
+assert len(a['strict_constraints'])==47 and all(x>0 for x in a['strict_constraints'].values())
+controls=[]
+for name,kk,ee,bb in [('next_grid',k+grid,eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]:
+ try:Outer.assembly(chain[-1],b,bridge,kk,eta=ee,beta=bb)
+ except AssertionError:controls.append(name)
+ else:raise AssertionError(name)
+result=dict(status='PASS_CONDITIONAL_SPLIT_CENTRE_ASSEMBLY',kappa=str(k),kappa_decimal=format(float(k),'.18f'),bit_lower=str(c),complex_lower=str(b),binding_component='bit',gain_over_pr425_percent=float(100*(k/Q(1048005508028206,10**18)-1)),bit_invoice=dict(prefix_bits=prefix.bit_length(),charged_prefix_bits=256,coefficient_bits=coefficient.bit_length(),two_level_coefficient_bits=two.bit_length(),charged_two_level_coefficient_bits=512,row_coefficient=row,live=W,physical=physical),strict_outer_constraints={n:str(x) for n,x in a['strict_constraints'].items()},outer_controls=controls,bootstrap=cutoffs,bit_template_sha256=g['template_sha256'],complex_template_sha256=cx['global_template_sha256'],scope='Finite research composition with explicit changed words, exact local and global replay and incremental phase evidence. All-size correlated dirty-bank, compressed-window, compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. This certificate makes no unconditional integer-multiplication or Lean-kernel claim.')
+(ROOT/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n')
+print(result['status'],result['kappa_decimal'],result['gain_over_pr425_percent'],result['bit_invoice'])
diff --git a/research/split-centres-global/code/complex_audit.py b/research/split-centres-global/code/complex_audit.py
new file mode 100644
index 0000000000..ba6789a3a6
--- /dev/null
+++ b/research/split-centres-global/code/complex_audit.py
@@ -0,0 +1,168 @@
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Read-back audit, independent of the Hamming producer and its row state."""
+import copy,gzip,hashlib,importlib.util,json,math,time
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');p=OUT/'FULL-WORD.json.gz'
+word=json.load(gzip.open(p));v=120;n=240+word['report']['R'];start=time.monotonic()
+def apply(e,rows):
+    if e[0]=='scale':
+        _,t,a,b,*_=e;q=Q(a,b);assert q
+        rows[t]={j:q*x for j,x in rows[t].items()}
+    else:
+        _,t,s,a,b,*_=e;q=Q(a,b);assert t!=s
+        for j,x in list(rows[s].items()):
+            z=rows[t].get(j,Q(0))+q*x
+            if z:rows[t][j]=z
+            else:rows[t].pop(j,None)
+def ident():return [{r:Q(1)} for r in range(n)]
+def inv(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    return e
+def dual(e):
+    e=inv(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1]
+    return e
+
+main=word['A']+word['cut']+word['B']
+assert all(not 120<=e[2]<240 for e in word['A']+word['B'] if e[0]=='add' and not 120<=e[1]<240)
+matrix=ident()
+for e in main:apply(e,matrix)
+print('full main columns',n,'replayed',flush=True)
+# Compute -A_Y^-1 B_S using only rows of the explicit main operator.
+dirty=[{} for r in range(n)]
+for r in range(v,2*v):dirty[r]={j:x for j,x in matrix[r].items() if j>=2*v}
+for e in word['precondition']:apply(e,dirty)
+comp=[]
+for r in range(v,2*v):
+    for j,q in sorted(dirty[r].items()):comp.append(['add',r,j,-q.numerator,q.denominator,[]])
+
+cleanup=[inv(e) for e in reversed(word['A']+word['B']) if not v<=e[1]<2*v]
+assert [e[:-1] for e in cleanup]==[e[:-1] for e in word['cleanup']]
+program=word['precondition']+comp+main+cleanup
+actual=ident()
+for e in program:apply(e,actual)
+expected=ident()
+for t in range(v):expected[v+t][t]=Q(1)
+assert actual==expected
+print('PASS exact arbitrary dirt and restored sources/helpers',flush=True)
+back=ident()
+for e in program:apply(dual(e),back)
+expected_back=ident()
+for t in range(v):expected_back[t][v+t]=Q(-1)
+assert back==expected_back
+print('PASS exact inverse-transpose on every column',flush=True)
+# Independent sparse vector controls avoid repeating a dense full replay.
+def vector(es,x):
+    x=list(map(Q,x))
+    for e in es:
+        if e[0]=='scale':x[e[1]]*=Q(e[2],e[3])
+        else:x[e[1]]+=Q(e[3],e[4])*x[e[2]]
+    return x
+sample=[((i*137+13)%101)-50 for i in range(n)]
+want=vector(program,sample)
+controls={
+    'missing_dirty_compensation':word['precondition']+main+cleanup,
+    'missing_Y_inverse_basis':comp+main+cleanup,
+    'missing_source_cleanup':word['precondition']+comp+main,
+    'wrong_dual_event_order':[dual(e) for e in reversed(program)],
+}
+for name,es in controls.items():
+    expected_sample=vector([dual(e) for e in program],sample) if name=='wrong_dual_event_order' else want
+    assert vector(es,sample)!=expected_sample,name
+
+# Orthogonal transvection and a port permutation bring the new geometry onto
+# the already fixed 120-port routing family. Every incidence is transformed.
+old=json.load(gzip.open('work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz'))
+def tau(x):return x^(43 if (x&43).bit_count()%2 else 0)
+assert 43 .bit_count()%2==0
+assert set(map(tau,word['ports']))==set(old['ports'])
+mapping={i:old['ports'].index(tau(q)) for i,q in enumerate(word['ports'])}
+mapping.update({v+i:v+mapping[i] for i in range(v)})
+mapping.update({r:r for r in range(2*v,n)})
+def basis(vs):
+    b={}
+    for x in vs:
+        for k in sorted(b,reverse=True):
+            if x>>k&1:x^=b[k]
+        if x:
+            k=x.bit_length()-1
+            for j in b:
+                if b[j]>>k&1:b[j]^=x
+            b[k]=x
+    return tuple(b[k] for k in sorted(b,reverse=True))
+def perp(x):return basis([z for z in range(1,512) if not (x&z).bit_count()%2])
+full=tuple(1<<i for i in range(8,-1,-1));frames=[(),full];fi={f:i for i,f in enumerate(frames)}
+def fid(f):
+    f=basis(f)
+    if f not in fi:fi[f]=len(frames);frames.append(f)
+    return fi[f]
+def canonical(e):
+    e=copy.deepcopy(e);e[1]=mapping[e[1]]
+    if e[0]=='add':e[2]=mapping[e[2]]
+    if e[-1] is not None:e[-1]=fid([tau(x) for x in e[-1]])
+    return e
+can={key:[canonical(e) for e in word[key]] for key in ('A','B','cut','cleanup','precondition')}
+can['compensation']=[canonical(e) for e in comp]
+can['start']=[fid([q]) for q in old['ports']]+[0]*(v+word['report']['R'])
+can['final']=[1]*v+[fid(perp(q)) for q in old['ports']]+[1]*word['report']['R']
+can['ports']=old['ports'];can['centers']=[mapping[r] for r in word['centers']]
+can['center_frames']=[fid([tau(x) for x in f]) for f in word['center_frames']]
+can['h']=9;can['v']=v;can['R']=word['report']['R'];can['frames']=frames
+cur=list(can['start']);paid=Counter();edges=set();incidences=0
+def climb(r,f):
+    old=cur[r]
+    assert basis(frames[old]+frames[f])==frames[f]
+    if old!=f:
+        delta=len(frames[f])-len(frames[old]);assert delta>0
+        edges.add((old,f));paid[delta]+=1;cur[r]=f
+for part in ('A','B'):
+    if part=='B':
+        assert all(cur[r]==f for r,f in zip(can['centers'],can['center_frames']))
+        assert all(cur[r]==0 for r in range(v,2*v))
+        for f in can['center_frames']:paid[len(frames[f])]+=1
+    for e in can[part]:
+        rs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        for r in rs:climb(r,e[-1]);incidences+=1
+for r,f in enumerate(can['final']):climb(r,f)
+assert dict(paid)=={int(r):x for r,x in word['report']['local_profile'].items()}
+assert sum(r*x for r,x in paid.items())==9*can['R']+240*8+72
+can['local_profile']=dict(sorted(paid.items()));can['edges']=sorted(edges)
+cp=OUT/'CANONICAL-WORD.json.gz';cp.write_bytes(gzip.compress(json.dumps(can,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+
+def engine(name):
+    p=Path('work/pr361/code/engines')/(name+'.py');s=importlib.util.spec_from_file_location('hamming_'+name,p)
+    m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,M2=engine('moment'),engine('base_two_moment');m,W=73,12720
+HG={int(r):z for r,z in word['report']['global_profile'].items()}
+root=M.certify(HG,m,W,True);b=Q(int(Q(root['lower'])*10**18),10**18);grid=Q(1,10**18)
+assert M.moment(HG,m,W,b,True)[1]<1<M.moment(HG,m,W,b+grid,True)[0]
+fallback=32*m*m*sum(HG.values())
+def second(a):
+    lo,hi=M2.moment(m,W,list(HG.items()),a)
+    l2,h2=M2.moment(m,W,[(1,fallback)],a)
+    return lo+l2/10**16,hi+h2/10**16
+assert second(b)[1]<1<second(b+grid)[0]
+coeff=Counter(str(Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])) for e in program)
+report={'status':'PASS_EXACT_SCALAR_AND_FRAME_RESEARCH_CANDIDATE_NOT_YET_ADMITTED',
+        'full_word_sha256':hashlib.sha256(p.read_bytes()).hexdigest(),
+        'canonical_word_sha256':hashlib.sha256(cp.read_bytes()).hexdigest(),
+        'live_columns_each_orientation':n,'arbitrary_helper_columns':can['R'],
+        'all_live_source_and_helper_rows_restored':True,'all_target_rows_correct':True,
+        'negative_controls_rejected':list(controls),'old_response_additions':len(comp),
+        'complete_forward_scalar_operations':len(program),'coefficient_histogram':dict(coeff),
+        'frames':len(frames),'nested_directed_edges':len(edges),'common_frame_incidences':incidences,
+        'orthogonal_transport_vector':43,'transported_ports_exactly_match_fixed_routes':True,
+        'local_profile':dict(sorted(paid.items())),
+        'prospective_complex_b':str(b),'prospective_b_float':float(b),
+        'prospective_gain_percent':float(100*(b/Q(999388595603943,10**18)-1)),
+        'two_rational_moment_engines':True,'next_b_grid_rejected':True,
+        'remaining':['new general scalar-interface proof integration','exact phase and emitted local/global program','finite invoice and outer assembly'],
+        'scope':'Substantial new scalar-network candidate. All parameter values remain prospective until the expanded scalar interface and complete phase-aware supplier are admitted.',
+        'seconds':time.monotonic()-start}
+(OUT/'SCALAR-FRAME-AUDIT.json').write_text(json.dumps(report,indent=2)+'\n')
+print('PASS prospective b',float(b),'gain',report['prospective_gain_percent'],'percent; seconds',report['seconds'],flush=True)
diff --git a/research/split-centres-global/code/complex_construct.py b/research/split-centres-global/code/complex_construct.py
new file mode 100644
index 0000000000..bbc61e57dc
--- /dev/null
+++ b/research/split-centres-global/code/complex_construct.py
@@ -0,0 +1,278 @@
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+INPUT=Path('work/complex-network/hamming');OUT=Path('split-centres');OUT.mkdir(exist_ok=True);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+def alloc():
+    n=len(cur);cur.append(());rows.append({});return n
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# All original-source loads precede source borrowing.
+own={};fl={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines']
+    for s in ids:
+        own[s]=alloc();add(own[s],s,1,(P[s],))
+
+packets={};retired={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)})
+    for e,F in zip(z['events'],z['event_frames']):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+    keys=[(p,epsilon) for p in it.combinations(c,2) for epsilon in (-1,1)]
+    for key,(reg,alpha) in zip(keys,z['outputs']):
+        a=mp[reg];alpha=Q(alpha);F=cur[a]
+        b=alloc();add(b,a,1,F)
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,rr in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(rr,alpha)
+    retired[c]=[mp[r] for r in z['dead_registers']]
+
+# Four coordinate sums per code block, reconstructed in the retired register
+# stock at its legal rank-four frame. The remaining eight rows retain a basis.
+block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];regs=retired[c];F=basis([P[s] for s in ids])
+    assert len(regs)==12 and len(F)==4
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    assert all(not rows[r] for r in regs[8:])
+    for i,reg in zip(c,regs[8:]):
+        for j,s in enumerate(ids):add(reg,regs[j],R[s][i],F)
+        block_totals[c,i]=reg
+
+# Eight global coordinate sums, with a single copy each for the centers. The
+# other copy is exactly the correction needed by the eight frame-line targets.
+global_totals={};centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    global_totals[i]=a
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+
+# Own-block and coordinate-frame corrections, one stream per code target.
+own_out={};tetrads={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines']
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        sources=tet[1-parity];xs=[own[s] for s in sources]
+        F=basis([P[s] for s in sources]);linear(xs,[[G[t][s] for s in sources] for t in targets],F)
+        for t,x in zip(targets,xs):own_out[t]=x
+
+# Cross-block M packets, shared by four targets, then two-output pair transforms.
+Ms={};consumers=defaultdict(list);pairs=[]
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for epsilon in (-1,1):
+            (a,alpha),(b,beta)=[packets[d,p,epsilon,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,epsilon]=(a,alpha)
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    for parity,tet in enumerate(tetrads[c]):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in tet:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                assert len(ts)==2;a,b=sorted(ts)
+                e2=R[a][q[0]]*R[a][q[1]]
+                assert e2==R[b][q[0]]*R[b][q[1]]
+                keys=[(c,p,eps),(c,q,e2)];pid=len(pairs)
+                selected=(pi==parity)  # different first partitions in the two tetrads
+                pairs.append({'targets':(a,b),'keys':keys,'selected':selected,
+                              'matrix':[[R[t][p[0]],R[t][q[0]]] for t in (a,b)]})
+                for key in keys:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    a,alpha=Ms[key];ordinary=[i for i in uses if not pairs[i]['selected']]
+    for j,pid in enumerate(ordinary):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+
+assert len(cur)-240==560,(len(cur)-240)
+
+# The selected target pairs borrow Y as the first packet destination. Their
+# two-shear output basis is compensated at frame zero and in the scatter table.
+phase=B;selected=[];output_basis=[]
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=Ms[key1],Ms[key2]
+    add(v+t,a,-Q(mat[0][0],2)*alpha,cur[a])
+    add(v+u,b,-Q(mat[0][1],2)*beta,cur[b])
+    selected.append((pid,t,u,mat))
+for pid,t,u,mat in selected:
+    F=basis(cur[v+t]+cur[v+u]);assert all((P[s]&p).bit_count()%2==0 for s in (t,u) for p in F)
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F)
+    output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+for t,r in own_out.items():add(v+t,r,-Q(1,2),hyper(P[t]))
+
+side=[dict(rows[v+t]) for t in range(v)]
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert side[t]==expected,('side identity',t)
+
+# Correct the eight-center scatter through the inverse two-output basis.
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8;by['c'][8]+=8;by['c'][1]+=8
+n=len(cur);Rcount=n-240
+assert sum(r*z for r,z in H.items())==9*Rcount+240*8+72
+
+def apply(event,matrix):
+    if event[0]=='add':
+        _,t,s,a,b,*_=event;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=event;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e,F=None):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    if F is not None:e[-1]=list(F)
+    return e
+cut=[]
+for t,rr in enumerate(scatter):
+    for i,q in enumerate(rr):
+        if q:cut.append(['add',v+t,centers[i],q.numerator,q.denominator,None])
+cleanup=[inverse(e,FULL) for e in reversed(A+B) if not v<=e[1]<2*v]
+
+# Exact clean replay checks the changed decoder and restored source basis.
+matrix=[{r:Q(1)} if r<v else {} for r in range(n)]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(n))
+
+m=73;T=8;L=9;W=7680+L*Rcount;globalH=Counter({r:z*L*T for r,z in H.items()})
+for r in (16,8,32,8,48,8,48,32,16):globalH[r]+=240*T
+globalH[1]+=L*Rcount
+assert m*W-sum(r*z for r,z in globalH.items())==2496
+low,high=0.,.003
+for _ in range(60):
+    q=(low+high)/2
+    moment=sum(r*z/(m*W)*(m/r)**q for r,z in globalH.items())+32*m*sum(globalH.values())/(10**16*W)*m**q
+    if moment<1:low=q
+    else:high=q
+report={'status':'EXACT_CLEAN_FULL_WORD_DISCOVERY_NOT_ADMITTED',
+        'h':9,'v':120,'R':Rcount,'cst':72,'local_profile':dict(sorted(H.items())),
+        'global_profile':dict(sorted(globalH.items())),'m':m,'W':W,
+        'complex_coarse_float':(low+high)/2,'baseline_b':0.000999388595603943,
+        'gain_percent_float':100*((low+high)/2/0.000999388595603943-1),
+        'scalar_operations_A':len(A),'scalar_operations_B':len(B),
+        'borrowed_output_pairs':len(output_basis),'centre_ranks':list(map(len,center_frames)),'source_columns_exact':120,
+        'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'retained_center_rows_exact':True,
+        'remaining':['full arbitrary-dirt program and independent replay','exact complex phases and global template','finite invoice and coefficient lowering','two rational prices and outer assembly']}
+full={'report':report,'ports':P,'root_lines':R,'A':A,'B':B,'centers':centers,'scatter':[[str(x) for x in r] for r in scatter],
+      'cut':cut,'cleanup':cleanup,'precondition':precondition,'center_frames':center_frames}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(full,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'FULL-DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/split-centres-global/code/complex_emit.py b/research/split-centres-global/code/complex_emit.py
new file mode 100644
index 0000000000..e5fe7b3489
--- /dev/null
+++ b/research/split-centres-global/code/complex_emit.py
@@ -0,0 +1,136 @@
+# Adapted from PR425 by icekylinx with Codex assistance.
+"""Emit both local programs, integrate the fixed nine-stage geometry, and bill.
+
+The expanded scalar interface is justified in PROOF.txt. This script does not
+claim a Lean proof or discharge the inherited all-size/analytic interfaces.
+"""
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp))
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R
+def digest(x):return hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+def basis(vs):
+    b={}
+    for x in vs:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def dual(e):
+    e=list(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1];e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    return e
+def scalar(e,back):
+    e=dual(e) if back else list(e)
+    if e[0]=='add':return ['add',['L',e[1]],['L',e[2]],e[3],e[4]]
+    return ['scale',['L',e[1]],e[2],e[3]]
+def primitive_bound(e):
+    if e[0] in ('clear','copy'):return 1
+    q=Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])
+    a,b=abs(q.numerator),q.denominator
+    assert b&(b-1)==0
+    if e[0]=='scale':
+        assert a&(a-1)==0
+        return abs(a.bit_length()-b.bit_length())+int(q<0)
+    # Exact binary Horner multiplication on a cleared private stream, repeated
+    # halving, signed accumulation into the target, then clear the private stream.
+    return 3+(a.bit_length()-1)+a.bit_count()+(b.bit_length()-1)
+
+def emit(back):
+    out=[];cur=c['start'].copy()
+    def event(e):out.append(e)
+    def scal(e,f):event(['scalar',e,f])
+    event(['phase','zero_frame_precondition'])
+    for e in c['precondition']+c['compensation']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['start'][r]==0 for r in regs)
+        scal(scalar(e,back),0)
+    event(['phase','entry_adapters'])
+    for r,f in enumerate(c['start']):event(['adapter','old_to_new',r,f])
+    def climb(r,f,part):
+        old=cur[r]
+        if old==f:return
+        assert basis(frames[old]+frames[f])==tuple(frames[f])
+        rank=len(frames[f])-len(frames[old]);assert rank>0
+        event(['climb',part,r,old,f,rank]);cur[r]=f
+    for part in ('A','centers','B','final'):
+        event(['phase',part])
+        if part in ('A','B'):
+            for e in c[part]:
+                regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+                for r in regs:climb(r,e[-1],part)
+                scal(scalar(e,back),e[-1])
+        elif part=='centers':
+            assert all(cur[r]==0 for r in range(v,2*v))
+            for k,r in enumerate(c['centers']):
+                cf=c['center_frames'][k];rank=len(frames[cf]);assert cur[r]==cf
+                C=['C',k];scal(['clear',C],0 if back else cf)
+                terms=[e for e in c['cut'] if e[2]==r]
+                if back:
+                    for e in terms:scal(['add',C,['L',e[1]],e[3],e[4]],0)
+                else:scal(['copy',C,['L',r]],cf)
+                event(['center',k,0 if back else cf,cf if back else 0,rank])
+                if back:scal(['add',['L',r],C,-1,1],cf)
+                else:
+                    for e in terms:scal(['add',['L',e[1]],C,e[3],e[4]],0)
+                scal(['clear',C],cf if back else 0)
+        else:
+            for r,f in enumerate(c['final']):climb(r,f,part)
+    event(['phase','exit_adapters'])
+    for r,f in enumerate(c['final']):event(['adapter','new_to_old',r,f])
+    event(['phase','full_frame_cleanup'])
+    for e in c['cleanup']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['final'][r]==1 for r in regs)
+        scal(scalar(e,back),1)
+    event(['phase','done'])
+    return out
+
+def check_local(events,back):
+    # Literal scalar replay of the emitted stream, including center lifetimes.
+    state={('L',r):{r:Q(1)} for r in range(n)};live=[];paid=Counter();prims=0;macros=0
+    for e in events:
+        if e[0]=='climb':assert not live;paid[e[5]]+=1
+        elif e[0]=='center':assert live==[e[1]];paid[e[4]]+=1
+        elif e[0]=='scalar':
+            op=e[1];tag=op[0];t=tuple(op[1]);macros+=1;prims+=2*primitive_bound(op)
+            if tag=='clear':
+                state[t]={}
+                if t[0]=='C' and t[1] in live:live.remove(t[1])
+            elif tag=='copy':state[t]=dict(state.get(tuple(op[2]),{}));live.append(t[1])
+            elif tag=='scale':state[t]={j:Q(op[2],op[3])*x for j,x in state[t].items()}
+            else:
+                s=tuple(op[2]);q=Q(op[3],op[4]);row=state.setdefault(t,{})
+                if t[0]=='C' and t[1] not in live:live.append(t[1])
+                for j,x in list(state.get(s,{}).items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+    assert not live and all(not row for r,row in state.items() if r[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert state['L',r]==expected,('emitted column mismatch',back,r)
+    assert dict(paid)=={int(r):z for r,z in c['local_profile'].items()}
+    return {'sha256':digest(events),'events':len(events),'scalar_macros':macros,
+            'real_component_primitive_bound':prims,'paid_profile':dict(sorted(paid.items())),
+            'all_columns':n,'private_centers_cleared':True,'private_coefficient_stream_cleared_after_each_macro':True}
+
+programs={};checks={}
+for name,back in [('forward',False),('backward',True)]:
+    programs[name]=emit(back);checks[name]=check_local(programs[name],back)
+    print('PASS emitted',name,checks[name]['events'],'events',flush=True)
+
+
+(OUT/'LOCAL-PROGRAMS.json.gz').write_bytes(gzip.compress(json.dumps(programs,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'LOCAL-CHECKS.json').write_text(json.dumps(checks,indent=2)+'\n')
diff --git a/research/split-centres-global/code/complex_integrate.py b/research/split-centres-global/code/complex_integrate.py
new file mode 100644
index 0000000000..ffa5c036d7
--- /dev/null
+++ b/research/split-centres-global/code/complex_integrate.py
@@ -0,0 +1,109 @@
+# Adapted from PR425 for heterogeneous centres by icekylinx, with Codex assistance.
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+OUT=Path('split-centres');cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp));audit=json.loads((OUT/'SCALAR-FRAME-AUDIT.json').read_text())
+phase=json.loads((OUT/'CLIFFORD-REVIEW.json').read_text());sha=lambda p:hashlib.sha256(Path(p).read_bytes()).hexdigest()
+assert phase['canonical_word_sha256']==audit['canonical_word_sha256']==sha(cp)
+assert phase['all_child_equalities_include_global_phase']
+programs=json.load(gzip.open(OUT/'LOCAL-PROGRAMS.json.gz'));checks=json.loads((OUT/'LOCAL-CHECKS.json').read_text())
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R;private_centres=len(c['centers'])
+for z in checks.values():z['paid_profile']={int(r):n for r,n in z['paid_profile'].items()}
+old=Path('work/complex-nine-native');template=json.load(gzip.open(old/'GLOBAL-TEMPLATE.json.gz'))
+data_phase=json.loads((old/'DATA-PHASES.json').read_text())
+assert template['exact_data_phase_recipe_sha256']==sha(old/'DATA-PHASES.json')
+assert data_phase['status']=='PASS_EXACT_Z4_DATA_ROUTE_IDLE_AND_TERMINAL_PHASES'
+m,T,L,k=73,8,9,4;W=2*v*k*T+L*R;physical=W+R+private_centres+2
+template['version']='hamming-mutable-basis-nine-v1';template['live']=W;template['physical']=physical
+template['local_programs']=programs;paid=Counter();assignments=set();event_count=0;scalar_primitives=0
+for call in template['calls']:
+    stage,rep,pair=call['stage'],call['replica'],call['pair'];ori=call['orientation']
+    owners=[[rep*2*k*v+(2*pair+r//v)*v+r%v,[1,stage,r%v]] for r in range(2*v)]
+    for r in range(R):
+        z=rep*R+r;bank,slot=divmod(z,T);owners.append([2*v*k*T+stage*R+bank,[2,slot]])
+        assignments.add((stage,rep,r,bank,slot))
+    assert len(owners)==n and len({(f,tuple(route)) for f,route in owners})==n
+    assert all(f<W for f,route in owners)
+    call['owners']=owners;call['local_program_sha256']=checks[ori]['sha256']
+    for r,z in checks[ori]['paid_profile'].items():paid[r]+=z
+    event_count+=checks[ori]['events'];scalar_primitives+=checks[ori]['real_component_primitive_bound']
+assert len(assignments)==L*T*R and len(template['calls'])==72
+for item in template['idle_children']:paid[item['rank']]+=item['replicas']
+paid[1]+=L*R
+assert dict(paid)=={int(r):z for r,z in json.load(gzip.open(OUT/'FULL-WORD.json.gz'))['report']['global_profile'].items()}
+mass=sum(r*z for r,z in paid.items());assert m*W-mass==2496
+template['bank_padding']['families']=list(range(7680,W))
+template['cover_final_correction']['families']=[0,W]
+template['cover_final_correction']['charged_calls_per_cover']=W
+for e in template['execution_schedule']:
+    if e['kind']=='bank_padding_cover_sweep':e['families']=[7680,W]
+    elif e['kind']=='translate_every_live_family':e.update(template['cover_final_correction'])
+template['private_namespace']={'centers':[W,W+private_centres],'reserved_tableau':[W+private_centres,W+private_centres+R],
+                               'coefficient':[physical-2,physical]}
+template['exact_local_clifford_recipe_sha256']=sha(OUT/'CLIFFORD-RECIPES.json')
+template['expanded_scalar_interface']='See PROOF.txt: mutable source basis, frame-zero output preconditioner, explicit dirty compensator, and full-frame inverse source/helper cleanup.'
+blob=json.dumps(template,sort_keys=True,separators=(',',':')).encode()
+(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+
+# Fresh finite overcharge, with the changed stock, scalar counts, coefficient
+# lowering, and private work reserve. No unchanged local invoice is assumed.
+compiler=64*(m+1)**3;macros=max(z['scalar_macros'] for z in checks.values());children=sum(checks['forward']['paid_profile'].values())
+adapters=16*(macros+children+n+private_centres)+64*m
+local_bound=max(z['real_component_primitive_bound'] for z in checks.values())+adapters*compiler
+bridges=[e for e in template['recipe'] if e['kind']=='bridge'];bridge_adds=2*v*T*len(bridges)
+terminal_shifts=k*v*T;terminal_moves=2*k*v*T
+nonlocal_items=4*v*T*L+2*v*T*L+2*L*T*R+sum(e['replicas'] for e in template['idle_children'])+L*R+bridge_adds+terminal_shifts+terminal_moves+W+physical
+outside=8*nonlocal_items+64*m
+pervertex=scalar_primitives+bridge_adds+terminal_shifts+terminal_moves+W+(72*adapters+outside)*compiler+64*physical
+r=m//2;group=2**(r*r)*math.prod(2**(2*i)-1 for i in range(1,r+1));stock=group*physical
+smass=group*mass;logical=group*pervertex+64;router=compiler*(logical+1)*(stock+1)**2
+GG,EE,C0=1<<30000,1<<100000,1<<210000;BB=smass+EE
+literal=2*GG*stock**2+8*smass+4*stock+4+32*m
+maxchild=max(paid);depth=2;assert m**depth>2*maxchild**depth
+assert local_bound<1<<48 and logical<1<<6050 and router<GG and literal<EE and BB<1<<100001
+assert 32*m*BB*BB<C0 and 2*BB+18<C0
+row=depth*stock.bit_length()+9909+252;assert row<20161
+
+def load(name):
+    sp=importlib.util.spec_from_file_location('hamming_integrate_'+name,Path('work/pr361/code/engines')/(name+'.py'))
+    mod=importlib.util.module_from_spec(sp);sp.loader.exec_module(mod);return mod
+Outer=load('outer');b=Q(audit['prospective_complex_b']);bit=Q(json.loads(Path('BIT-PRICE.json').read_text())['lower'])
+eta=Q(1,10**12);beta=Q(1,10**9);grid=Q(1,10**18)
+s=Q(int(((1-beta)*min(b,bit)-grid)*10**18),10**18);assert s<bit
+chain=[Q(384599,10**10)];cutoffs=[]
+for _ in range(3):
+    a=chain[-1];z=(1-s)*s+s*a;gap=min(s-z,1-z-s,1-z-s*(1-a),1-s)
+    assert a<z<s<1-z and gap>0
+    bound=max(math.ceil(36/gap**2),math.ceil(2*(4+512)/gap))
+    assert bound*gap**2>=36 and bound*gap>=2*(4+512)
+    cutoffs.append(str(bound));chain.append(z)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},
+        'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}
+q=chain[-1]*(1-2*eta);ticks=(1-eta)*q/(1+q)/grid;kap=Q((ticks.numerator-1)//ticks.denominator,10**18)
+assembly=Outer.assembly(chain[-1],b,bridge,kap,eta=eta,beta=beta)
+try:Outer.assembly(chain[-1],b,bridge,kap+grid,eta=eta,beta=beta)
+except AssertionError:pass
+else:raise AssertionError('next kappa grid accepted')
+result={'status':'PASS_NEW_STRUCTURAL_PROGRAM_AND_FINITE_ASSEMBLY_PENDING_REPLAY',
+        'canonical_word_sha256':sha(cp),'scalar_audit_sha256':sha(OUT/'SCALAR-FRAME-AUDIT.json'),
+        'exact_phase_receipt_sha256':sha(OUT/'CLIFFORD-REVIEW.json'),'global_template_sha256':hashlib.sha256(blob).hexdigest(),
+        'local_program_checks':checks,'R':R,'m':m,'live':W,'physical':physical,
+        'bank_assignments':len(assignments),'rank_mass':mass,'deficit':2496,
+        'global_profile':dict(sorted(paid.items())),'emitted_local_events_all_calls':event_count,
+        'finite_invoice':{'local_primitive_bound':local_bound,'local_adapters':adapters,
+                          'pervertex':pervertex,'physical_stock_bits':stock.bit_length(),
+                          'router_bits':router.bit_length(),'literal_bits':literal.bit_length(),
+                          'physical_row_coefficient':row,'retained_row_coefficient':20161,
+                          'compiler':compiler,'G_exponent':30000,'E_exponent':100000,'C0_exponent':210000,
+                          'required_C0_bits':(32*m*BB*BB).bit_length(),'halving_degree':depth,
+                          'halving_integer_inequality':[m**depth,2*maxchild**depth]},
+        'complex_b':str(b),'bit_c':str(bit),'prospective_kappa':str(kap),'kappa_float':float(kap),
+        'log2_kappa':math.log2(float(kap)),
+        'kappa_gain_percent':float(100*(kap/Q(998390813251625,10**18)-1)),
+        'strict_outer_constraints':{name:str(z) for name,z in assembly['strict_constraints'].items()},
+        'next_kappa_grid_rejected':True,'bootstrap_cutoffs_log2':cutoffs,
+        'scope':'New finite scalar interface with a written conjugation proof, conditional on inherited all-size compiler, precision/tape and analytic transfer. Independent emitted-program replay and fresh package replay still required before final promotion.'}
+(OUT/'INTEGRATION.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS prospective kappa',float(kap),'gain',result['kappa_gain_percent'],'percent',flush=True)
diff --git a/research/split-centres-global/code/complex_phases.py b/research/split-centres-global/code/complex_phases.py
new file mode 100644
index 0000000000..88d6afa045
--- /dev/null
+++ b/research/split-centres-global/code/complex_phases.py
@@ -0,0 +1,24 @@
+"""Bind unchanged exact phase evidence, or regenerate all selected phase pairs."""
+import gzip,hashlib,json,os,subprocess,sys
+from pathlib import Path
+P=Path(__file__).resolve().parent.parent;O=Path('split-centres')
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+c=json.load(gzip.open(O/'CANONICAL-WORD.json.gz'))
+r=json.loads((P/'inputs/complex-phase-receipt.json').read_text())
+raw=gzip.decompress((P/'inputs/complex-phase-recipes.json.gz').read_bytes());recipes=json.loads(raw)
+# Bind the exact decoded witness, independently of gzip implementation metadata.
+assert hashlib.sha256(gzip.decompress((O/'CANONICAL-WORD.json.gz').read_bytes())).hexdigest()==r['canonical_word_payload_sha256']
+r['canonical_word_sha256']=sha(O/'CANONICAL-WORD.json.gz')
+assert hashlib.sha256(raw).hexdigest()==r['recipe_sha256']
+edges=set(map(tuple,c['edges']))|{(a,b) for f in c['center_frames'] for a,b in ((f,0),(0,f))}
+assert {(z['old'],z['new']) for z in recipes['children']}==edges
+assert len(recipes['children'])==len(edges) and len(recipes['endpoint_adapters'])==240
+for z in recipes['children']:assert z['rank']==abs(len(c['frames'][z['old']])-len(c['frames'][z['new']]))
+if os.environ.get('E8_REPLAY_PHASES')=='1':
+ subprocess.run([sys.executable,'-B',str(P/'code/complex_phases_full.py')],check=True)
+ assert (O/'CLIFFORD-RECIPES.json').read_bytes()==raw
+else:
+ (O/'CLIFFORD-RECIPES.json').write_bytes(raw)
+ r['validation_mode']='Reuse exact phase evidence bound to the unchanged canonical word and recipe hashes'
+ (O/'CLIFFORD-REVIEW.json').write_text(json.dumps(r,indent=2)+'\n')
+print('PASS source-bound phase recipes',len(edges))
diff --git a/research/split-centres-global/code/complex_phases_full.py b/research/split-centres-global/code/complex_phases_full.py
new file mode 100644
index 0000000000..b5a5bd64b4
--- /dev/null
+++ b/research/split-centres-global/code/complex_phases_full.py
@@ -0,0 +1,39 @@
+# Adapted from PR425 for heterogeneous centres by icekylinx with Codex assistance.
+"""Exact phase-aware lowering of every used edge of the new structural word."""
+import gzip,hashlib,json,sys,time
+from collections import Counter
+from pathlib import Path
+sys.path.insert(0,str(Path('work/odd-stages').resolve()))
+from clifford_exact import *
+
+OUT=Path('split-centres');P=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(P));n=c['h'];frames=c['frames'];start=time.monotonic();ops=[]
+for U in frames:
+    op=canonical_frame(n,U)
+    L=[u|(u<<n) for u in U]+[v<<n for v in nullspace(U,n)]
+    pre=[x|(z<<n) for x,z,p in inverse(op.tab)[n:]]
+    assert rank(L)==n and rank(L+pre)==n
+    assert rank([x for x,z,p in op.tab[n:]])==len(U)
+    ops.append(op)
+edges=set(map(tuple,c['edges']))|{(a,b) for f in c['center_frames'] for a,b in ((f,0),(0,f))};recipes=[];hist=Counter()
+for i,(a,b) in enumerate(sorted(edges)):
+    op=ops[a].adjoint().then(ops[b]);rec,compiled=lower_child(op)
+    assert rec['rank']==abs(len(frames[a])-len(frames[b]))
+    hist[rec['rank']]+=1;recipes.append({'old':a,'new':b,**rec})
+    if i%200==0:print('exact phase edges',i,'/',len(edges),'seconds',time.monotonic()-start,flush=True)
+adapters=[];F=fourier(n)
+for i,q in enumerate(c['ports']):
+    for role,old,f in [('source',cgate(n,q),c['start'][i]),
+                       ('target',cgate(n,q).adjoint().then(F),c['final'][c['v']+i])]:
+        rec,compiled=lower_child(old.adjoint().then(ops[f]));assert rec['rank']==0
+        adapters.append({'port':i,'role':role,'frame':f,**rec})
+raw=json.dumps({'children':recipes,'endpoint_adapters':adapters},sort_keys=True,separators=(',',':')).encode()
+(OUT/'CLIFFORD-RECIPES.json').write_bytes(raw)
+result={'status':'PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES',
+        'canonical_word_sha256':hashlib.sha256(P.read_bytes()).hexdigest(),
+        'frames':len(frames),'directed_edges':len(edges),'ranks':dict(hist),
+        'endpoint_adapters':len(adapters),'all_child_equalities_include_global_phase':True,
+        'recipe_sha256':hashlib.sha256(raw).hexdigest(),'seconds':time.monotonic()-start,
+        'scope':'Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations.'}
+(OUT/'CLIFFORD-REVIEW.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS exact local phases',result['seconds'],'seconds',flush=True)
diff --git a/research/split-centres-global/code/complex_replay.py b/research/split-centres-global/code/complex_replay.py
new file mode 100644
index 0000000000..e9f0490478
--- /dev/null
+++ b/research/split-centres-global/code/complex_replay.py
@@ -0,0 +1,177 @@
+# Adapted for heterogeneous centres by icekylinx with Codex assistance.
+"""Independent read-back of the serialized local/global instruction stream."""
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');P=OUT/'GLOBAL-TEMPLATE.json.gz'
+ir=json.load(gzip.open(P));c=json.load(gzip.open(OUT/'CANONICAL-WORD.json.gz'))
+integration=json.loads((OUT/'INTEGRATION.json').read_text())
+assert hashlib.sha256(gzip.decompress(P.read_bytes())).hexdigest()==integration['global_template_sha256']
+assert c['ports']==json.load(gzip.open('work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz'))['ports']
+v,R,h=c['v'],c['R'],c['h'];n=2*v+R;frames=c['frames']
+def contains(a,b):
+    for x in a:
+        for y in b:
+            if x>>(y.bit_length()-1)&1:x^=y
+        if x:return False
+    return True
+def local(events,back):
+    rows={('L',r):{r:Q(1)} for r in range(n)}
+    norm={('L',r):Q(1) for r in range(n)};prefix=Q(1);cur=c['start'].copy();private={}
+    hist=Counter();phases=[];entry=[];exit=[];centers=[];matrix_hash=hashlib.sha256()
+    allowed=['zero_frame_precondition','entry_adapters','A','centers','B','final','exit_adapters','full_frame_cleanup','done']
+    for event in events:
+        tag=event[0]
+        if tag=='phase':
+            phases.append(event[1]);assert phases==allowed[:len(phases)]
+            if event[1]=='A':assert entry==list(enumerate(c['start']))
+            if event[1]=='centers':assert all(cur[r]==0 for r in range(v,2*v))
+            if event[1]=='full_frame_cleanup':assert cur==c['final'] and exit==list(enumerate(c['final']))
+            assert not private
+        elif tag=='adapter':
+            assert event[3]==(c['start'] if event[1]=='old_to_new' else c['final'])[event[2]]
+            (entry if event[1]=='old_to_new' else exit).append((event[2],event[3]))
+        elif tag=='climb':
+            _,part,r,a,b,rank=event
+            assert not private and phases[-1]==part and cur[r]==a
+            assert contains(frames[a],frames[b]) and rank==len(frames[b])-len(frames[a])>0
+            hist[rank]+=1;cur[r]=b
+        elif tag=='center':
+            _,k,a,b,rank=event
+            assert phases[-1]=='centers' and private=={('C',k):a}
+            cf=c['center_frames'][k];cr=len(frames[cf])
+            assert (a,b,rank)==((0,cf,cr) if back else (cf,0,cr))
+            private['C',k]=b;hist[rank]+=1;centers.append(k)
+        elif tag=='scalar':
+            _,e,f=event;op=e[0];target=tuple(e[1]);source=tuple(e[2]) if op in ('copy','add') else None
+            if target[0]=='C' and op=='clear':
+                assert private.get(target,f)==f
+                private.pop(target,None)
+            else:
+                for r in (target,source):
+                    if r is None:continue
+                    if r[0]=='L':assert cur[r[1]]==f,('common frame',r,cur[r[1]],f)
+                    else:
+                        if r==target and r not in private:private[r]=f
+                        assert private[r]==f
+            if op=='clear':rows[target]={};norm[target]=Q(0)
+            elif op=='copy':rows[target]=dict(rows[source]);norm[target]=norm[source]
+            elif op=='scale':
+                q=Q(e[2],e[3]);a,b=abs(q.numerator),q.denominator
+                assert a&(a-1)==0 and b&(b-1)==0
+                rows[target]={j:q*x for j,x in rows[target].items()};norm[target]*=abs(q)
+            else:
+                q=Q(e[3],e[4]);a,b=abs(q.numerator),q.denominator
+                assert source!=target and b&(b-1)==0
+                # Independent symbolic replay of the cleared coefficient work.
+                w=0
+                for bit in bin(a)[2:]:w=2*w+int(bit)
+                assert Q(w,b)*(1 if q>0 else -1)==q
+                prefix=max(prefix,Q(a)*norm[source])
+                norm[target]=norm.get(target,Q(0))+abs(q)*norm[source]
+                row=rows.setdefault(target,{})
+                for j,x in list(rows[source].items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+            prefix=max(prefix,norm[target])
+        else:raise AssertionError(tag)
+    assert phases==allowed and centers==list(range(len(c['centers']))) and not private
+    assert all(not row for reg,row in rows.items() if reg[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert rows['L',r]==expected
+    # A 192-bit local payload allowance vastly dominates even coefficient work.
+    assert prefix<2**192
+    return hist,{'all_exact_columns':n,'prefix_l1_upper':str(prefix),
+                 'prefix_bits_upper':prefix.numerator.bit_length()-prefix.denominator.bit_length()+1,
+                 'charged_payload_bits':192,'private_work_erased':True}
+
+profiles={};checks={}
+for name in ('forward','backward'):
+    profiles[name],checks[name]=local(ir['local_programs'][name],name=='backward')
+    assert dict(profiles[name])=={int(r):z for r,z in c['local_profile'].items()}
+    print('independent emitted replay PASS',name,flush=True)
+controls=[]
+for name,mut in [
+    ('wrong_scale',lambda es:next(e for e in es if e[0]=='scalar' and e[1][0]=='scale')[1].__setitem__(2,3)),
+    ('missing_center',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center'))),
+    ('wrong_common_frame',lambda es:next(e for e in es if e[0]=='scalar' and e[2]!=0).__setitem__(2,0)),
+    ('wrong_child_rank',lambda es:next(e for e in es if e[0]=='climb').__setitem__(5,99)),
+]:
+    es=copy.deepcopy(ir['local_programs']['forward']);mut(es)
+    try:local(es,False)
+    except (AssertionError,KeyError):controls.append(name)
+    else:raise AssertionError('mutation accepted: '+name)
+
+def global_check(t):
+    assert t['live']==12720 and t['physical']==13298
+    # Eight data-wire scalar columns, independently recomposed.
+    matrix=[[int(i==j) for j in range(8)] for i in range(8)]
+    for e in t['recipe']:
+        if e['kind']=='local':
+            a=2*e['pair'];b=a+1;dst,src,q=(a,b,-1) if e['reverse'] else (b,a,1)
+            matrix[dst]=[x+q*y for x,y in zip(matrix[dst],matrix[src])]
+        elif e['kind']=='bridge':
+            i,j,q=e['dst'],e['src'],e['coefficient']
+            matrix[2*i]=[x+q*y for x,y in zip(matrix[2*i],matrix[2*j])]
+            matrix[2*j+1]=[x-q*y for x,y in zip(matrix[2*j+1],matrix[2*i+1])]
+        else:
+            assert e['kind']=='terminal';old=copy.deepcopy(matrix)
+            for i in range(4):matrix[2*i]=old[2*i+1];matrix[2*i+1]=[-x for x in old[2*i]]
+    assert matrix==[[int(i==j) for j in range(8)] for i in range(8)]
+    seen=set();hist=Counter();pairs={e['stage']:e for e in t['recipe'] if e['kind']=='local'}
+    for call in t['calls']:
+        stage,rep,pair=call['stage'],call['replica'],call['pair']
+        assert (stage,rep) not in seen;seen.add((stage,rep))
+        assert pair==pairs[stage]['pair']
+        assert call['orientation']==('backward' if pairs[stage]['reverse'] else 'forward')
+        assert len(call['owners'])==800
+        for r,(fam,route) in enumerate(call['owners']):
+            if r<240:assert fam==rep*960+(2*pair+r//120)*120+r%120 and route==[1,stage,r%120]
+            else:
+                z=rep*560+r-240;assert fam==7680+stage*560+z//8 and route==[2,z%8]
+        assert len(set((f,tuple(r)) for f,r in call['owners']))==800
+        for r,z in profiles[call['orientation']].items():hist[r]+=z
+    assert seen=={(s,r) for s in range(9) for r in range(8)}
+    for child in t['idle_children']:hist[child['rank']]+=child['replicas']
+    assert t['bank_padding']=={'families':list(range(7680,12720)),'axis':72,'child_rank':1}
+    hist[1]+=5040
+    assert t['cover_final_correction']['families']==[0,12720]
+    assert t['cover_final_correction']['charged_calls_per_cover']==12720
+    assert t['execution_schedule'][-1]=={'kind':'translate_every_live_family',**{k:v for k,v in t['cover_final_correction'].items() if k!='kind'}}
+    assert 73*12720-sum(r*z for r,z in hist.items())==2496
+    return hist
+H=global_check(ir)
+for name,mut in [('missing_padding',lambda t:t['bank_padding']['families'].pop()),
+                 ('aliased_owner',lambda t:t['calls'][0]['owners'][241].__setitem__(1,[2,0])),
+                 ('missing_cover_phase',lambda t:t['cover_final_correction'].__setitem__('charged_calls_per_cover',0))]:
+    t=copy.deepcopy(ir);mut(t)
+    try:global_check(t)
+    except (AssertionError,KeyError):controls.append(name)
+    else:raise AssertionError('global mutation accepted: '+name)
+assert dict(H)=={int(r):z for r,z in integration['global_profile'].items()}
+
+def load(name):
+    sp=importlib.util.spec_from_file_location('replay_hamming_'+name,Path('work/pr361/code/engines')/(name+'.py'))
+    m=importlib.util.module_from_spec(sp);sp.loader.exec_module(m);return m
+M,B=load('moment'),load('base_two_moment');b=Q(integration['complex_b']);grid=Q(1,10**18)
+assert M.moment(H,73,12720,b,True)[1]<1<M.moment(H,73,12720,b+grid,True)[0]
+def other(a):
+    lo,hi=B.moment(73,12720,list(H.items()),a)
+    l2,h2=B.moment(73,12720,[(1,32*73**2*sum(H.values()))],a)
+    return lo+l2/10**16,hi+h2/10**16
+assert other(b)[1]<1<other(b+grid)[0]
+result={'status':'PASS_INDEPENDENT_NEW_STRUCTURAL_IR_REPLAY',
+        'template_sha256':integration['global_template_sha256'],'local':checks,
+        'mutation_controls_rejected':controls,'all_eight_global_scalar_columns':True,
+        'bank_owners_and_padding_exact':True,'paid_profile':dict(sorted(H.items())),
+        'two_rational_moment_engines':True,'complex_b':str(b),
+        'next_b_grid_rejected':True,
+        'scope':'Independent finite replay; retains the written generic scalar-interface lemma and inherited all-size/analytic assumptions.'}
+(OUT/'INDEPENDENT-REPLAY.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS independent local/global replay and two exact moments',flush=True)
diff --git a/research/split-centres-global/inputs/bit-geometry.json.gz b/research/split-centres-global/inputs/bit-geometry.json.gz
new file mode 100644
index 0000000000..19725bec46
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diff --git a/research/split-centres-global/inputs/bit-r767.json.gz b/research/split-centres-global/inputs/bit-r767.json.gz
new file mode 100644
index 0000000000..807cea53eb
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diff --git a/research/split-centres-global/inputs/complex-data-phases.json.gz b/research/split-centres-global/inputs/complex-data-phases.json.gz
new file mode 100644
index 0000000000..22154a8c58
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diff --git a/research/split-centres-global/inputs/complex-phase-receipt.json b/research/split-centres-global/inputs/complex-phase-receipt.json
new file mode 100644
index 0000000000..23d650bc53
--- /dev/null
+++ b/research/split-centres-global/inputs/complex-phase-receipt.json
@@ -0,0 +1,23 @@
+{
+  "status": "PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES",
+  "canonical_word_sha256": "79ff8e19335d5d5d1563ef0bc218106945d6a2b88ece53ee24bb3d88b2594ba3",
+  "fresh_edges": 248,
+  "reused_exact_edges": 2670,
+  "prior_recipe_sha256": "ecd793998109e76a139afcf5a3d83376cbc27f6364fd5fbc9e5645d129b2f791",
+  "frames": 956,
+  "directed_edges": 2918,
+  "ranks": {
+    "1": 1424,
+    "3": 168,
+    "8": 24,
+    "5": 294,
+    "2": 784,
+    "4": 224
+  },
+  "endpoint_adapters": 240,
+  "all_child_equalities_include_global_phase": true,
+  "recipe_sha256": "242fe77af077973e1933524fe5c7ff3b68bef14b1f6938e024827de78d954492",
+  "seconds": 17.302232877002098,
+  "scope": "Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations.",
+  "canonical_word_payload_sha256": "be2d8d412b948bce50a0fc852ab4c01f57bff4c3c8272da80c09be5bcdf253bf"
+}
diff --git a/research/split-centres-global/inputs/complex-phase-recipes.json.gz b/research/split-centres-global/inputs/complex-phase-recipes.json.gz
new file mode 100644
index 0000000000..03dc5fbe5e
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diff --git a/research/split-centres-global/inputs/complex-ports.json.gz b/research/split-centres-global/inputs/complex-ports.json.gz
new file mode 100644
index 0000000000..ccbdc0596c
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diff --git a/research/split-centres-global/inputs/complex-template.json.gz b/research/split-centres-global/inputs/complex-template.json.gz
new file mode 100644
index 0000000000..975ce5c0df
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diff --git a/research/split-centres-global/inputs/e8-r865.json.gz b/research/split-centres-global/inputs/e8-r865.json.gz
new file mode 100644
index 0000000000..8bec1751f7
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diff --git a/research/split-centres-global/notices/NOTICE-PR352.md b/research/split-centres-global/notices/NOTICE-PR352.md
new file mode 100644
index 0000000000..4f9a0194a3
--- /dev/null
+++ b/research/split-centres-global/notices/NOTICE-PR352.md
@@ -0,0 +1,33 @@
+# Attribution and provenance
+
+Prepared by DaysSky, assisted with Claude. Apache-2.0 (see `LICENSE`) applies to the new code and to the inherited Apache-2.0
+code below; third-party notices are preserved where files are vendored.
+
+- **Complex supplier: the E8 unit** (`code/complex/inputs/e8/`): Jacob Sussman, jacobalansussman/wht-power-saving-lean
+  at `9c94857bbaee886f8649edee0bc2d3c738f9555e` (Apache-2.0, Copyright 2026 Jacob Sussman; his `LICENSE` and `NOTICE`
+  are vendored beside the files). The certificate `tools/certificate/gcert1-e8-r783.json.gz`, the 24 Lean modules and
+  the comparator configuration of his kernel-checked theorem `wht_main_block_B2Ge8x`, his Lean-data generators
+  (`tools/gx/{gxgen,gxrate,gxbind,gxunit,gxcore,gsmirror,gxpaths,regen_check,regen_check_e8}.py`,
+  `tools/gen/{foldlib,foldgen,gen_rates,gen_sharp}.py` and templates) and his stand-alone `tools/e8/replay.py` are
+  vendored byte-identical and sha-pinned in `code/complex/inputs/complex/source-pins.json`. His README credits
+  devices from this repository in the unit: slot reuse with a compensating read (jamesyc #124, eumemic #143), late
+  pairing (Chafik Boukhalfa #200/#233), the in-place pair (icekylinx #184, carried in ikeboy's #191/#193).
+- **Bit word, Design T, twin condensation, checkers and engines** (`data/bit/`, `code/builders/`, `code/checkers/`,
+  `code/pricing/`, `code/export_p10.py`, `code/stage_cohort.py`): unchanged from LJH-217's PR #346 at
+  `11b4de5ff8ed5fccf55d4af1043358d257308e8e`, which builds on DreamingOfClouds' PR #325 p10b word and PR #315 engines
+  (#285/#276 gen5/gen4 lineage on eumemic's PR168 generator and source527 package, PR #200's physical rules, hcg890
+  and Jacob Sussman's five-stage architecture, Evan McKinney's completed banks), utcorvusvolat-dotcom's w3 Design T,
+  twin condensation and verifier (PR #310) and PR #266's official checkers. See PR #346's notice for detail.
+  `json.hpp`: Niels Lohmann, MIT license in its header.
+- **Complex checks** (`code/complex/portable_complex.py`, `code/complex/code/`, `code/complex/inputs/complex/`):
+  PR #315's portable complex checks as ported to p = 10 in PR #346 (#256/#233/#202/#200/#194/#184 lineage:
+  icekylinx, Chafik Boukhalfa, Avi Eisenberg, eumemic and others). Jacob Sussman's `gx.check1`, `gxcore` and pinned
+  Lean chain sources under `code/complex/inputs/complex/sources` are unchanged from PR #346 (byte-identical at
+  `9c94857` except his `ORIGIN.md`, kept at `f010392`).
+- **New here**: `code/complex/code/scatter.py` and the generalization of the label, scalar, splice and guard checks
+  from the paired-cube star scatter with h centres of rank h − 2 to any gx scatter (table or star) with any number
+  of retained totals of any rank (regression: on PR #346's p = 10 program the generalized checks give byte-identical
+  scalar schedules, splice programs, primitive expansions, ledger and precision guard); the generalized final-climb
+  partition; the E8 pins; the Lean-binding and replay steps of `certify_complex.py`; `verify.sh` changes.
+
+Credits do not imply endorsement or review by the credited authors.
diff --git a/research/split-centres-global/notices/NOTICE.md b/research/split-centres-global/notices/NOTICE.md
new file mode 100644
index 0000000000..c244e3f56a
--- /dev/null
+++ b/research/split-centres-global/notices/NOTICE.md
@@ -0,0 +1,47 @@
+# Attribution and provenance
+
+Prepared by Dylan Crow, with Anthropic Claude assistance. Apache-2.0 (see `LICENSE`) applies to the new code and to the
+inherited Apache-2.0 code. Third-party notices are preserved where files are vendored.
+
+## New in this package
+
+- The E8 bit word `bitE8-r865` and its producer (`code/bit/producer/`).
+- The record exporter.
+- The independent checker and the controls.
+- The centre-count CP-SAT proof.
+- The generalized bit-side checkers, each with a documented default that reproduces the original:
+  - `NCOPY` in `legality_h.cpp` and `columns_h.cpp`;
+  - the `--gram` parameter in `gram_frames.py`;
+  - the label-family parameters in `geometry_g.py`;
+  - h and replicas in `tile_g.py`;
+  - h and T in `certify_bit_g.py`;
+  - NCOPY and the route template in `finite_g.py`.
+- The receipt assembler.
+- The secondary `seven_stage.py`.
+
+## Vendored
+
+- **`code/complex/`, `code/pricing/`**: unchanged from PR #352 (DaysSky) at `04b4c3c478b5bd8797d2663d89d8db4dfd0ad9f2`. This
+  includes:
+  - Jacob Sussman's E8 unit, Lean data, generators and replay, from jacobalansussman/wht-power-saving-lean at `9c94857`
+    (Apache-2.0, Copyright 2026 Jacob Sussman; his `LICENSE`/`NOTICE` are beside the files);
+  - PR #315's engines (`moment.py`, `base_two_moment.py`, `outer.py`, `prime_witnesses.py`).
+  See `NOTICE-PR352.md`.
+- **`code/bit/regression/`**: unmodified from PR #352 / PR #346 (LJH-217):
+  - `legality_h_pr346.cpp` and `columns_h_pr346.cpp` (PR #266's official cohort checkers as generalized in h by #346);
+  - `stage_cohort.py`, `prime_new.py`, `tile_check.py`, `cost.py`, `certify_bit.py`.
+  The generalized checkers in `code/bit/checkers/` derive from these, and from the source527/p10 packages'
+  `finite_check.py`, `geometry527.py` and `global_lowering.py`, whose lineage is:
+  - eumemic's source527 package;
+  - PR #200 (Chafik Boukhalfa);
+  - PR234 (hcg890 / Henry Grant), on Jacob Sussman's five-stage architecture;
+  - Evan McKinney's completed banks;
+  - the p = 10 ports by DreamingOfClouds and Chafik Boukhalfa.
+- **`code/secondary/bridged.py`**: unchanged from PR #363 (DaysSky) at `9df55dad6ddd05c3458793dfd82d1c2fe0ddbbb4`.
+  See `NOTICE-PR363.md`.
+- **`data/regression-p10/BASE-*`**: PR #325's p10b word as exported in PR #352 (DreamingOfClouds; #352 `data/bit`).
+- **`data/regression-p10/receipts-loans/`**: verification receipts of agent G's p = 10 passive-loans package, used only as
+  regression input.
+- **`json.hpp`**: Niels Lohmann, MIT license in its header.
+
+The E8 label family on the bit side follows Jacob Sussman's introduction of the E8 family for the complex supplier.
diff --git a/research/split-centres-global/notices/PR386.txt b/research/split-centres-global/notices/PR386.txt
new file mode 100644
index 0000000000..28cfebeb08
--- /dev/null
+++ b/research/split-centres-global/notices/PR386.txt
@@ -0,0 +1,25 @@
+Prepared by Zhihao Chen with substantial OpenAI Codex assistance.
+New compressed nine-stage bit geometry, source-bound global template,
+independent audit, finite bill, combined certificate and documentation:
+Apache License 2.0, the repository LICENSE.
+
+Pinned dependency research/e8-bit is reproduced without modification from
+Dylan Crow (utcorvusvolat-dotcom), with Anthropic Claude assistance, PR #370:
+https://github.com/CrocSwap/integer-mult-bounds/pull/370
+commit b7fe9cdf2da009c947ff6b334c562bc190b30373.
+All LICENSE, NOTICE.md, NOTICE-PR352.md and NOTICE-PR363.md files are retained.
+The local E8 bit word and its producer are their contribution, not ours.
+
+Pinned dependency research/nine-stage-complex-e8 is the independently
+developed complex component from PR #377, commit
+d0a620fcc99ba012468d61d01f5bb14007076d50:
+https://github.com/CrocSwap/integer-mult-bounds/pull/377
+Its inherited sources, source notices and licenses remain unchanged.
+
+Jacob Sussman introduced the E8 family and complex unit. The preserved
+upstream notices credit source527/eumemic, PR234/hcg890, PR266, PR315,
+PR346/LJH-217, PR352/DaysSky, PR363/DaysSky, Chafik Boukhalfa,
+DreamingOfClouds, Evan McKinney and other original contributors.
+
+The portable bits/stdc++.h shim contains standard-library includes only;
+it changes neither inherited algorithms nor their verification checks.
diff --git a/research/split-centres-global/notices/PR426-SOURCE-PINS.json b/research/split-centres-global/notices/PR426-SOURCE-PINS.json
new file mode 100644
index 0000000000..24a25d4342
--- /dev/null
+++ b/research/split-centres-global/notices/PR426-SOURCE-PINS.json
@@ -0,0 +1,1116 @@
+{
+  "files": [
+    {
+      "commit": "b07cf2f3fdffcbccca86c88a0c33b32dfce4bfe9",
+      "path": "vendor/source376/two_alias.py",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "5046a050e168266aff6488d27ca6525469c844118fbaced9af2b3dde8e13065c",
+      "source_path": "research/e8-far-helper-composition/two_alias.py"
+    },
+    {
+      "commit": "b07cf2f3fdffcbccca86c88a0c33b32dfce4bfe9",
+      "path": "vendor/source376/candidate_from378.py",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "b97c57e03fb570caab63bd82bf00664b5abea7eda8db3adfed69fc20efd82fb6",
+      "source_path": "research/e8-far-helper-composition/candidate_from378.py"
+    },
+    {
+      "commit": "b07cf2f3fdffcbccca86c88a0c33b32dfce4bfe9",
+      "path": "vendor/source376/candidate_frames.py",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "2b8d10ff732e030eb643478b3da0a91753dc77314eeb882a51eafdb871d935e2",
+      "source_path": "research/e8-far-helper-composition/candidate_frames.py"
+    },
+    {
+      "commit": "b07cf2f3fdffcbccca86c88a0c33b32dfce4bfe9",
+      "path": "vendor/source376/transport.py",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "264f6fc385532a25ae7f99774c2cb33e6ff6943fdbca546cfa000fb9e551fafb",
+      "source_path": "research/e8-far-helper-composition/transport.py"
+    },
+    {
+      "commit": "b07cf2f3fdffcbccca86c88a0c33b32dfce4bfe9",
+      "path": "vendor/source376/LICENSE",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+      "source_path": "research/e8-far-helper-composition/LICENSE"
+    },
+    {
+      "commit": "b07cf2f3fdffcbccca86c88a0c33b32dfce4bfe9",
+      "path": "vendor/source376/NOTICE.md",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "604f9225eee50bc7bc5cb8bfd33c2598e700466278d03fa06cfbb74c2b8e0d8e",
+      "source_path": "research/e8-far-helper-composition/NOTICE.md"
+    },
+    {
+      "commit": "dcebad83e4d7e6a5643ba8edfb432b0ba0dd1826",
+      "path": "vendor/source395/construct.py",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "2b49d8b1f24f6e642d3cc81142a3ad8dfacead60280dc0df0a1326daa97acc0b",
+      "source_path": "research/e8-signed-prefix/construct.py"
+    },
+    {
+      "commit": "7844f72c6051a4408284c3092490687061675c1a",
+      "path": "vendor/source401/architecture/audit.py",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "c69bd2ac387a944ffa33bb9660f7ee407ca75648ec937217851780333df28f22",
+      "source_path": "research/e8-response-subspaces/architecture/audit.py"
+    },
+    {
+      "commit": "7844f72c6051a4408284c3092490687061675c1a",
+      "path": "vendor/source401/architecture/banks.py",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "7a8d81894dd7c35f05122bca19c5fc30f04ddf0dc4f2c8d73e334cdd3b64e396",
+      "source_path": "research/e8-response-subspaces/architecture/banks.py"
+    },
+    {
+      "commit": "7844f72c6051a4408284c3092490687061675c1a",
+      "path": "vendor/source401/architecture/bridge.py",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "92456fe1df26f51233fa5f8b96c1f8dd6118df3f3b385654c26de8c205db6bb0",
+      "source_path": "research/e8-response-subspaces/architecture/bridge.py"
+    },
+    {
+      "commit": "7844f72c6051a4408284c3092490687061675c1a",
+      "path": "vendor/source401/architecture/deps/json.hpp",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "aaf127c04cb31c406e5b04a63f1ae89369fccde6d8fa7cdda1ed4f32dfc5de63",
+      "source_path": "research/e8-response-subspaces/architecture/deps/json.hpp"
+    },
+    {
+      "commit": "7844f72c6051a4408284c3092490687061675c1a",
+      "path": "vendor/source401/architecture/inputs/BANK-PATTERNS.json",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "5d29feadc8f6b4d946cfdf26455e4211e1213616ae033625e924d1ad30d61bae",
+      "source_path": "research/e8-response-subspaces/architecture/inputs/BANK-PATTERNS.json"
+    },
+    {
+      "commit": "7844f72c6051a4408284c3092490687061675c1a",
+      "path": "vendor/source401/architecture/inputs/DATA-PHASES.json",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "sha256": "47225c2ce696432aa9df6f422ae784aaa91bef651757f4266d0ea4edbff74694",
+      "source_path": "research/e8-response-subspaces/architecture/inputs/DATA-PHASES.json"
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+    "manifest_sha256": "389ac12de894730bd534f9a00d604866dd400175e32bd1204920dd98eafb8888",
+    "package": "research/e8-coupled-bit-retiming",
+    "scope": "Complete frozen source tree is retained beside this extension, without modifying any original bytes."
+  }
+}
diff --git a/research/split-centres-global/notices/PR426.md b/research/split-centres-global/notices/PR426.md
new file mode 100644
index 0000000000..2a7a8c0c6b
--- /dev/null
+++ b/research/split-centres-global/notices/PR426.md
@@ -0,0 +1,53 @@
+# Sources and attribution
+
+This extension preserves the full frozen PR389 package at b3c45822ca847aec8c0c019bb04db30881fc2966.
+All notices and licenses in that package continue to apply, including Jacob
+Sussman's original gx/E8 construction and Dylan Crow's bit word.
+
+applecrusher PR376 supplies the two exact equal-helper aliases, frame repairs,
+two subsequent rank-six to rank-five moves, and deterministic transport.
+Dugongue PR390 supplies target-prefix difference restoration and its sufficient
+main-only Y-to-Y compiler extension. Rohan Arun PR395 supplies the signed
+extension; its original source file and exact function bytes are retained.
+The fixed signed selection here is reconstructed on the R779 word, rather than
+claiming another contributor's selected witness as new discovery.
+
+ai-nanachi, with substantial OpenAI Codex assistance, supplies two further
+two-donor clean substitutions, 55 clean-reset bit helper reuses, 54 subsequent
+bit frame moves, changed complete supplier replays and exact composition.
+The first contribution's frame search and exact record are preserved separately.
+The headline gain comes from the changed complex supplier. The bit gain is
+reported separately because it does not change the binding complex ceiling.
+No worldwide priority or global optimality is claimed.
+
+Source byte identities and original commit paths are in SOURCE-PINS.json.
+New contributions are Apache-2.0; original source-specific notices and licenses
+are retained in the frozen parent and vendor directories.
+
+Dugongue [PR401](https://github.com/CrocSwap/integer-mult-bounds/pull/401)
+at 7844f72c6051a4408284c3092490687061675c1a supplies arbitrary entrance
+subspaces, exact even/degenerate two-sided normalization, mixed banks and
+independent readback. Dugongue
+[PR404](https://github.com/CrocSwap/integer-mult-bounds/pull/404)
+at 12f488264cdd74a3b60d0fb534f4955792384f5c supplies the expanded shared-donor
+selection and sufficient nested-donor construction. Our private nested-flag
+experiments ran independently around this public update; no priority over
+PR404 is claimed. applecrusher's PR376 at
+7aa9d9f0247bb60c0519704bbca18990011e2a37 supplies the additional rank-eight
+to rank-seven frame change, frozen through PR404's composition source.
+Our contribution is the explicitly mapped R779 composition, all-pair fresh
+phase replay, full changed supplier/bit checks, and independent clean-reset
+bit mechanism. PR404's incompatible overlapping target recovery is excluded.
+No source-specific numerical gains are added to the headline.
+
+Chafik Boukhalfa, with Anthropic Claude assistance, supplies the checker-clean
+re-pivoting from [PR412](https://github.com/CrocSwap/integer-mult-bounds/pull/412)
+at 616d9d678c00d79693b869934464003ba5b8d1b1. The four ordered groups originate
+in Rohan Arun's [PR409](https://github.com/CrocSwap/integer-mult-bounds/pull/409);
+the eight enlargements originate in eumemic's
+[PR410](https://github.com/CrocSwap/integer-mult-bounds/pull/410).
+Exact selected source bytes, commit paths and licenses are retained through
+the frozen PR412 composition in vendor/source412. This submission maps these
+relations onto R779, checks both unchanged original checker families,
+recomputes every chronological omission, and freshly admits every phase pair.
+No independently reported numerical savings are added together.
diff --git a/research/split-centres-global/notices/SUSSMAN-NOTICE b/research/split-centres-global/notices/SUSSMAN-NOTICE
new file mode 100644
index 0000000000..63aa295646
--- /dev/null
+++ b/research/split-centres-global/notices/SUSSMAN-NOTICE
@@ -0,0 +1,290 @@
+Walsh-Hadamard power saving (wht-power-saving-lean)
+Copyright 2026 Jacob Sussman
+
+Repository: https://github.com/jacobalansussman/wht-power-saving-lean
+
+This repository is not a project of OpenAI. OpenAI did not write, review or
+endorse it. The package name "OAI" and the namespace "OAI.PowerSaving" are
+those of openai/math and are kept only because the new files extend that
+development.
+
+This repository is not a project of CrocSwap/integer-mult-bounds either. Its
+authors did not write, review or endorse it. Section 6 says what is taken
+from their repository.
+
+This repository contains files from, and files derived from, the repository
+"openai/math" (https://github.com/openai/math), family 130, "Exact Fourier
+transforms below n log n", at commit fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.
+That repository is published under the Apache License, Version 2.0. A copy of
+the licence is in the file LICENSE. The upstream repository has no NOTICE file
+and its licence text names no copyright holder; the files are attributed here
+to the authors of openai/math (OpenAI).
+
+1. Unmodified upstream files.
+   The 89 files under OAI/Computability/ are byte-for-byte copies of the files
+   with the same paths under lean/ in openai/math at the commit above. They
+   have not been changed. Modified copies of some of them are under
+   Work/Fourier/ and are listed in section 7.
+   One more file of openai/math is here unchanged, outside the Lean build:
+   third-party/openai-math/lean/ComparatorChallenges/UniformFourier.lean is a
+   byte-for-byte copy of lean/ComparatorChallenges/UniformFourier.lean at the
+   commit above (the statement of OpenAI's Fourier challenge). It is included
+   so that the modified copy named in section 2 can be compared with it.
+
+2. Files that contain upstream text.
+   - Work/CarrierCheck/ChallengeB2Ke16x.lean,
+     Work/CarrierCheck/ChallengeB2Ke16xR.lean,
+     Work/GCert/Data/ChallengeB2Gp193x.lean and the text template
+     tools/gen/templates/ChallengeB2L16x.lean.txt each contain, as their
+     lines 22-270, lines 9-257 of
+     lean/ComparatorChallenges/UniformFourier.lean of openai/math (the RAM cost
+     model), unchanged. Everything else in these files was written for this
+     repository.
+   - Work/Fourier/UniformFourierChallenge.lean is a modified copy of
+     lean/ComparatorChallenges/UniformFourier.lean of openai/math (the
+     statement of OpenAI's Fourier challenge, 336 lines). Changes: a comment
+     was added at the top; the exponent 1 - 1/(10^(13:ℕ)) was replaced by
+     1 - 7474546/(10^(10:ℕ)); seven names received the suffix "Z"
+     (decimalExponent, decimalTime, TimeBounds, DFTGoal, ConvGoal,
+     transform_main, convolution_main). Everything else in the file is the
+     upstream text, unchanged. See section 7.
+   - Work/Scratch/Engine.lean and Work/Block/Engine.lean contain copies of
+     proofs of openai/math, changed for this repository: sections 1, 2 and 5
+     of Work/Scratch/Engine.lean are upstream proofs with the batch layout
+     renamed, and both files contain a copy of the private upstream theorem
+     "hills_project" (lean/OAI/Computability/FourierTransform/
+     TensorProgram.lean) with its envelope generalised. The comments in the
+     two files mark these places.
+   - lakefile.lean is adapted from lean/lakefile.lean of openai/math: the same
+     package name, toolchain, package option and Mathlib pin; every other
+     dependency was removed and the libraries of this repository were added.
+     lean-toolchain is a byte-for-byte copy of lean/lean-toolchain.
+     lake-manifest.json lists Mathlib and its dependencies at the revisions of
+     lean/lake-manifest.json.
+   - RELATED-WORK.md reproduces the BibTeX entries of two manuscripts of
+     openai/math.
+
+3. New files that build on upstream proofs.
+   The other files under WHTCheck/ and Work/ were written for this
+   repository. They import the upstream files, and several of them generalise
+   or adapt proofs of upstream files (for example Work/Block/Recursion.lean,
+   which says so in its header). They are changes and additions made for this
+   repository and are not part of openai/math.
+
+4. How the new files were made.
+   Jacob Sussman made the new files on 2026-10-08 and 2026-10-09 by directing
+   a team of AI agents (Claude). The agents wrote the new Lean files, the
+   certificate data and the generator scripts. See README.md, section 4.
+
+5. Ideas taken from other public work.
+   The network of the first result uses ideas published by others, among them
+   the helper circuit "NStar3" (Swapnil-jain/integer-mult-kappa, which credits
+   CrocSwap pull request #36 and Paureel for parts of it), its transfer to
+   family 130 (shea256/fourier-transform-below-nlogn), and "carrier links" and
+   "whole-residual batching" (pull requests to CrocSwap/integer-mult-bounds).
+   No file of Swapnil-jain/integer-mult-kappa or of
+   shea256/fourier-transform-below-nlogn is included here. One comment in
+   Work/Scratch/Engine.lean quotes three counts reported in
+   Swapnil-jain/integer-mult-kappa and names that source. The general frame
+   lemma that Work/GFrame proves is stated in
+   notes/general-clifford-frames.tex of CrocSwap/integer-mult-bounds; its Lean
+   proof was written for this repository. The credits, with links, are in
+   RELATED-WORK.md.
+
+6. Data derived from CrocSwap/integer-mult-bounds (second result).
+   The helper circuit of the second result is the paired-cube circuit of the
+   repository "CrocSwap/integer-mult-bounds"
+   (https://github.com/CrocSwap/integer-mult-bounds), in the state of its pull
+   request #193. It is the design of that community: icekylinx (pull requests
+   #144 and #184), eumemic (#168, and #117 behind its modules), ikeboy /
+   Avi Eisenberg (#191 and #193), with an664 (#128) credited there for the
+   workspace-sharing principle. That repository is published under the Apache
+   License, Version 2.0 (the same licence text as the file LICENSE). Its
+   NOTICE file begins "A sharper exponent for integer multiplication /
+   Copyright 2026 Douglas Colkitt" and says that the community release "is
+   not solely Douglas Colkitt's work". A complete copy of that NOTICE file, as
+   it is at the head of pull request #193, is in
+   third-party/CrocSwap-integer-mult-bounds/NOTICE.
+
+   The data were taken from these files of that repository. They were loaded
+   as data by programs written for this repository; no program of that
+   repository was run, and none is included here.
+   - at the head of pull request #168 (eumemic),
+     4a3c769e5c5430e7114c4d3e099ff34664677f17:
+       references/paired-cube/sources/local_L1.json
+       references/paired-cube/sources/tmod_TE_TD_TB3_1_1_4_full_6.0617964e-4.json
+       references/paired-cube/sources/pmod_J0_full_6.0666810e-4.json
+       references/paired-cube/sources/qmod_climb3u_best.json
+       references/paired-cube/selected-module/matching-arcs.json
+       references/paired-cube/physical/frames.json
+   - at the head of pull request #193 (ikeboy),
+     187e1010ac8b259af8e9b5166f68b64bc27b4b47:
+       research/source-assisted-v4/data/physical-pairs.json
+
+   Files of this repository that contain data derived from them:
+   tools/certificate/gcert1-p11-pr193.json.gz and the Lean data modules
+   generated from it, Work/GCert/Data/Gen/P193*.lean and the files they import
+   from Work/GCert/Data/Gen/P193/; its block counts are also in the generated
+   modules Work/GCert/Data/P193Price.lean, RateB2Gp193.lean, RateB2Gp193x.lean
+   and InstB2Gp193.lean.
+   Changes made: the circuit was rebuilt from those data as one explicit,
+   renumbered list of additions with a table of frames, in the certificate
+   format "gcert/1" of this repository; its 1,980 in-place steps were written
+   as pairs of additions with rescaled coefficients; the Lean data modules
+   were generated from that list. No file of that repository is included
+   unchanged, except the copy of its NOTICE file named above.
+
+   Notices of that NOTICE file that pertain to these data, quoted:
+
+     Paired-cube and shared-core extension, 9 October 2026
+     Copyright 2026 icekylinx
+
+     Source-assisted common-frame extension (2026-10-09)
+     Copyright 2026 icekylinx. Apache-2.0.
+     Substantial dependency: eumemic PR168,
+     fd25adb7fbaa12ee761d02c733c54d1d2a7687ee
+
+   The full text of both notices, and the notices of the work they build on,
+   are in the copy named above. The credits, with links and with the words of
+   pull request #193 about its own sources, are in README.md ("Whose circuit
+   this is") and in RELATED-WORK.md, section 1.
+
+7. Modified copies of upstream files (third result).
+   The files listed below are copies of files of openai/math at the commit
+   above, changed for this repository. Each begins with a comment that names
+   the upstream file it is derived from and states what was changed. The
+   upstream originals under lean/OAI/Computability/ are in this repository
+   as well, unchanged (section 1), and the copies import them. The upstream
+   challenge file lean/ComparatorChallenges/UniformFourier.lean is in this
+   repository in both forms: unchanged under third-party/openai-math/
+   (section 1) and modified (section 2).
+
+   - Work/Fourier/ArbitraryLength.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/ArbitraryLength.lean (224
+     lines; 159 of them unchanged in the copy). Changes: identifiers renamed
+     on 64 lines (18 names: 15 with the suffix Z, 3 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/Asymptotics.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/Asymptotics.lean (187 lines;
+     112 of them unchanged in the copy). Changes: identifiers renamed on 74
+     lines (32 names: 26 with the suffix Z, 6 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+   - Work/Fourier/Axioms.lean: written for this repository (not a copy of an
+     upstream file).
+   - Work/Fourier/ConvolutionProgram.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/ConvolutionProgram.lean (100
+     lines; 77 of them unchanged in the copy). Changes: identifiers renamed
+     on 22 lines (10 names: 9 with the suffix Z, 1 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/Goal.lean: written for this repository; contains lines of
+     upstream files: of its 7 code lines, 6 are lines of
+     lean/OAI/Computability/FourierTransform/Goal.lean (original lines 35,
+     75-77, 79, 81): unchanged: its lines 25; with identifiers renamed: its
+     lines 21, 24, 26, 28, 30.
+   - Work/Fourier/Main.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/Main.lean (151 lines; 90 of
+     them unchanged in the copy). Changes: identifiers renamed on 59 lines
+     (40 names: 35 with the suffix Z, 5 with Z inserted); 1 import line
+     replaced by 2; 24 comment lines added; other code lines changed: 1 of
+     the original, 1 of the copy (copy line 59).
+   - Work/Fourier/Seam.lean: written for this repository; contains lines of
+     upstream files: of its 122 code lines, 15 are lines of
+     lean/OAI/Computability/FourierTransform/TensorProgram.lean (original
+     lines 36-37, 95-96): unchanged: its lines 93-94, 113-114, 141-142,
+     163-164, 185-187, 194-196; with identifiers renamed: its lines 184; 3
+     are lines of lean/OAI/Computability/FourierTransform/TensorSaving.lean
+     (original lines 83-84, 114): with identifiers renamed: its lines 45-46,
+     59; 1 is a line of lean/OAI/Computability/FourierTransform/Main.lean
+     (original line 60): with identifiers renamed: its lines 213.
+   - Work/Fourier/SectorAlgorithm.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/SectorAlgorithm.lean (224
+     lines; 162 of them unchanged in the copy). Changes: identifiers renamed
+     on 61 lines (17 names: 13 with the suffix Z, 4 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/SynchronizedAlgorithm.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/SynchronizedAlgorithm.lean (126
+     lines; 94 of them unchanged in the copy). Changes: identifiers renamed
+     on 31 lines (12 names: 10 with the suffix Z, 1 with Z inserted, 1
+     other), the other being "canopy" to "Grove.canopy" (5 lines); 1 import
+     line replaced by 1; 16 comment lines added; no other change to the
+     code.
+   - Work/Fourier/TransformProgram.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/TransformProgram.lean (146
+     lines; 94 of them unchanged in the copy). Changes: identifiers renamed
+     on 51 lines (21 names: 19 with the suffix Z, 2 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/UniformBounds.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/UniformBounds.lean (183 lines;
+     115 of them unchanged in the copy). Changes: identifiers renamed on 67
+     lines (29 names: 25 with the suffix Z, 4 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+   - Work/Fourier/UniformFourierChallenge.lean: modified copy of
+     lean/ComparatorChallenges/UniformFourier.lean (336 lines; 328 of them
+     unchanged in the copy). Changes: identifiers renamed on 7 lines (7
+     names: 7 with the suffix Z); 12 comment lines added; other code lines
+     changed: 1 of the original, 1 of the copy (copy line 281).
+   - Work/Fourier/WorkingCompiler.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingCompiler.lean (153
+     lines; 104 of them unchanged in the copy). Changes: identifiers renamed
+     on 48 lines (14 names: 14 with the suffix Z); 1 import line replaced by
+     1; 15 comment lines added; no other change to the code.
+   - Work/Fourier/WorkingPreparation.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingPreparation.lean (212
+     lines; 156 of them unchanged in the copy). Changes: identifiers renamed
+     on 55 lines (30 names: 28 with the suffix Z, 2 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/WorkingTransform.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingTransform.lean (119
+     lines; 91 of them unchanged in the copy). Changes: identifiers renamed
+     on 27 lines (9 names: 8 with the suffix Z, 1 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+
+   Changes made to the eleven copied proof files: every declaration received
+   the letter "Z" in its name (as a suffix of its own name, or of the name
+   of the declaration it belongs to), so that it does not collide with the
+   upstream declaration of the same name; the upstream exponent "alpha"
+   (1 - 2/10^11) and the bound "hills" defined from it were replaced by
+   "alphaZ" (1 - 7474547/10^10) and "hillsZ", which are defined in
+   Work/Fourier/Seam.lean, and the single use of the upstream theorem
+   "hills_program" by "hillsZ_program"; the five definitions of the upstream
+   statement that contain its exponent (decimalExponent, decimalTime,
+   TimeBounds, DFTGoal, ConvGoal) were replaced by the versions of
+   Work/Fourier/Goal.lean, whose exponent is 1 - 7474546/(10^(10:ℕ));
+   the import lines point to the copies; a header comment was added.
+      Two further changes: in the copy of Main.lean the same constant stands
+   once as the literal 2/10^11 and was replaced there too, and the two
+   final theorems of that copy received a documentation comment; in the
+   copy of SynchronizedAlgorithm.lean the name "canopy" was written out as
+   "Grove.canopy" in 5 places, because the short name is shadowed in the
+   larger environment of the copy. The script also renamed three names
+   inside upstream comments; the comments are otherwise the upstream ones
+   and describe the upstream network.
+   The proofs are those of openai/math. The copies were made by the script
+   tools/fourier/mkchain.py of this repository.
+
+   Work/Fourier/Goal.lean contains copies of those five definitions of
+   lean/OAI/Computability/FourierTransform/Goal.lean, with the exponent
+   replaced and the suffix "Z" on the five names.
+
+   Work/Fourier/Seam.lean was written for this repository. It repeats the
+   statement of the upstream theorem "hills_program" (TensorProgram.lean) and
+   the definition of "hills" (TensorSaving.lean) with the two names replaced;
+   its header says so.
+
+   The work of others that the third result follows (danadran01, shea256,
+   eumemic) is credited in README.md ("Whose reduction this is") and in
+   RELATED-WORK.md, section 1. No file of their repositories is included
+   here.
+
+Not included in this repository and fetched by the build: Mathlib
+(https://github.com/leanprover-community/mathlib4, Apache License 2.0) and its
+dependencies. The comparator (https://github.com/leanprover/comparator) is a
+separate tool and is not included.
diff --git a/research/split-centres-global/proofs/INHERITED-COMPLEX-GEOMETRY.txt b/research/split-centres-global/proofs/INHERITED-COMPLEX-GEOMETRY.txt
new file mode 100644
index 0000000000..c4150cb693
--- /dev/null
+++ b/research/split-centres-global/proofs/INHERITED-COMPLEX-GEOMETRY.txt
@@ -0,0 +1,161 @@
+Independent compressed nine-stage complex component
+
+Claim and retained assumptions
+
+The fixed E8 local invocation has h=9, v=120, R=783 and copied rank loss
+cst=72. The construction below has m=73, live stock 14727 per complete
+orthogonal cover, and paid profile
+  1:157599, 2:43488, 3:37296, 4:10080, 5:15480, 6:23832,
+  7:3096, 8:7488, 9:576, 16:3840, 32:3840, 48:3840.
+It is a conditional complex component, not an integer multiplication bound.
+The local E8 invocation theorem, general Clifford rank-zero compiler,
+complete-stream tape primitives, common fine-grid precision, and retained
+analytic recurrence interfaces are assumptions retained from the fixed local
+source package. The new finite construction and its charges are supplied
+here. No new Lean kernel proof is asserted. Final bit-side admission and
+outer assembly are separate obligations.
+
+Exact operator convention
+
+For q in F2^m, let X_q be translation by q and
+  C_q = ((1+i) I + (1-i) X_q)/2.
+Then C_q^2=X_q and C_q fixes the uniform vector. Write C_all for the product
+over the coordinate vectors. An invertible binary matrix G acts by the
+literal address permutation P_G. All products of C_q are commuting exact
+Gaussian-dyadic operators. Their multiplier on Fourier character y is
+i^(sum epsilon_q * parity(q.y)). Modulo 4, parity expands as its linear sum
+minus twice its pair sum, so this multiplier is an exact Z4 quadratic form.
+Equality of these forms proves equality including the scalar phase.
+
+For arbitrary local subspaces U, including degenerate ones, use the
+deterministic canonical representative from clifford_exact.py. A basis G
+whose first columns span U gives K_G = D_Q P_G, with
+Q=I+G^(-T)G^(-1), and T_U=K_G C_[dim U] K_G^(-1).
+Its preimage Lagrangian is {(u,u+w): u in U, w in U^perp}. Thus a nested
+transition has Fourier rank equal to the dimension difference. The supplied
+compiler produces two explicit monomial operators around one rank-r C child.
+Its equality is checked both as a signed Pauli tableau and on a nonzero
+exact Gaussian state vector, which fixes the otherwise missing global phase.
+All 946 local frames, all 3120 used directed transitions, and all 240 old/new
+source/target adapters are checked. No rank-only replacement is made.
+
+Compressed window and data routes
+
+Use V=F2^9 direct_sum (F2^8)^8 with the ordinary dot product. Let E_s be the
+first s exterior eight-dimensional blocks, for 0<=s<=8. The exact window
+representative of local U is T_U tensor C_Es. A nested transition cancels
+the common exterior tensor factor exactly and keeps its original rank.
+Conjugating the whole window by any cover permutation preserves this fact.
+The old/new endpoint adapters are the checked local adapters tensored with
+identity, followed by the declared address conjugation. This proves the
+window lift directly; a divisibility assumption m=multiple_of_h is not used.
+
+Every supplied port q has odd weight and a zero coordinate. The explicit
+orthogonal matrix U_q in data_phases.py maps e0 to q: swap e0 with a zero
+coordinate e_j when necessary, then use the even-vector transvection
+x -> x + ((q+e_j).x)(q+e_j). Its remaining columns are an orthonormal basis
+of q^perp. For s>0, rho_s,q exchanges that complement in the local block
+with exterior block s and fixes q and all other exterior coordinates.
+It is a symmetric orthogonal involution. The stage data owners are
+g=d*rho_s,q, with rho_0,q=I, so the right factors are bijections of O(73,2).
+
+Use canonical data levels X_s=C_[0,9+8s), Y_s=X_s C_q^(-1), and initially
+X_(-1)=C_q, Y_(-1)=I. The routed stage starts at level s-1 and ends at level s.
+Their binary preimages agree with the window endpoints. Exact phase
+polynomials determine the translation that reconciles each endpoint, and
+the template applies that translation. There are 3840 nonzero such
+translations across the 120 port types and nine stages, before replica
+multiplicity. These operators are not silently identified from equal
+binary matrices.
+
+Four-pair scalar chain and idle children
+
+Starting with F_0 (Y_0 += X_0), for j=0,1,2,3 apply B_j (X_j -= Y_j),
+then for j<3 apply X_j += X_(j+1), Y_(j+1) -= Y_j, apply F_j, and undo
+that bridge. The last pair has B_3,F_3 without a following bridge.
+Afterwards apply, in descending j=2,1,0, X_(j+1)+=X_j and Y_j-=Y_(j+1).
+Finally exchange each pair by newX=oldY, newY=-oldX. The complete signed
+integer scalar matrix is the identity; omission of every bridge fails.
+
+Before a bridge, advance the idle pair to the active pair's level. The
+two advances for the newly used pairs have ranks (16,8), (32,8), (48,8).
+The final advances have ranks 48,32,16,0. Each rank occurs on both members
+of the pair, each of 120 ports, and each of eight replicas. A nested idle
+transition is factored in the explicit orthonormal basis U_q direct_sum I.
+Its exact Z4 phase is reconciled by the stored translation after that child.
+
+The final Y endpoint is C_all C_q^(-1). A source began at C_q, so its
+unadjusted exchange route would be C_all C_q^(-2)=C_all X_q. Applying the
+literal X_q to each final Y before the signed exchange removes this factor.
+The corresponding 120 omission controls fail. This correction is charged.
+
+Banks and arbitrary correlated dirt
+
+There are eight replicas of each of the four data pairs, hence 7680 data
+families. Each stage has 783 independent bank families. Number a local
+helper occurrence by z=783*replica+helper. It uses bank floor(z/8) and slot
+z mod 8, with its nine-dimensional residual assigned to coordinates
+[9*slot,9*slot+9). A paid coordinate C child at coordinate 72 completes
+each bank. All eight whole residuals and this padding fill dimension 73.
+Thus there are 9*783=7047 bank families and live stock 14727.
+
+Let Pi_slot swap the first nine coordinates with the assigned block. The
+local invocation at class d uses the bank class g=d*Pi_slot^(-1). Its
+residual at that owner is P_g C_block P_g^(-1). Right multiplication is a
+bijection. Local helpers sharing one bank have distinct slots, hence
+different right factors and different actual bank classes for every d.
+All data and private families are disjoint from banks. The checker verifies
+these injections for all 72 invocation/replica templates and 56376 residual
+assignments. A complete cover sweep for one replica finishes before the
+next begins. The local dirty invocation is block diagonal on helpers at
+its endpoint and permits arbitrary correlated helper values. Therefore
+overlap between different invocations does not impose a cleanliness or
+independence assumption. At each bank class, the eight residuals and the
+padding are coordinate factors in one common conjugated basis, and their
+exact product is P_g C_all P_g^(-1).
+
+One more exact correction is essential. Orthogonality alone does not imply
+that P_g commutes with C_all as an exact operator. In fact
+  P_g C_all P_g^(-1) = C_all X_delta(g),
+  delta(g)_i = (weight(row_i(g))-1)/2 mod 2.
+The quadratic terms cancel by row orthogonality and the remaining even
+linear terms give the displayed translation. Both sides fix the uniform
+vector, fixing the global scalar. Apply X_delta(g) to EVERY final live
+family in cover class g, after the bank padding and signed data exchange.
+The template includes and charges all 14727 corrections per cover. This
+identity is also checked on every orthogonal matrix in dimensions 1..5.
+
+Finite work and recurrence charges
+
+The source emitter is regenerated and revalidated in both orientations.
+It accounts for 1242936 local events over 72 invocations, with all copied
+center and dirty-tableau lifetimes intact. Forward and backward scalar
+words freshly replay all 1023 independent dirty live columns. Only the
+private work starts at zero. Work comprises 783 tableau streams, nine
+reserved center streams (eight used), and one coefficient stream. Each
+invocation completes and erases its private work before the next. Physical
+stock is therefore 15520 per cover; scalar-only work is excluded from the
+recursion-volume denominator.
+
+GLOBAL-REVIEW.json records the complete recomputed finite overcharge, with
+64*(73+1)^3 compiler groups per rank-zero adapter, source-counted scalar
+primitives, and overcharges for all data routes, bank selectors, phases,
+padding, bridges, exchanges and cover corrections. The O(73,2) order is
+2^(36^2)*product(2^(2i)-1,i=1..36); its bit length is 2628. The recomputed
+router fits 2^30000, the literal charge fits 2^100000, and the precision
+guard fits C0=2^210000. No even-dimensional orthogonal-order formula is used.
+
+Largest child 48 does not satisfy one-layer halving. Instead
+73^2=5329>2*48^2=4608, so two nested children have width strictly below
+half the parent, including floors. The general depth is bounded by
+2*ceil(log2 e), with direct small leaves. For B=s+E the completed-child
+semantic induction has 2B(73-48)-s-E=49B>0. The resulting conservative
+complete-row coefficient is 2*2642+9909+252=15445<20161, retaining the
+external bit/base-row allowance as an explicit interface assumption.
+The inherited bad-branch envelope is priced conservatively as before.
+
+Two independent rational moment engines admit
+b=999240641319551/10^18 and exclude b+10^-18 for the source-bound profile.
+The rank mass is 1072575, and 73*14727-1072575=2496=8*(8*120-9*72).
+This complex component exceeds 1/1024 but does not improve the current
+bit bottleneck. No improved final kappa or completed PR milestone follows.
diff --git a/research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt b/research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt
new file mode 100644
index 0000000000..31efe31268
--- /dev/null
+++ b/research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt
@@ -0,0 +1,191 @@
+Compressed nine-stage E8 bit supplier and combined conditional bound
+
+Claim and source assumptions
+
+The conditional combined value is
+  kappa = 998243154231047 / 10^18 = 0.000998243154231047 > 1/1024.
+It is approximately 2^-9.9683211064. This is a conditional finite construction
+in the inherited supplier framework, not a Lean proof of integer multiplication.
+No priority claim is made.
+
+The E8 bit word, its 120 root lines, all 865 helpers, and nine retained totals
+are taken without modification from Dylan Crow's PR #370, commit
+b7fe9cdf2da009c947ff6b334c562bc190b30373. Its raw word has SHA256
+1fb726ea3818fe0837cceb0dd22a71a0814f064e5e781628104610d6468e0e55.
+The original verification is rerun, including regeneration, independent
+1105-column F2 checking, official record legality/formal columns, all-frame
+Gram and prime witnesses, negative controls, and the original regression set.
+Its five-stage c is 904072820242522/10^18, insufficient by itself for -10.
+
+The complex supplier is the separately reconstructed compressed nine-stage
+component from PR #377, with b = 999240641319551/10^18. Its complete source,
+notices, exact Clifford and Z4 phase checks, global template and finite bill
+remain included. In particular, its terminal X_q and every-live-family
+X_delta(g) corrections are retained; equality of binary matrices is not
+substituted for equality of complex operators.
+
+The inherited all-size weighted bit compiler, tape/prime/precision and
+analytic transfer interfaces remain conditional. PR #370's explicit admission
+of nine copied totals at h=8 is retained. The complex local E8 theorem,
+Clifford compiler, common fine-grid, restored-row and analytic interfaces
+remain conditional exactly as stated in the companion component. The new
+window, banking and two-level finite charges are described below rather
+than inferred from a rank histogram.
+
+Exact bit operators and compressed ambient space
+
+Over an admitted odd address field, the E8 form is G=I_8/2. For a nondegenerate
+subspace U, write P_U for its orthogonal projector. On the doubled address
+space define
+  D_U = [[I-P_U, P_U], [P_U, I-P_U]].
+Thus D_U is an exact involution. If U is contained in V then
+D_V D_U = D_(V intersect U-perp), with rank dim(V)-dim(U). Also
+  D_I D_P = D_(I-P).
+These are literal address matrices. Unlike the complex C operators, they
+have no hidden scalar phase. The auditor reconstructs all 944 rational
+projectors and checks all 3289 used nested pairs, in both orientations.
+
+Set V_global = Q^8 direct_sum (Q^7)^8, m=64, with form I_64/2.
+Let E_s be the first s exterior 7-blocks, s=0,...,8. At stage s lift the
+entire local word by replacing U with U direct_sum E_s. Both ends of every
+local transition contain the same E_s, so it cancels exactly; the child
+projector and rank are unchanged. This holds for copied totals as well:
+the temporary transforms between the source and scatter frames, whose
+common E_s cancels. COPY/ERASE windows remain sequential and immutable.
+No assumption that m is a multiple of 9h is used.
+
+Port routes
+
+The reference root is q*=2e_0. For every root q, the checked product g_q
+of at most two E8 root reflections sends q* to plus or minus q. Let A_q be
+its last seven columns. They form an orthonormal basis of q-perp:
+  A_q^T A_q=I_7, A_q A_q^T=I_8-P_q, P_q=q q^T/4.
+For stage s>0 use, on the local block and exterior block s,
+  rho_(s,q) = [[P_q, A_q], [A_q^T, 0]],
+and fix all other coordinates. For s=0 use the identity. These matrices
+are orthogonal involutions. Conjugating the lifted endpoints gives
+  (P_q,E_s) -> (I_8,E_(s-1)),    (I_8,E_s) -> (I_8,E_s),
+  (0,E_s)   -> (I_8-P_q,E_(s-1)),
+  (I_8-P_q,E_s) -> (I_8-P_q,E_s).
+These equalities are checked as exact rational matrices for every port.
+Each nontrivial route has a replayed elementary factorization, at most
+77 factors, with denominators 1,2,4. Omitting a factor fails. Thus all
+routes remain defined at every odd address prime; there is no new odd
+exceptional prime. The existing local prime witnesses are rerun separately.
+
+Nine-stage scalar recipe and deferred endpoint completion
+
+Use four data pairs (X_j,Y_j). Start with F_0: Y_0 += X_0. For j=0,...,3,
+apply B_j: X_j -= Y_j; when j<3 insert the two shears
+  X_j += X_(j+1), Y_(j+1) -= Y_j;
+apply F_j; then undo those two shears. After all stages, for j=2,1,0 apply
+  X_(j+1) += X_j, Y_j -= Y_(j+1).
+Finally replace (X_j,Y_j) by (Y_j,-X_j). The complete signed integer
+8-by-8 scalar matrix is the identity. Omitting any of the eighteen
+individual bridge shears changes it.
+
+Each B_j is the reflected inverse of the actual local record stream:
+reverse the order, negate ADD coefficients, replace U by U-perp, and
+turn ERASE into a fresh COPY from the original unchanged center. No erase
+is inverted. PR #370 stores zero in the ERASE rank field; the reflected
+COPY rank is freshly derived from its two frames, giving rank 8. Both
+oriented streams replay all 1105 independent input columns and close work.
+
+Before each bridge the newly used pair is advanced to the active level.
+The two idle increments are (14,7), (28,7), (42,7). Endpoint completion of
+the earlier pairs is deferred to the final stage, with ranks 42,28,14,0.
+Every increment acts on both members of every port pair and every replica.
+The schedule checker requires equal complete frames at every bridge.
+The signed terminal exchange completes the data transform using the exact
+identity D_I D_P=D_(I-P). Scalar replay on 8745 independent columns includes
+960 data and 7785 separate stage-helper inputs. All are restored after
+the exchange; the reflected copy work closes to zero.
+
+Whole-block banks and arbitrary correlated dirt
+
+Use eight replicas. There are 4*2*120*8=7680 data families. For each stage,
+number a local helper occurrence by z=865*replica+helper, and assign it
+to bank floor(z/8), slot z mod 8. There are 865 banks at each of nine
+stages. Each slot is one whole 8-dimensional coordinate block in Q^64.
+The eight slots are mutually perpendicular and fill the ambient space;
+no padding child is needed. Live recursion stock is 7680+9*865=15465.
+Nine private center slots are reserved and excluded from recursion volume,
+so charged physical stock is 15474. Only one such slot is used at a time.
+
+Let Pi_slot exchange the first eight coordinates with its bank block.
+For a cover class d in O(I_64/2,F_q), the helper owner is the bank class
+g=d Pi_slot^-1, and a data owner is d rho_(s,q). Right multiplication is a
+bijection of the finite cover. Within every local invocation, helpers in
+the same bank have different slots, hence different actual cover classes;
+all data and work families are disjoint from banks. All 62280 assignments
+are checked, and every physical bank receives each of its eight slots once.
+
+The local all-column theorem permits arbitrary helper inputs, including
+correlations created by earlier invocations. After its endpoint each helper
+has only the known residual D_H. The common E_s cancels, so no cleanliness
+assumption is imposed by a previous bank action. Complete cover sweeps run
+sequentially. At a fixed bank owner g the residuals are D on the eight
+orthogonal coordinate blocks conjugated by g. They commute and multiply
+to D_I. Since diag(g,g) commutes with the literal head/tail exchange D_I,
+no complex-style cover phase correction is needed on the bit side.
+This is a symbolic finite cover proof, not an enumeration of O(64,F_q).
+
+Actual emitted ledger
+
+The source-bound template emits 72 local invocations and 1355328 events.
+All local COPY/ERASE and helper lifetimes are rechecked. Its paid profile is
+  1:149472, 2:67824, 3:32256, 4:30096, 5:22176, 6:144,
+  7:5760, 8:1296, 14:3840, 28:3840, 42:3840.
+There are 320544 paid children, rank mass 987264 and deficit
+  64*15465-987264 = 2496 = 8*(8*120-9*72).
+The independent auditor recomputes the profile from the emitted template
+and rejects missing idle/bridge/exchange/invocation events, bank-slot aliasing,
+understated stock, a missing local MOVE and a wrong reflected COPY charge.
+
+Finite cost, precision allowance and two-level halving
+
+The largest child is 42, so one-level halving is false. Two levels suffice:
+  2*42^2=3528 < 64^2=4096.
+Floors only reduce descendant widths. The exact one-level moment, including
+the inherited 10^-16 bad-branch envelope, is strictly below one; composing
+two levels squares this contraction. The finite composite may be used with
+the inherited halving-based compiler and direct small leaves.
+
+The old five-stage 104-bit payload-prefix guard is not reused. Fresh local
+cancellation-free row bounds are 742 forward and 6308 reverse. For five
+forward calls, four reflected calls and eighteen bridge shears, the bound
+  2^18 * 742^5 * 6308^4
+has 117 bits. We explicitly charge 192 bits per nine-stage block. The actual
+source operations, copy episodes, 77-factor routes, selectors, all owner
+adapters and this prefix bound enter certify.py's finite coefficient. It
+has 117 bits; the charged two-level coefficient has 269 bits and is bounded
+by 2^512. This deliberately increases the finite cutoff, rather than passing
+the old 104-bit assertion. The exact three bootstrap cutoff inequalities
+are checked using the changed coefficient.
+
+For cover/routing enumeration use the inherited coarse q^(m^2+1) bound;
+two levels and the retained additive row charges give
+  2*(64^2+1)+9909+252 = 18355 < 20161.
+The explicit rational bit routes introduce only powers of two. The new
+finite constants fit well below the companion bridge's 2^30000 reserve,
+and the common external C0=2^210000 and row allowance 20161 are retained.
+As for the companion complex component, the general compiler/common-grid
+interfaces are assumptions; no new Lean formalization is asserted.
+
+Exact price and combined assembly
+
+Two independent rational moment engines, both with the 10^-16 envelope,
+admit c=1057833103534317/10^18 and reject c+10^-18. The complex supplier
+therefore binds. With eta=10^-12 and beta=10^-9 choose
+  s=999240640320309/10^18 < (1-beta)*b < c.
+Start a0=384599/10^10 and apply a_(j+1)=(1-s)s+s*a_j three times. The retained
+outer assembly at (a3,b) admits kappa=998243154231047/10^18. All 47 strict
+constraints are positive; the next 10^-18 kappa grid point is rejected.
+The strict excess over 1/1024 is 21680654231047/10^18. Final kappa is about
+24.0286% above frozen #361, within the explicitly retained assumptions.
+
+Attribution: Dylan Crow / Anthropic Claude for PR #370's new local bit word;
+Jacob Sussman for E8 and the complex unit; the inherited source527, PR234,
+PR266, PR315, PR346, PR352 and PR363 contributors as listed in the preserved
+notices; Zhihao Chen with OpenAI Codex assistance for this compressed bit
+composition, its independent audit, and the combined nine-stage package.
diff --git a/research/split-centres-global/proofs/PR425-COMPLEX.txt b/research/split-centres-global/proofs/PR425-COMPLEX.txt
new file mode 100644
index 0000000000..41061757ce
--- /dev/null
+++ b/research/split-centres-global/proofs/PR425-COMPLEX.txt
@@ -0,0 +1,211 @@
+Hamming packets with mutable source and target bases
+Conditional finite extension of the complex E8 supplier
+
+1. What is new
+
+The old r783 word keeps source values fixed and does not read target registers.
+Those are sufficient restrictions on a scalar word, not necessary conditions
+for a common-frame linear program. The new word uses 680 helper registers:
+
+  * source registers themselves carry one branch of a simultaneous signed
+    packet computation;
+  * retired packet registers retain a full source basis, from which the eight
+    central coordinate sums are reconstructed;
+  * 56 pairs of targets carry a first two-output butterfly, with its input
+    basis explicitly compensated at frame zero and in the center decoder;
+  * an exact inverse on all source/helper registers is executed at their
+    common full frame after the last recursive climb.
+
+No recursive work is deleted from the ledger. A helper is counted for its
+entire lifetime, including unused final climbs. All 120 sources and targets
+retain their original line/full and zero/hyperplane endpoint ranks.
+
+The new local histogram is
+  {1:2248, 2:896, 3:168, 4:336, 5:392, 8:24, 9:8}.
+Its rank mass is 9*680 + 240*8 + 72 = 8112. There are 4072 local children.
+There are more local children than in the old r783 word, but substantially
+less helper rank mass; the complete moment, not a count proxy, decides gain.
+
+2. Exact Hamming geometry and signed packet algebra
+
+Use the pinned PR370 table of 120 E8 root lines in Construction-A coordinates:
+eight coordinate lines 2e_i and 112 sign lines on the 14 weight-four Hamming
+blocks. For integer representatives r_s, let G_st = r_s dot r_t / 2.
+The matrix C_st = 1 + G_st mod 2 has binary rank nine. The construction gives
+an explicit orthonormal realization p_s in F_2^9 with
+
+  p_s dot p_t = C_st,  and  p_s dot p_s = 1.
+
+Consequently the nonzero off-diagonal entries of G/2 occur only where a source
+line lies in the target hyperplane. The rank-eight central factorization is
+
+  (G/2)_ts = sum_i r_ti r_si / 4.
+
+For a source Hamming block d, a coordinate pair {i,j} in d, and epsilon=+-1,
+define the signed face packet
+
+  P(d,ij,epsilon) = sum_{s in d, r_si*r_sj=epsilon} r_si x_s.
+
+Each packet has four terms and its binary port span has rank three. Split
+the eight sign lines of a block into its two parity tetrads. Each tetrad pair
+occurs in two face packets with independent signed coefficient rows. The two
+rows are formed simultaneously by two determinant-one shears, rather than
+forming independent one-output sums. The packet factory uses its eight source
+registers and sixteen additional helpers. Its twelve retired registers can
+be oriented to retain a full rank-eight source basis. Exact elimination on
+that stock produces four coordinate sums without allocating more helpers.
+
+This comparison of an individual factory is not a claim that the whole old
+supplier used 48 helpers per block. The relevant complete counts are 783 and
+680, both charged with their full actual profiles.
+
+For two target/source blocks whose intersection is {i,j}, the contribution
+to target t is -r_ti P(d,ij,r_ti*r_tj)/2. The remaining within-block and
+coordinate-line contributions are explicit four-output signed transforms.
+Every one of the 14400 rational decoder entries is rechecked. Adding the
+eight coordinate centers leaves precisely the identity matrix on sources.
+
+The binary transvection x -> x+(x dot 43)*43 is orthogonal because 43 has
+even weight. It maps the constructed port set exactly to the old fixed E8
+port set. All frames and register indices are transported, so the old nine-
+window data routes and their global phase correction apply to exactly the
+same ordered ports, without introducing an unproved new covering geometry.
+
+3. General scalar-interface lemma
+
+Write z=(x,s) for the source and arbitrary dirty helper streams, and y for
+the targets. Permit scalar additions and invertible dyadic scalings between
+registers at the same current label. No target may feed a z register. The
+raw A/center/B word therefore has block form
+
+  z' = U z,
+  y' = V y + J x + K s,
+
+where U and V are invertible, and the retained-center operations are included
+in J and K. The actual word has J=I after its adjusted center scatter. The
+checks compute every coefficient over Q, rather than inferring it from a
+desired sparsity pattern.
+
+At frame zero, before entry adapters or recursive children, execute
+
+  y <- V^{-1} y - V^{-1} K s.
+
+Both y and s have label zero there. The code emits the literal inverse of
+the 56 disjoint two-output target bases and a direct, charged dyadic old-
+response matrix with 13216 additions. There is no uncharged oracle for K.
+It is computed from the explicit scalar word and serialized. All coefficient
+work is cleared immediately after its use.
+
+After the last main gate, finish every z register's climb to the full frame,
+then execute U^{-1} by reversing and inverting the non-target gates. These
+gates are legal at one common full frame, including helper-to-source gates.
+The result is exactly
+
+  (x,s,y) -> (x,s,y+x).
+
+The second orientation is the inverse transpose: negate and transpose every
+addition and invert every scale in the SAME event order. Each retained
+center is implemented by the transposed gather/child/scatter stream. The
+result is (x,s,y) -> (x-y,s,y). Both orientations are replayed on all 920
+independent live columns, including all 680 arbitrary helper columns.
+Missing compensation, missing output preconditioning, missing cleanup and
+the wrong inverse-transpose order are rejected.
+
+Why the scalar argument lifts to exact complex labels: for each binary
+subspace F use the exact canonical representative L(F). A climb from A to B
+acts as L(B)L(A)^{-1}. If two registers share F, a scalar addition commutes
+with their common L(F), as does a scalar scaling. Induction through the
+actual stream therefore gives the block-diagonal conjugation of its scalar
+matrix by the current labels. Center copies explicitly move from full to
+zero, or zero to full in the other orientation. The preconditioner uses
+only label-zero registers, and the z cleanup uses only full-label registers.
+Thus the proof never moves a scalar operation across unequal labels or
+identifies two frames merely because their ranks agree.
+
+Every used canonical frame, nested transition, center direction and endpoint
+adapter is independently lowered by the exact Gaussian Clifford compiler.
+Equalities include global phase. The old restricted gx gate-shape checker
+is not used to admit this new interface; the stronger explicit matrix and
+common-frame checks replace its source-immutability/target-read restrictions.
+This is a written finite algebraic extension, not a new Lean theorem.
+
+4. Complete programs and work lifetimes
+
+Each orientation emits 27537 events, including startup, entry/exit adapters,
+all recursive climbs, eight sequential center children, scalar operations
+and final cleanup. Temporary centers are initialized, used and erased one
+at a time. No center or coefficient work stream survives a live child.
+
+All added coefficients are dyadic. To apply a/2^j, compute |a| times the
+source by binary Horner additions on a cleared private stream, halve j
+times, accumulate with its sign, and clear the private stream. In-place
+scales are signed powers of two. Every such primitive is charged. This
+introduces no new denominator prime. Independent replay bounds the actual
+cancellation-free prefix norms, including coefficient work; a 192-bit local
+payload allowance is retained conservatively.
+
+5. Nine-window composition and finite bill
+
+Use the previously verified m=73 compressed nine-window geometry, four data
+pairs, eight replicas, and the original signed bridges, idle children,
+terminal exchange, terminal translations and full-cover phase correction.
+The source scalar identity and its negative inverse-transpose are exactly
+the two local interfaces consumed by that unchanged geometry.
+
+There are 680 whole-block banks per stage, each containing eight rank-nine
+helper blocks plus one paid rank-one padding child. The live width is
+
+  W = 240*4*8 + 9*680 = 13800.
+
+The conservative physical width is W+680+9+2=14491. The old-response matrix
+uses no persistent tableau, but the old-size reserve is still charged.
+The emitted owner table has 48960 distinct stage/replica/helper assignments.
+The new global profile is
+
+  {1:167976, 2:64512, 3:12096, 4:24192, 5:28224,
+   8:7488, 9:576, 16:3840, 32:3840, 48:3840}.
+
+Its rank deficit is 73*13800 - sum(r*H_r) = 2496. The maximum child is 48,
+and 73^2 > 2*48^2 supplies the same charged two-level halving argument.
+
+The finite bill is recomputed from the new scalar programs, bank owners,
+work stock and adapter counts. It is not asserted unchanged. The local
+primitive bound fits 2^48; the tape router fits 2^30000; the literal envelope
+fits 2^100000; the precision envelope fits 2^210000. The physical row
+coefficient is 15445, below the explicitly inherited external allowance
+20161. Full-cover corrections apply to all 13800 live families.
+
+6. Conditional numerical conclusion and retained assumptions
+
+Two independent rational moment engines, with the inherited 10^-16 bad-
+branch envelope, accept
+
+  b = 1049104978040580 / 10^18 = 0.001049104978040580
+
+and reject the next 10^-18 grid point. With the unchanged bit parameter
+c=0.001057833103534317, three bootstrap steps and all 47 strict outer
+conditions give the prospective finite-assembly value
+
+  kappa = 1048005508028206 / 10^18
+        = 0.001048005508028206, approximately 2^-9.898137985359.
+
+The finite statement is conditional on the same all-size weighted compiler,
+common fine grid, restored-row/base allowance, tape/prime/precision and
+analytic transfer interfaces as the retained nine-stage result. The new
+scalar-interface lemma above and its serialized program are additional
+reviewable material, not an appeal to gx accepting a program outside its
+grammar. No unconditional integer-multiplication theorem is claimed.
+The result is approximately +4.97% over the locally verified retimed bound,
+and remains well short of 2^-9. A fresh extracted-package replay is required
+by this research workflow before publication or final promotion.
+
+Attribution
+
+The root table and the motivation to use Hamming coordinates come from the
+already pinned PR370 bit package (Dylan Crow, with Anthropic Claude assistance).
+The E8 complex label family, original scalar word and gx interfaces are due
+to Jacob Sussman. The retained complex admission, pricing and global analytic
+interfaces are credited in the original package notices and PROOF.txt.
+The mutable-basis packet word, transported geometry, expanded scalar proof,
+new finite program and the present checks were developed in this local
+research session by Zhihao Chen with OpenAI Codex assistance.
diff --git a/research/split-centres-global/proofs/PR426.md b/research/split-centres-global/proofs/PR426.md
new file mode 100644
index 0000000000..e589cfbf50
--- /dev/null
+++ b/research/split-centres-global/proofs/PR426.md
@@ -0,0 +1,108 @@
+# Construction, dependencies and sufficient argument
+
+The fixed complex witness starts from Chafik Boukhalfa's far-retimed E8 word
+and applecrusher's two equal-helper substitutions and two frame refinements.
+It additionally replaces helper 556 by -2 times helpers 354 and 461, then
+helper 576 by -2 times helpers 402 and 478 after compaction. Exact clean
+linear forms agree at every substituted read. The backward upper-frame and
+forward nested repairs retain copied-total pins and final address caps.
+R is 779. The actual new dirty response and cleanup are regenerated: equality
+on clean values alone is not the arbitrary-dirt proof.
+
+The signed prefix restoration is the PR390/395 bracket. For 25 disjoint
+targets, subtract lambda times the donor before the prefix, emit the exact
+source/write-version/frame difference, and restore lambda times that donor
+at the common recovery frame. Lambda is +1 or -1. The full rational main
+operator and all retained totals agree with the explicit same-width R779
+baseline on all 1,019 independent columns. Source/helper subwords agree
+exactly, so the new baseline's explicit dirty response and cleanup remain
+valid. The changed compiler permits a main Y read only when its target is Y;
+helper-to-X remains forbidden. Both signed orientations and private lifetimes
+are freshly admitted, with all actual Clifford phases and physical incidences.
+
+The shared entrance construction follows PR401/404. Each pivot p satisfies
+K_p + sum_d a_pd K_d = 0 in the explicit baseline response. Four re-pivots
+from PR412 replace the basis of these same relations, including the
+half-valued donor that otherwise fails the original sixths-denominator
+condition. PR410 enlarges eight entrance subspaces. Removed original helpers
+556 and 577 are mapped explicitly onto our R779 word. The shared layer has
+192 pivots, rank mass 350, and 496 literal unit shears. Its pivots and donors
+are disjoint, so this layer alone has (S-I)^2=0.
+
+PR409's four ordered groups, with PR412's two additional re-pivots, prepend
+55 more shears and admit ten further pivots. The combined word has 202
+gauges of rank mass 360 and 551 entrance shears. The complete chronological
+prefix need not have (S-I)^2=0. We check its actual product M S, all retained
+totals, and that every gauged target-response column is zero. Every entrance
+source is read before any earlier entrance operation writes it.
+
+Every one of the 551 omission controls is recomputed from the suffix
+response. If shear t += q s is removed, its suffix response is multiplied
+by -q times the original independent s column: earlier operations leave s
+unchanged by the read-before-write condition. A nonzero response is required
+for each omission; the entire changed scalar schedule is also replayed for
+sampled omissions. No global donor/pivot disjointness is assumed here. Both
+unchanged original gx.check1 and gxcore.mirror checkers pass, including the
+native denominator conditions. Every actual nested transition is charged.
+
+PR376's additional target201/helper491 frame change from rank eight to seven
+is checked for full operator equality and nested paid paths before gauging.
+PR404's target125/124 overlapping-prefix recovery requires a different
+chronological input and is not imported. Its numerical gain is not included.
+
+Each entrance chart is normalized explicitly. Even and degenerate E_p use
+the full two-sided exact Clifford factorization of F T_E inverse. The right
+inverse adapter precedes the entire old-response invocation; the left inverse
+adapter follows all main and helper cleanup. Both orientations retain every
+unitary address operator in the inverse-adjoint chronology. Rank-zero adapters
+are costed. All old/new/reflected Gaussian child pairs are recomputed,
+including Pauli signs and global phase. Newly assigned mixed-bank coordinate
+permutations and inverse owners are emitted and independently decoded.
+Padding is an exact fixed integer witness, not a claim of solver optimality.
+
+The new bit operation differs from the preceding all-dirt reset: a retired
+helper only needs its clean X-content zeroed before a new logical helper is
+placed in the same slot. An arbitrary residual helper value is allowed. The
+new helper basis determines a newly computed initial D compensation. C is
+the reversed helper subword, restoring every physical helper, including its
+original independent dirt. Each reset is checked exactly before reuse; the
+retired slot has no later original use, the new helper has no earlier use,
+and copied totals are protected. The combined word is checked over every
+independent binary column. It uses 55 fewer helpers (822 to 767). The initial 27 reuses and 26 frame
+moves are followed by two fixed rounds of 14 reuses and 14 frame moves.
+The later resets use exact two- or three-parent clean forms; every parent
+and all rebuilt dirty compensation are charged and independently checked. Integer signed-prefix bounds, lifting,
+copied-center controls, routes and whole-bank packing are recomputed rather
+than inferred from the clean calculation.
+
+The complex assembly has dimension 73, 14,286 live and
+15,075 physical families, 734 banks per stage, deficit 2,496,
+maximum child rank 48 and halving degree two. The bit assembly has dimension
+56, 10,409 live families, deficit 1,512 and halving degree two. Actual row
+coefficients fit the common 20,161 reserve. Both finite invoices and both
+exact rational moment engines retain the positive 10^-16 fallback. Adjacent
+10^-24 complex coarse grid points are rejected; the unchanged bit coarse
+grid remains 10^-18. The exact outer assembly uses positive eta=10^-24,
+beta=10^-18, eight finite bootstrap continuations and a 10^-27 grid; it
+checks 47 strict constraints and invalid eta/beta/adjacent-point controls.
+
+The complex coefficient is 254951444354246755323/250000000000000000000000. The bit coefficient is
+104575879789097/100000000000000000. The resulting conditional kappa is 40750673324589432209923/40000000000000000000000000.
+Using the preceding unchanged bit supplier with this same complex coefficient
+gives 203354853562950029967497/200000000000000000000000000, where the bit side
+binds. The new clean-reuse bit supplier removes that bottleneck. Its exact
+additional kappa contribution is recorded as the difference from this fair
+control; the combined witness is limited by the new complex coefficient.
+
+All original files are manifest-bound and immutable. A copied supplier tree
+is changed only through asserted literal edits. DERIVATION.json records every
+old/new digest, changed pin and textual difference. Both full predecessor
+supplier suites run before the changed admission. Expected records are checked
+after recomputation, rather than used to obtain a PASS.
+
+This is a sufficient finite conditional construction. The inherited all-size
+recursive suppliers, canonical/rank-zero compiler, compressed Clifford windows,
+dirty banking/cover, routing, restored-row, fixed tape, common-grid, Gaussian
+precision/recovery and analytic interfaces remain assumptions. No new full
+Lean theorem or unconditional integer-multiplication exponent is asserted.
+The target kappa > 0.002 is not attained by this witness.
diff --git a/research/split-centres-global/vendor/clifford_exact.py b/research/split-centres-global/vendor/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/split-centres-global/vendor/clifford_exact.py
@@ -0,0 +1,149 @@
+"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals.
+Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d.
+The tableau is supplemented by a literal circuit, so global phases are kept.
+"""
+from dataclasses import dataclass
+
+def parity(x):return x.bit_count()&1
+def rank(rows):
+ p={}
+ for x in rows:
+  while x:
+   b=x.bit_length()-1
+   if b not in p:p[b]=x;break
+   x^=p[b]
+ return len(p)
+def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<<j for j in range(n)) for i in range(n))
+def mv(rows,x):return sum(parity(r&x)<<i for i,r in enumerate(rows))
+def inv(rows,n):
+ a=[r|(1<<(n+i)) for i,r in enumerate(rows)]
+ for j in range(n):
+  k=next(i for i in range(j,n) if a[i]>>j&1);a[j],a[k]=a[k],a[j]
+  for i in range(n):
+   if i!=j and a[i]>>j&1:a[i]^=a[j]
+ assert [r&((1<<n)-1) for r in a]==[1<<i for i in range(n)]
+ return tuple(r>>n for r in a)
+def basis_extend(cols,n):
+ out=[]
+ for x in list(cols)+[1<<i for i in range(n)]:
+  if rank(out+[x])>len(out):out.append(x)
+ assert len(out)==n
+ return tuple(out)
+def nullspace(rows,n):
+ a=list(rows);p=[];k=0
+ for j in range(n):
+  t=next((i for i in range(k,len(a)) if a[i]>>j&1),None)
+  if t is None:continue
+  a[t],a[k]=a[k],a[t]
+  for i in range(len(a)):
+   if i!=k and a[i]>>j&1:a[i]^=a[k]
+  p.append(j);k+=1
+ return tuple((1<<j)|sum(((a[i]>>j)&1)<<v for i,v in enumerate(p)) for j in range(n) if j not in p)
+def pmul(a,b):
+ x,z,p=a;y,w,q=b
+ return x^y,z^w,(p+q+2*parity(z&y))%4
+def identity(n):return tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,0) for i in range(n)])
+def apply(T,p):
+ n=len(T)//2;x,z,ph=p;out=(0,0,ph)
+ for i in range(n):
+  if x>>i&1:out=pmul(out,T[i])
+ for i in range(n):
+  if z>>i&1:out=pmul(out,T[n+i])
+ return out
+def compose(A,B):return tuple(apply(A,p) for p in B)
+def inverse(T):
+ n=len(T)//2;cols=[x|(z<<n) for x,z,p in T];rows=transpose(cols,2*n);cols_inv=transpose(inv(rows,2*n),2*n);out=[]
+ for j,w in enumerate(cols_inv):
+  x=w&((1<<n)-1);z=w>>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4))
+ return tuple(out)
+def qvalue(Q,alpha,x,n):
+ return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4
+def mul_i(a,p):
+ x,y=a;p%=4
+ return [(x,y),(-y,x),(-x,-y),(y,-x)][p]
+@dataclass
+class Op:
+ n:int
+ tab:tuple
+ circuit:list
+ def then(self,b):
+  assert self.n==b.n
+  return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit)
+ def adjoint(self):
+  circ=[]
+  for e in reversed(self.circuit):
+   if e[0]=='P':circ.append(('P',inv(e[1],self.n)))
+   elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2])))
+   elif e[0]=='C':circ.append(('C',e[1],-e[2]))
+   elif e[0]=='phase':circ.append(('phase',(-e[1])%4))
+   else:circ.append(e)
+  return Op(self.n,inverse(self.tab),circ)
+ def zero_state(self,basis=0):
+  N=1<<self.n;vec=[(0,0)]*N;vec[basis]=(1,0);den=0
+  for e in self.circuit:
+   if e[0]=='P':
+    v=[(0,0)]*N
+    for x,a in enumerate(vec):v[mv(e[1],x)]=a
+    vec=v
+   elif e[0]=='X':vec=[vec[x^e[1]] for x in range(N)]
+   elif e[0]=='D':vec=[mul_i(a,qvalue(e[1],e[2],x,self.n)) for x,a in enumerate(vec)]
+   elif e[0]=='phase':vec=[mul_i(a,e[1]) for a in vec]
+   elif e[0]=='C':
+    q,sgn=e[1:];v=[]
+    for x,(a,b) in enumerate(vec):
+     c,d=vec[x^q]
+     # C=(1+i)I/2+(1-i)X/2; inverse conjugates both coefficients.
+     v.append((a-sgn*b+c+sgn*d,b+sgn*a+d-sgn*c))
+    vec=v;den+=1
+   else:raise AssertionError(e)
+   while den and all((a&1)==(b&1)==0 for a,b in vec):vec=[(a//2,b//2) for a,b in vec];den-=1
+  return vec,den
+def ident(n):return Op(n,identity(n),[])
+def perm(n,G):
+ cols=transpose(G,n);gi=inv(G,n)
+ return Op(n,tuple([(a,0,0) for a in cols]+[(0,a,0) for a in gi]),[('P',tuple(G))])
+def diag(n,Q,alpha=None):
+ Q=tuple(Q);assert transpose(Q,n)==Q
+ alpha=tuple(alpha) if alpha is not None else tuple((Q[i]>>i)&1 for i in range(n))
+ assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n))
+ return Op(n,tuple([(1<<i,Q[i],alpha[i]) for i in range(n)]+[(0,1<<i,0) for i in range(n)]),[('D',Q,alpha)])
+def cgate(n,q,sgn=1):
+ return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(q if q>>i&1 else 0,1<<i,(3*sgn)%4 if q>>i&1 else 0) for i in range(n)]),[('C',q,sgn)])
+def xgate(n,b):return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,2*((b>>i)&1)) for i in range(n)]),[('X',b)])
+def fourier(n,axes=None):
+ out=ident(n)
+ for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<<i))
+ return out
+def hadamard(n,axes):
+ axes=list(axes);Q=tuple(1<<i if i in axes else 0 for i in range(n));S=diag(n,Q)
+ return S.then(fourier(n,axes)).then(S)
+def canonical_frame(n,U):
+ r=len(U)
+ if r==0:return ident(n)
+ if r==n:return fourier(n)
+ G=transpose(basis_extend(U,n),n);gi=inv(G,n);Q=tuple((1<<i)^sum(parity(gi_i&gi_j)<<j for j,gi_j in enumerate(transpose(gi,n))) for i,gi_i in enumerate(transpose(gi,n)))
+ K=perm(n,G).then(diag(n,Q))
+ return K.adjoint().then(fourier(n,range(r))).then(K)
+def monomial(op):
+ n=op.n;T=op.tab;assert all(x==0 and p%2==0 for x,z,p in T[n:]);G=transpose([x for x,z,p in T[:n]],n);b=mv(G,sum((p//2)<<i for i,(x,z,p) in enumerate(T[n:])))
+ gt=transpose(G,n);cols=[mv(gt,z) for x,z,p in T[:n]];Q=transpose(cols,n);alpha=[(p-2*parity(b&z))%4 for x,z,p in T[:n]]
+ out=diag(n,Q,alpha).then(perm(n,G)).then(xgate(n,b));assert out.tab==T
+ vec,den=op.zero_state();assert den==0 and all(a==(0,0) for i,a in enumerate(vec) if i!=b);phase=[(1,0),(0,1),(-1,0),(0,-1)].index(vec[b]);out=out.then(Op(n,identity(n),[('phase',phase)]));assert out.zero_state()==op.zero_state()
+ return out,dict(matrix_rows=G,offset=b,quadratic_rows=Q,linear_Z4=alpha,phase=phase)
+def lower_child(op):
+ n=op.n;Bcols=[x for x,z,p in op.tab[n:]];r=rank(Bcols)
+ if not r:
+  mon,rec=monomial(op);return dict(rank=0,left=rec,right=None),mon
+ G=transpose(basis_extend(Bcols,n),n);A=inv(G,n);PA=perm(n,A);part=op.then(PA);Bcols=[x for x,z,p in part.tab[n:]];Dcols=[z for x,z,p in part.tab[n:]]
+ picks=[];selected=[]
+ for j,x in enumerate(Bcols):
+  if rank(selected+[x])>len(selected):picks.append(j);selected.append(x)
+ assert len(picks)==r and all(x>>r==0 for x in Bcols)
+ Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<<r)-1) for j in picks],r)
+ Qsmall=tuple(sum(parity(row&col)<<j for j,col in enumerate(transpose(Bi,r))) for row in Dr);Q=Qsmall+(0,)*(n-r);DQ=diag(n,Q)
+ V=part.then(DQ).then(hadamard(n,range(r)));assert all(x==0 for x,z,p in V.tab[n:]);Vmon,Vrec=monomial(V)
+ S=diag(n,tuple(1<<i if i<r else 0 for i in range(n)))
+ left=S.adjoint().then(DQ.adjoint()).then(PA.adjoint());right=Vmon.then(S.adjoint()).then(xgate(n,(1<<r)-1))
+ lmon,lrec=monomial(left);rmon,rrec=monomial(right);compiled=rmon.then(fourier(n,range(r))).then(lmon)
+ assert compiled.tab==op.tab and compiled.zero_state()==op.zero_state()
+ return dict(rank=r,left=lrec,right=rrec),compiled
diff --git a/research/split-centres-global/vendor/engines/base_two_moment.py b/research/split-centres-global/vendor/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/split-centres-global/vendor/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/split-centres-global/vendor/engines/moment.py b/research/split-centres-global/vendor/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/split-centres-global/vendor/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/split-centres-global/vendor/engines/outer.py b/research/split-centres-global/vendor/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/split-centres-global/vendor/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/split-centres-global/vendor/export_records.py b/research/split-centres-global/vendor/export_records.py
new file mode 100644
index 0000000000..3632d37048
--- /dev/null
+++ b/research/split-centres-global/vendor/export_records.py
@@ -0,0 +1,72 @@
+"""Export a bitE8/1 word to the PR249 record format read by PR #266's official cohort checkers and PR #315's engines.
+usage: python3 export_records.py word.json[.gz] OUTDIR   ->  OUTDIR/{249-records.bin,249-states.json,frames.json}
+Records are int32 six-tuples: MOVE(0,role,old,new,rank,0), ADD(1,dst,src,1,frame,phase), COPY(2,centre,temp,frame,ZERO,rank),
+ERASE(3,centre,temp,frame,ZERO,0).  A multi-source gate becomes one ADD per source, preceded by the MOVEs of every
+register of the gate to the gate frame.  Frames: integer basis rows B (label vectors of the frame's root lines in the
+word's coordinates, a rational basis) and integer annihilator rows A (standard dot product), as PR #266 expects.
+Dylan Crow, with Anthropic Claude assistance; Apache-2.0."""
+import sys, json, gzip, struct, os
+from fractions import Fraction as Fr
+from math import gcd
+def load(p):
+    with (gzip.open(p,'rt') if p.endswith('.gz') else open(p)) as f: return json.load(f)
+c=load(sys.argv[1]); out=sys.argv[2]; os.makedirs(out,exist_ok=True)
+v,R,h=c['v'],c['R'],c['h']; n=2*v+R; lines=c['lines']
+def basis(idx):
+    rows=[]; piv=[]; B=[]
+    for i in idx:
+        x=[Fr(a) for a in lines[i]]
+        for p,r in zip(piv,rows):
+            if x[p]: f=x[p]/r[p]; x=[a-f*b for a,b in zip(x,r)]
+        nz=[k for k in range(h) if x[k]]
+        if nz: rows.append(x); piv.append(nz[0]); B.append(list(lines[i]))
+    return B,rows,piv
+def annihilator(rows,piv):
+    # rows in echelon (pivot columns piv); free columns give the null space of the row space under the dot product
+    # reduce to RREF
+    R_=[r[:] for r in rows]
+    for i,(p,r) in enumerate(zip(piv,R_)):
+        R_[i]=[a/r[p] for a in r]
+    for i,p in enumerate(piv):
+        for j in range(len(R_)):
+            if j!=i and R_[j][p]: f=R_[j][p]; R_[j]=[a-f*b for a,b in zip(R_[j],R_[i])]
+    free=[k for k in range(h) if k not in piv]; A=[]
+    for f in free:
+        a=[Fr(0)]*h; a[f]=Fr(1)
+        for i,p in enumerate(piv): a[p]=-R_[i][f]
+        L=1
+        for x in a: L=L*x.denominator//gcd(L,x.denominator)
+        ai=[int(x*L) for x in a]; g=0
+        for x in ai: g=gcd(g,abs(x))
+        A.append([x//g for x in ai])
+    return A
+frames={}
+for k,idx in enumerate(c['frames']):
+    B,rows,piv=basis(idx); A=annihilator(rows,piv) if B else [[int(i==j) for j in range(h)] for i in range(h)]
+    assert all(sum(a*b for a,b in zip(x,y))==0 for x in A for y in B) and len(A)+len(B)==h
+    frames[str(k)]=dict(dim=len(B),B=B,A=A)
+dim=[frames[str(k)]['dim'] for k in range(len(c['frames']))]
+ZERO=[k for k in range(len(dim)) if dim[k]==0]; assert len(ZERO)==1; ZERO=ZERO[0]
+cur=list(c['start']); rec=[]
+def move(r,f):
+    if cur[r]!=f: rec.append((0,r,cur[r],f,dim[f]-dim[cur[r]],0)); cur[r]=f
+def run(gates,ph):
+    for f,d,srcs in gates:
+        for r in [d]+srcs: move(r,f)
+        for s in srcs: rec.append((1,d,s,1,f,ph))
+run(c['D'],1); run(c['A'],2)
+temp=n
+for k,q in enumerate(c['ret']):
+    fq=cur[q]; rec.append((2,q,temp,fq,ZERO,dim[fq]))
+    for t,row in enumerate(c['scatter']):
+        if k in row: rec.append((1,v+t,temp,1,ZERO,3))
+    rec.append((3,q,temp,fq,ZERO,0))
+run(c['B'],4); run(c['C'],5)
+for r in range(n): move(r,c['final'][r])
+with open(out+'/249-records.bin','wb') as f:
+    for e in rec: f.write(struct.pack('<6i',*e))
+st=dict(n=n,v=v,h=h,R=R,ZERO=ZERO,initial={str(r):c['start'][r] for r in range(n)},final={str(r):c['final'][r] for r in range(n)},
+        retained_totals=c['ret'],source_owned_roles=[],regs=[])
+json.dump(st,open(out+'/249-states.json','w'),sort_keys=True,separators=(',',':'))
+json.dump(dict(frames=frames),open(out+'/frames.json','w'),sort_keys=True,separators=(',',':'))
+print('exported',len(rec),'records,',len(frames),'frames, n',n,'ZERO',ZERO)
diff --git a/research/split-centres-global/vendor/hamming_packets.py b/research/split-centres-global/vendor/hamming_packets.py
new file mode 100644
index 0000000000..c129996656
--- /dev/null
+++ b/research/split-centres-global/vendor/hamming_packets.py
@@ -0,0 +1,253 @@
+"""A structural prototype: mutable source bases and simultaneous signed packets.
+
+Input geometry is the pinned PR370 Hamming E8 root table. The binary realization,
+packet construction, two-shear synthesis and arbitrary-dirt replay below are new
+local experiments. This does NOT produce a complete improved E8 supplier.
+"""
+import gzip
+import hashlib
+import itertools as it
+import json
+import random
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('work/complex-network/hamming');OUT.mkdir(parents=True,exist_ok=True)
+SRC=Path('work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz')
+word=json.load(gzip.open(SRC));roots=word['lines'];v=len(roots)
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in roots] for a in roots]
+C=[sum((1^(G[i][j]&1))<<j for j in range(v)) for i in range(v)]
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+
+def inside(a,b):return basis(a+b)==b
+
+indices=[]
+for i,row in enumerate(C):
+    if len(basis([C[j] for j in indices]+[row]))>len(indices):indices.append(i)
+assert len(indices)==9
+gram=[sum(((C[i]>>j)&1)<<k for k,j in enumerate(indices)) for i in indices]
+def ip(a,b):
+    return sum(((a>>i)&1)*((gram[i]&b).bit_count()&1) for i in range(9))&1
+orth=[]
+for step in range(9):
+    choices=[x for x in range(1,512) if ip(x,x) and all(not ip(x,y) for y in orth)]
+    chosen=next(x for x in choices if step==8 or any(y!=x and not ip(x,y) for y in choices))
+    orth.append(chosen)
+assert all(ip(x,y)==int(i==j) for i,x in enumerate(orth) for j,y in enumerate(orth))
+ports=[]
+for i in range(v):
+    row=sum(((C[i]>>j)&1)<<k for k,j in enumerate(indices))
+    ports.append(sum(((row&e).bit_count()&1)<<k for k,e in enumerate(orth)))
+assert len(set(ports))==v and all(p.bit_count()&1 for p in ports)
+assert all(((ports[i]&ports[j]).bit_count()&1)==((C[i]>>j)&1) for i in range(v) for j in range(v))
+
+blocks=defaultdict(list);frame_lines={}
+for i,r in enumerate(roots):
+    support=tuple(k for k,x in enumerate(r) if x)
+    if len(support)==4:blocks[support].append(i)
+    else:assert len(support)==1;frame_lines[support[0]]=i
+assert len(blocks)==14 and all(len(xs)==8 for xs in blocks.values())
+
+def sparse_add(rows,t,s,q):
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+
+def simulate(n,events):
+    rows=[{r:Q(1)} for r in range(n)]
+    for t,s,q in events:sparse_add(rows,t,s,q)
+    return rows
+
+def serialize(events):return [[t,s,q.numerator,q.denominator] for t,s,q in events]
+
+packet_table={};module_receipts=[];all_programs=[]
+for block,ids in sorted(blocks.items()):
+    ids=sorted(ids);pos={s:i for i,s in enumerate(ids)}
+    tetrads=[sorted(s for s in ids if sum(roots[s][k]<0 for k in block)%2==p) for p in (0,1)]
+    assert all(len(t)==4 for t in tetrads)
+    faces=[]
+    for i,j in it.combinations(block,2):
+        for epsilon in (-1,1):
+            support=[s for s in ids if roots[s][i]*roots[s][j]==epsilon]
+            content={s:Q(roots[s][i]) for s in support}
+            frame=basis([ports[s] for s in support]);assert len(frame)==3
+            key=(block,(i,j),epsilon);packet_table[key]=(content,frame)
+            faces.append((key,content,frame))
+    pair_uses=defaultdict(list)
+    for f,(_,content,frame) in enumerate(faces):
+        for tet in tetrads:
+            pair=tuple(s for s in tet if s in content)
+            assert len(pair)==2
+            pair_uses[pair].append(f)
+    assert len(pair_uses)==12 and all(len(fs)==2 for fs in pair_uses.values())
+    bysource=defaultdict(list)
+    for pair in sorted(pair_uses):
+        for s in pair:bysource[s].append(pair)
+    # One of the three pair branches is carried by x itself, two by helpers.
+    regs={};nextreg=8;events=[];event_frames=[];cur=[basis([ports[s]]) for s in ids]
+    start=list(cur);dead=[]
+    def add(t,s,q,F):
+        assert t!=s and inside(cur[t],F) and inside(cur[s],F)
+        cur[t]=cur[s]=F;events.append((t,s,Q(q)));event_frames.append(F)
+    for s in ids:
+        for j,pair in enumerate(sorted(bysource[s])):
+            if j==0:reg=pos[s]
+            else:
+                reg=nextreg;nextreg+=1;cur.append(());start.append(())
+                add(reg,pos[s],1,basis([ports[s]]))
+            regs[pair,s]=reg
+    assert nextreg==24
+    partial={}
+    for pair,fs in sorted(pair_uses.items()):
+        s,t=pair;a,b=regs[pair,s],regs[pair,t];f,g=fs
+        alpha,beta=faces[f][1][s],faces[f][1][t]
+        gamma,delta=faces[g][1][s],faces[g][1][t]
+        assert alpha*delta-beta*gamma in (-2,2)
+        F=basis([ports[s],ports[t]]);assert len(F)==2
+        add(a,b,beta/alpha,F)
+        k=gamma/(delta-gamma*beta/alpha)
+        add(b,a,k,F)
+        partial[f,pair]=(a,alpha)
+        partial[g,pair]=(b,delta-gamma*beta/alpha)
+    pre_packets=simulate(24,events)
+    def clean_rank(registers):
+        piv={}
+        for reg in registers:
+            row=[pre_packets[reg].get(i,Q(0)) for i in range(8)]
+            for j in sorted(piv):
+                q=row[j]
+                if q:row=[a-q*b for a,b in zip(row,piv[j])]
+            j=next((i for i,q in enumerate(row) if q),None)
+            if j is not None:
+                q=row[j];piv[j]=[a/q for a in row]
+        return len(piv)
+    choices=[[value for (ff,pair),value in partial.items() if ff==f] for f in range(12)]
+    rng=random.Random(38639);orientation=None
+    for trial in range(4096):
+        bits=rng.randrange(1<<12)
+        if clean_rank([pieces[1-((bits>>f)&1)][0] for f,pieces in enumerate(choices)])==8:
+            orientation=bits;break
+    assert orientation is not None
+    outputs=[]
+    for f,(key,content,F) in enumerate(faces):
+        pieces=[value for (ff,pair),value in partial.items() if ff==f]
+        assert len(pieces)==2
+        if orientation>>f&1:pieces.reverse()
+        (a,alpha),(b,beta)=pieces
+        add(a,b,beta/alpha,F)
+        outputs.append((a,alpha));dead.append(b)
+    assert len(set(r for r,a in outputs))==12 and len(set(dead))==12
+    assert not set(dead)&{r for r,a in outputs}
+    core=simulate(24,events)
+    for f,(reg,scale) in enumerate(outputs):
+        clean={ids[j]:scale*x for j,x in core[reg].items() if j<8 and x}
+        assert clean==faces[f][1]
+
+    # Probe complete borrowing: output each packet, cancel its old dirt at label
+    # zero, then undo every source/helper operation at the full frame.
+    # Actual supplier consumers and their remaining chronology are NOT inferred.
+    n=36;main=events.copy();dirt=[];chosen_targets=[]
+    for f,(reg,scale) in enumerate(outputs):
+        main.append((24+f,reg,scale))
+        for j,q in core[reg].items():
+            if j>=8:dirt.append((24+f,j,-scale*q))
+        valid=[t for t in range(v) if all((ports[t]&x).bit_count()%2==0 for x in faces[f][2])]
+        assert valid;chosen_targets.append(valid[0])
+    cleanup=[(t,s,-q) for t,s,q in reversed(events)]
+    actual=simulate(n,dirt+main+cleanup)
+    for r in range(24):assert actual[r]=={r:Q(1)}
+    for f in range(12):
+        expected={24+f:Q(1)}
+        expected.update({pos[s]:q for s,q in faces[f][1].items()})
+        assert actual[24+f]==expected
+    # A mutation of the compensator must corrupt at least one arbitrary dirt column.
+    wrong=simulate(n,main+cleanup)
+    assert any(wrong[r]!=actual[r] for r in range(24,36))
+    # Inverse-transpose: transpose and negate each elementary shear in the SAME
+    # event order. Reversing as well would generally compute the wrong map.
+    dual=simulate(n,[(s,t,-q) for t,s,q in dirt+main+cleanup])
+    for r in range(n):
+        expected={r:Q(1)}
+        if r<8:
+            expected.update({24+f:-content[ids[r]] for f,(_,content,F) in enumerate(faces) if ids[r] in content})
+        assert dual[r]==expected
+    receipt={'block':block,'source_lines':ids,'packets':12,'pair_butterflies':12,
+             'packet_additions':len(events),'live_source_registers_borrowed':8,
+             'helper_registers':16,'total_source_and_helper_registers':24,
+             'retired_register_clean_rank':8,
+             'independent_pair_branch_comparison_helpers':48,
+             'comparison_scope':'48 is a specified independent two-input-form implementation, not the helper count of the current r783 supplier.',
+             'frame_rank_counts':dict(Counter(map(len,event_frames))),
+             'all_dirty_columns_forward_and_inverse_transpose':n,
+             'compensator_omission_rejected':True,
+             'scope':'A 12-output packet factory and probe sinks. Not a complete 120-port supplier or global frame schedule.'}
+    module_receipts.append(receipt)
+    all_programs.append({'receipt':receipt,'start_frames':start,'events':serialize(events),
+                         'event_frames':event_frames,'outputs':[[r,str(q)] for r,q in outputs],
+                         'dead_registers':dead,
+                         'dirt':serialize(dirt),'cleanup':serialize(cleanup),
+                         'probe_target_ports':[ports[t] for t in chosen_targets]})
+
+# Reconstruct the entire signed E8 neighbour correction from the packet family.
+# This proves all 120 rational source columns of the abstract decomposition.
+decomposition=[]
+for target,r in enumerate(roots):
+    row=defaultdict(Q);terms=[];support=[i for i,x in enumerate(r) if x]
+    if len(support)==4:
+        c=tuple(support)
+        for d in blocks:
+            inter=tuple(sorted(set(c)&set(d)))
+            if len(inter)!=2:continue
+            i,j=inter;epsilon=r[i]*r[j];content,F=packet_table[d,inter,epsilon]
+            coefficient=-Q(r[i],2)
+            assert all((ports[target]&p).bit_count()%2==0 for p in F)
+            for s,a in content.items():row[s]+=coefficient*a
+            terms.append({'source_block':d,'pair':inter,'epsilon':epsilon,'coefficient':str(coefficient)})
+        for s in blocks[c]+list(frame_lines.values()):
+            if s!=target and G[target][s]:row[s]-=Q(G[target][s],2)
+    else:
+        i=support[0]
+        for d in blocks:
+            if i in d:
+                for s in blocks[d]:row[s]-=Q(roots[s][i],2)
+    expected={s:-Q(G[target][s],2) for s in range(v) if s!=target and G[target][s]}
+    assert {s:a for s,a in row.items() if a}==expected
+    # Eight coordinate centers recover the diagonal after side corrections.
+    for s in range(v):
+        center=sum(Q(r[i]*roots[s][i],4) for i in range(8))
+        assert center+row.get(s,Q(0))==int(s==target)
+    decomposition.append({'target':target,'cross_block_packets':terms,'side_support':len(expected)})
+
+program_path=OUT/'PACKET-PROGRAMS.json.gz'
+program_path.write_bytes(gzip.compress(json.dumps(all_programs,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+report={'status':'PASS_STRUCTURAL_PACKET_PROTOTYPE_NOT_A_NEW_SUPPLIER',
+        'source_sha256':hashlib.sha256(SRC.read_bytes()).hexdigest(),
+        'binary_address_dimension':9,'binary_gram_rank':len(indices),
+        'binary_ports':ports,'root_lines':roots,
+        'binary_gram_identity':'p_s dot p_t = 1 + (root_s dot root_t / 2) mod 2',
+        'modules':module_receipts,'signed_packets':len(packet_table),
+        'full_target_decomposition_columns':120,'full_target_decomposition_entries':120*120,
+        'program_sha256':hashlib.sha256(program_path.read_bytes()).hexdigest(),
+        'decomposition':decomposition,
+        'remaining':['Joint scheduling and charging of all packet fan-outs and target accumulations',
+                     'Forming all eight centers from the available mixed source basis without an uncharged restore',
+                     'Full 120-port arbitrary-dirt forward/backward program and restored work stocks',
+                     'Exact complex adapters and global phases; finite invoice; two independent prices and outer assembly'],
+        'no_new_coarse_b_or_kappa_claim':True}
+(OUT/'PROTOTYPE.json').write_text(json.dumps(report,indent=2)+'\n')
+print('PASS: 14 factories, 168 signed packets; each factory uses 8 source + 16 helper registers')
+print('PASS: exact dirty forward and inverse-transpose columns, omission controls, all 14400 decoder entries')
+print('NOT A SUPPLIER: global scheduling, mixed-basis centers, phase and full price remain open')
diff --git a/research/split-centres-global/verify.py b/research/split-centres-global/verify.py
new file mode 100644
index 0000000000..01d78bf0d1
--- /dev/null
+++ b/research/split-centres-global/verify.py
@@ -0,0 +1,51 @@
+"""Verify the selected two-supplier composition using Python's standard library."""
+import argparse,gzip,hashlib,json,os,shutil,subprocess,sys
+from pathlib import Path
+assert __debug__, 'Assertions must remain enabled'
+ROOT=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser(description=__doc__)
+ap.add_argument('output',type=Path,help='A new output directory outside this package')
+ap.add_argument('--replay-phases',action='store_true',help='Recompute all selected Gaussian phase pairs instead of reusing their source-bound evidence')
+a=ap.parse_args();out=a.output.resolve()
+assert not out.exists() and not out.is_relative_to(ROOT)
+def snapshot():
+ return {p.relative_to(ROOT).as_posix():hashlib.sha256(p.read_bytes()).hexdigest() for p in ROOT.rglob('*') if p.is_file() and p.name!='MANIFEST.json'}
+manifest=json.loads((ROOT/'MANIFEST.json').read_text());assert snapshot()==manifest['files'],'Source manifest mismatch'
+sources=json.loads((ROOT/'SOURCES.json').read_text())
+for z in sources['imported_files']:
+ data=(ROOT/z['path']).read_bytes();assert hashlib.sha256(data).hexdigest()==z['sha256']
+ if 'source_sha256' in z:assert hashlib.sha256(gzip.decompress(data)).hexdigest()==z['source_sha256']
+out.mkdir(parents=True)
+def copy(src,dst):
+ p=out/dst;p.parent.mkdir(parents=True,exist_ok=True)
+ data=(ROOT/src).read_bytes();p.write_bytes(gzip.decompress(data) if src.endswith('.gz') and not dst.endswith('.gz') else data)
+for src,dst in [
+ ('inputs/e8-r865.json.gz','work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz'),
+ ('inputs/complex-ports.json.gz','work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz'),
+ ('inputs/complex-template.json.gz','work/complex-nine-native/GLOBAL-TEMPLATE.json.gz'),
+ ('inputs/complex-data-phases.json.gz','work/complex-nine-native/DATA-PHASES.json'),
+ ('inputs/bit-geometry.json.gz','inherited/bit-geometry.json.gz'),
+ ('vendor/clifford_exact.py','work/odd-stages/clifford_exact.py')]:copy(src,dst)
+for name in ('moment','base_two_moment','outer'):copy('vendor/engines/'+name+'.py','work/pr361/code/engines/'+name+'.py')
+p=out/'bit426-source-centres';p.mkdir();(p/'bit-input.json').write_bytes(gzip.decompress((ROOT/'inputs/bit-r767.json.gz').read_bytes()))
+env=dict(os.environ,E8_OUTPUT=str(out),E8_REPLAY_PHASES=str(int(a.replay_phases)),PYTHONDONTWRITEBYTECODE='1');env.pop('PYTHONOPTIMIZE',None)
+steps=[]
+def run(name,file,*args):
+ with (out/(name+'.log')).open('w') as log:
+  r=subprocess.run([sys.executable,'-B',str(ROOT/file),*map(str,args)],cwd=out,env=env,stdout=log,stderr=subprocess.STDOUT)
+ if r.returncode:
+  print((out/(name+'.log')).read_text()[-16000:],file=sys.stderr,flush=True)
+  raise RuntimeError((name,r.returncode,str(out/(name+'.log'))))
+ steps.append(name);print('PASS',name,flush=True)
+run('hamming_packets','vendor/hamming_packets.py')
+for name in ('complex_construct','complex_audit','complex_emit','complex_phases','bit_construct'):run(name,'code/'+name+'.py')
+run('bit_export','vendor/export_records.py',p/'bit-source-centres.json',p/'records')
+run('bit_global','code/bit_global.py','--source',p,'--local-check',p,'--out',p/'global')
+run('bit_audit','code/bit_audit.py','--local-check',p,'--out',p/'global')
+for name in ('bit_price','complex_integrate','complex_replay','combined'):run(name,'code/'+name+'.py')
+assert snapshot()==manifest['files'],'Package modified during verification'
+r=json.loads((out/'RESULT.json').read_text());expected=json.loads((ROOT/'EXPECTED.json').read_text())
+for key,value in expected.items():assert r[key]==value,(key,r[key],value)
+r['verification_steps']=steps;r['phase_mode']='full replay' if a.replay_phases else 'source-bound unchanged evidence';r['manifest_sha256']=hashlib.sha256((ROOT/'MANIFEST.json').read_bytes()).hexdigest()
+(out/'RESULT.json').write_text(json.dumps(r,indent=2)+'\n')
+print('PASS conditional kappa',r['kappa_decimal'])