Mister-Meeseeks · Oct 12, 2026 · Oct 12, 2026
diff --git a/.github/workflows/mixed-prefix-fourway.yml b/.github/workflows/mixed-prefix-fourway.yml
@@ -0,0 +1,27 @@
+name: Four-provider mixed-prefix witness
+on:
+  pull_request:
+    paths:
+      - 'research/mixed-prefix-fourway/**'
+      - '.github/workflows/mixed-prefix-fourway.yml'
+  push:
+    paths:
+      - 'research/mixed-prefix-fourway/**'
+      - '.github/workflows/mixed-prefix-fourway.yml'
+  workflow_dispatch:
+permissions:
+  contents: read
+jobs:
+  replay:
+    runs-on: ubuntu-latest
+    timeout-minutes: 45
+    strategy:
+      fail-fast: false
+      matrix:
+        python: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: '${{ matrix.python }}'
+      - run: python -B research/mixed-prefix-fourway/verify.py --work "${{ runner.temp }}/mixed-prefix-fourway"
diff --git a/research/mixed-prefix-fourway-validation/BASELINE-REUSE.json b/research/mixed-prefix-fourway-validation/BASELINE-REUSE.json
@@ -0,0 +1,22 @@
+{
+  "status": "PASS_UNCHANGED_BASE_AND_BYTE_IDENTICAL_PUBLISHED_EVIDENCE",
+  "base_commit": "db0e57bc7f36b5ac0fc844ad7ce1396165ee6647",
+  "evidence_pr": 572,
+  "evidence_commit": "0c3a7d1b0d99dbc6a1cc5ec1675ddd74aa959586",
+  "evidence_path": "research/multicold-width7-validation/baseline",
+  "files": {
+    "baseline-resume.log": "e5715bcd35d33b2762d7df45fce78999d1a716454b720b9d7bb63e3c571f78b7",
+    "BASELINE-RESUMED.json": "2a7d3b792ab347fb7c327fa2f243ccfd9313a6bdbd8509cb675d04f33e79ba7a",
+    "RESULT.json": "33bc04b619f1bfdeb339a741f7122d8c2515926874bb22102a15641ec866d9dc",
+    "verify-strips.log": "f62466bab477b4ea1066772065f8ff99d61877830c0999c0bda53ba34fa110cc",
+    "verify-tests.log": "743abf8cc411dbf7076fd6d2acf0cb4a5c4e1b069e61fe05014ce0532016cc26",
+    "baseline-make-verify.log": "ec80055542eb33d9478fbd169ebdd79cb9461904c189b56367d9cd864e28cb76",
+    "verify-clones.log": "a2af495e06a165c67b55b270f8aa5718b4bd39a1c0caad6630bdb9e69cc2a160",
+    "verify-positive.log": "87266f3f3ae86ad60dde8cd266d4efd4bab359f7ab712648628ec9c437cbae86",
+    "verify-joint.log": "10ea12f4f165d20002f3b706814b01519894549584f653adbb0f65bee529c1f7",
+    "verify-pair.log": "5aecc2fe47225cd313054c3224442dededd7601c49737b9f9f205cda21490ff9",
+    "toolchain/openmp-check.cpp": "f54dd7a5bf5d4b2f7a731acbe382db7c40c00185973cda6035569fd3d7019a1c",
+    "toolchain/cxx-openmp": "b3badefa5ed1983e3d4a71efec3001ebf321889fd0a58cef466e048b61132b15"
+  },
+  "scope": "Previously completed 18 groups, including gen4-bank-verify, on the identical baseline. Initial aggregate exited 2 at the OpenMP toolchain; six resumed groups passed after the toolchain fix. This is reused evidence, not a fresh aggregate run."
+}
diff --git a/research/mixed-prefix-fourway-validation/CROSS-PLATFORM.json b/research/mixed-prefix-fourway-validation/CROSS-PLATFORM.json
@@ -0,0 +1,110 @@
+{
+  "environments": {
+    "linux": {
+      "environment": {
+        "python": "3.12.3",
+        "python_full": "3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]",
+        "system": "Linux-6.17.0-1032-nvidia-aarch64-with-glibc2.39",
+        "zlib": "1.3",
+        "zlib_runtime": "1.3"
+      },
+      "receipt_sha256": "2194d888c82e5602b7a204e6b215d1de67b6040bf5e8ebef2e8352b46512b55a",
+      "seconds": 607.3298252341338,
+      "stages": 30
+    },
+    "macos": {
+      "environment": {
+        "python": "3.14.8",
+        "python_full": "3.14.8 (main, Sep 30 2026, 17:55:09) [Clang 21.0.0 (clang-2100.3.34.2)]",
+        "system": "macOS-27.0.1-arm64-arm-64bit-Mach-O",
+        "zlib": "1.2.12",
+        "zlib_runtime": "1.2.12"
+      },
+      "receipt_sha256": "1502878d3c5f3867e387ccd6150bcd222319ca180eac4ee9e381e52faa5c73aa",
+      "seconds": 541.0748718749965,
+      "stages": 30
+    }
+  },
+  "invoice_all_numerical_and_semantic_fields_equal": true,
+  "invoice_omitted_raw_reference_fields": [
+    "template_sha256",
+    "parent_template_sha256",
+    "owner_audit_sha256",
+    "controller_audit_sha256",
+    "providers.*.artifacts"
+  ],
+  "provider_artifact_semantic_sha256": {
+    "plain_eight": {
+      "CANONICAL-WORD.json.gz": "4bd83a3946bf7f5f4d0c1fee1ce5cc23749fbe1d1c2e39b94b749eac93f44e13",
+      "CLIFFORD-RECIPES.json": "b32e904cac5f4ac2b9a80a50dfd112ced1e44a2eab1ee24149c501f0d6979748",
+      "CLIFFORD-REVIEW.json": "b877cf8e80b1940512d272d027871deca0ca8a876db23751dfc4844272b2ad2a",
+      "INDEPENDENT-LOCAL-REPLAY.json": "4c404ae021e507934ab5f0f2a39ceb4260fe2faa0e7f6ab0b59cb2423baf591b",
+      "LOCAL-CHECKS.json": "becd709ef7328b5e45036c3691499028c1f03471cdea9b82e3b513a3d2452347",
+      "LOCAL-PROGRAMS.json.gz": "f6c3816f94d7a3140550fa01001d6fa2b86ad94011588ccc2596202baa7ddd0e",
+      "RESIDUAL-ADAPTERS.json": "538c4a1fd46a44575c17d30586fe773d50b5f857be8c81aed37ffcbbec3a995c"
+    },
+    "plain_four": {
+      "CANONICAL-WORD.json.gz": "12c85e9ddef0ff565207b6ecc198e9f154423736b14d62567b2f9c1545dc6539",
+      "CLIFFORD-RECIPES.json": "9f7b1d5bfcd937fb25778402cda7e71ccc1ae0e0e7f2b65a380dc231ad6f36fa",
+      "CLIFFORD-REVIEW.json": "66e70f02def7215e9d56e1346b72376b9374c9920626a0e9909564b058c5e976",
+      "INDEPENDENT-LOCAL-REPLAY.json": "f62751047d19673d4b209f7b2999e875074f73e36f73adceeb6fd17619df8f4b",
+      "LOCAL-CHECKS.json": "6220c00ac6b561c2d8c794aeb48b24c7420042cbc4e15a9ab541181eb4aff887",
+      "LOCAL-PROGRAMS.json.gz": "a2c3bd0e38b598eea185d2b56b257815802b739cf6fcd2af769817abc31ddeb4",
+      "RESIDUAL-ADAPTERS.json": "538c4a1fd46a44575c17d30586fe773d50b5f857be8c81aed37ffcbbec3a995c"
+    },
+    "prefix_width7_eight": {
+      "CANONICAL-WORD.json.gz": "72310df524313ca91e7dd0de0c1a2772a4437a79b5f8d34222234c35159b495b",
+      "CLIFFORD-RECIPES.json": "3323144380012a59c59e56348dd56d17da0f93e7783415efdaabe6fd5d3edadc",
+      "CLIFFORD-REVIEW.json": "695a862d36f9912c4b090b3e0d3b2682308dfe5759fb9fbea21ffbb156759631",
+      "INDEPENDENT-LOCAL-REPLAY.json": "53680341eb55288af90cbf346ed94ac930ec2c8d5df622e335a1757c509172de",
+      "LOCAL-CHECKS.json": "943e6ef6c31405fd033192406856f444e2d9058e1b03e24532540751b9f7ece8",
+      "LOCAL-PROGRAMS.json.gz": "a946b6da61abc8cd9443f4fd4ea591e6462070fb5c7ad6ab521d27ebdf6c9809",
+      "RESIDUAL-ADAPTERS.json": "608eca0714d2bab99178c3ae3cb9da3eaedd955bcc82eb878128e7ce8d5ede71"
+    },
+    "width7_eight": {
+      "CANONICAL-WORD.json.gz": "7dd0eb8f3100a1b444cf64c78cf542731993cc7b59a875c9f4fc914aa9d9f02a",
+      "CLIFFORD-RECIPES.json": "d6dd182cb81d8b962b1ba6e6a04352309c38de894fa601634781220f6115ab8a",
+      "CLIFFORD-REVIEW.json": "7209672a038afa8ea8a17b8cc4a9be3f1b5df93560826b17fba4dae0212b35d9",
+      "INDEPENDENT-LOCAL-REPLAY.json": "6bb8841989f5d185df36d2b42757b2f3e778a1fea5572d7b41ff87c172b429aa",
+      "LOCAL-CHECKS.json": "9374807e98eec6ec5bab0a42771d35e479f0741610c44bba6a6be9c10f3ffbdf",
+      "LOCAL-PROGRAMS.json.gz": "e9c9e720f4b199c3e32175f4043333a90f30a57770385f9906a83bfac7a4bf30",
+      "RESIDUAL-ADAPTERS.json": "68cfb6a4924ca512fdf9d678618b7dfa420e90ec0e5b559e20358cd5a2bfe602"
+    }
+  },
+  "result": {
+    "assembly_controls": 109,
+    "bit_lower": "413456747036699736067/250000000000000000000000",
+    "complex_lower": "320683070652636948893/200000000000000000000000",
+    "complex_profile": {
+      "1": 169296,
+      "2": 41043,
+      "3": 25943,
+      "4": 13824,
+      "48": 1817,
+      "5": 4032,
+      "6": 4032,
+      "7": 3,
+      "8": 576
+    },
+    "conservative_complex_lower": "1603415350469063711949/1000000000000000000000000",
+    "conservative_kappa": "160084852536971/100000000000000000",
+    "controller_controls": 16,
+    "generated_reference_controls": 36,
+    "generated_semantic_controls": 36,
+    "kappa": "400212132038723/250000000000000000",
+    "kappa_decimal": "0.001600848528154892",
+    "provider_counts": {
+      "plain_eight": 4,
+      "plain_four": 2,
+      "prefix_width7_eight": 58,
+      "width7_eight": 8
+    },
+    "recompression_controls": 4,
+    "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. Four fixed plain/width-seven/joint-prefix per-invocation providers composed with cited unchanged PR543 bit supplier. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification.",
+    "status": "PASS_FOUR_PROVIDER_MIXED_PREFIX_FULL_COLD_ADMISSION"
+  },
+  "result_sha256": "eaa75361679536e5b68ea72a7a91e0f8e4dcf1a900d545d346d99ca6089a79e9",
+  "scope": "Two independent executions of the same frozen source; all proof-relevant provider identities and all numerical/semantic invoice fields agree. Raw compressed containers, timings, absolute paths and their derived receipt hashes are not claimed byte-identical.",
+  "source_manifest_sha256": "6a804eb28134da69813960e231ae9609d6786b3452d46f8936d03766a2dc2407",
+  "status": "PASS_TWO_ENVIRONMENT_COLD_REPLAY_AND_PROOF_CONTENT_EQUALITY"
+}
diff --git a/research/mixed-prefix-fourway-validation/FRONTIER-PREPUBLICATION.json b/research/mixed-prefix-fourway-validation/FRONTIER-PREPUBLICATION.json
@@ -0,0 +1 @@
+[{"headRefOid":"eac6f7e378ab622dac50a2fd4b7ef6eab014de44","number":575,"title":"Conditional κ = 0.001600770286423653: joint prefixes in all 72 complex calls"},{"headRefOid":"f3e0af901f88f2fd3a213224ad3b59a16b5f4688","number":574,"title":"Conditional κ = 0.00160073442456167: PR568 eight-cold provider at PR571's nine plain calls"},{"headRefOid":"576e6ec9f442ed4c0e171821ff70f1856629778c","number":573,"title":"[Lean] Connect eight-tape parameter setup to the real ceiling logarithm"},{"headRefOid":"0c3a7d1b0d99dbc6a1cc5ec1675ddd74aa959586","number":572,"title":"Eight-cold / width-seven composition and cold replay: conditional κ = 0.001600535778621932"}]
diff --git a/research/mixed-prefix-fourway-validation/README.md b/research/mixed-prefix-fourway-validation/README.md
@@ -0,0 +1,61 @@
+# Four-provider cold replay evidence
+
+The frozen source manifest is `6a804eb28134da69813960e231ae9609d6786b3452d46f8936d03766a2dc2407`.
+
+| Environment | Full cold time | Top-level stages | Result |
+|---|---:|---:|---|
+| macOS arm64, Python 3.14.8, zlib 1.2.12 | 541.075 s | 30 | PASS |
+| Linux aarch64, Python 3.12.3, zlib 1.3 | 607.330 s | 30 | PASS |
+
+Each run starts from an absent output directory and rebuilds the complete
+pinned PR572/PR568 dependency chain before the new providers and whole-owner
+allocation. No retained provider proof outputs are reused in either final run.
+The result is `kappa=0.001600848528154892`; both `RESULT.json` files are
+byte-identical with SHA-256 `eaa75361679536e5b68ea72a7a91e0f8e4dcf1a900d545d346d99ca6089a79e9`.
+
+`CROSS-PLATFORM.json` compares all seven proof-content identities for each
+of the four providers and every numerical/semantic invoice field. It names
+the raw-reference fields omitted from the invoice comparison. Those references
+are validated against actual files during each run. Compressed containers,
+timings, absolute paths and derived raw-reference hashes are environment-specific.
+
+Both environments retain root and nested receipt chains, named proof artifacts,
+logs, local omission and phase checks, owner/invoice audits and all admission
+controls. Every run passes 16 owner mutations, 109 assembly mutations, four
+phase timing accept/reject pairs, four actual recompressions, 36 proof-content
+mutations and 36 reference/metadata mutations. Source files are unchanged after
+execution; `SOURCE-VALIDATION.json` records all 273 original Git-blob comparisons.
+GitHub CI is a separate execution and is not implied by these receipts.
+
+## Preliminary correction
+
+The initial v1 run on each platform completed the pinned parent replay but
+failed at a root packaging path: it looked for `PROMOTION.json` in
+`eight-cold-word` instead of `eight-multicold-word`. The corrected source receipt
+is byte-identical to the earlier PR569 receipt. No mathematical check failed.
+A diagnostic continuation with the completed Mac parent then passed all
+remaining stages; it is identified as retained-parent evidence, not a cold run.
+V2 fixes both receipt paths and explicitly rejects optimized Python before
+creating output. Both final full runs above were restarted from absent output
+directories. The mathematical construction, owner allocation and rate did not
+change. The v1 source inventory, failed Mac log and diagnostic log are retained
+in `preliminary/`.
+
+## Repository baseline
+
+The unchanged baseline is `db0e57bc7f36b5ac0fc844ad7ce1396165ee6647`.
+`BASELINE-REUSE.json` identifies byte-identical evidence already published in
+PR572 at `0c3a7d1b0d99dbc6a1cc5ec1675ddd74aa959586`. All 18 top-level `make verify`
+groups passed across its initial and resumed runs, including `gen4-bank-verify`.
+The first invocation passed twelve groups, then exited 2 because Apple clang
+rejected `-fopenmp`. After validating a run-owned libomp compiler wrapper with
+four workers, the failed group and five remaining groups passed. No source or
+assertion changed. This is reused baseline evidence, not a new aggregate run.
+
+The construction remains conditional on the assumptions listed in the source
+README and PROOF. These receipts establish finite admission, not a complete
+multiplication theorem, a practical speedup, or kappa = 1.
+
+The full diff has nine trailing-blank-line warnings, all confined to pinned
+vendored sources. Newly authored code, workflow and validation documentation
+pass the whitespace check; original vendored bytes remain intact.
diff --git a/research/mixed-prefix-fourway-validation/SOURCE-VALIDATION.json b/research/mixed-prefix-fourway-validation/SOURCE-VALIDATION.json
@@ -0,0 +1,10 @@
+{
+  "status": "PASS_ALL_VENDOR_FILES_MATCH_PINNED_GIT_COMMITS",
+  "files": 273,
+  "by_source": {
+    "pr572": 252,
+    "pr571": 7,
+    "pr569": 14
+  },
+  "source_pins_sha256": "901e1a22f0170a0f8abbf4aa298ded70e8f76ad0e11da3ef6d8426ff82a30ba4"
+}
diff --git a/research/mixed-prefix-fourway-validation/baseline/BASELINE-RESUMED.json b/research/mixed-prefix-fourway-validation/baseline/BASELINE-RESUMED.json
@@ -0,0 +1,104 @@
+[
+  {
+    "group": "verify-strips",
+    "exit_code": 0,
+    "seconds": 133.46484483301174,
+    "command": [
+      "uv",
+      "run",
+      "--python",
+      "3.14",
+      "--with",
+      "sympy==1.14.0",
+      "--with",
+      "numpy==2.3.5",
+      "make",
+      "verify-strips"
+    ]
+  },
+  {
+    "group": "verify-clones",
+    "exit_code": 0,
+    "seconds": 149.81662425003015,
+    "command": [
+      "uv",
+      "run",
+      "--python",
+      "3.14",
+      "--with",
+      "sympy==1.14.0",
+      "--with",
+      "numpy==2.3.5",
+      "make",
+      "verify-clones"
+    ]
+  },
+  {
+    "group": "verify-positive",
+    "exit_code": 0,
+    "seconds": 27.34550804202445,
+    "command": [
+      "uv",
+      "run",
+      "--python",
+      "3.14",
+      "--with",
+      "sympy==1.14.0",
+      "--with",
+      "numpy==2.3.5",
+      "make",
+      "verify-positive"
+    ]
+  },
+  {
+    "group": "verify-joint",
+    "exit_code": 0,
+    "seconds": 128.56256879202556,
+    "command": [
+      "uv",
+      "run",
+      "--python",
+      "3.14",
+      "--with",
+      "sympy==1.14.0",
+      "--with",
+      "numpy==2.3.5",
+      "make",
+      "verify-joint"
+    ]
+  },
+  {
+    "group": "verify-pair",
+    "exit_code": 0,
+    "seconds": 115.92115266702604,
+    "command": [
+      "uv",
+      "run",
+      "--python",
+      "3.14",
+      "--with",
+      "sympy==1.14.0",
+      "--with",
+      "numpy==2.3.5",
+      "make",
+      "verify-pair"
+    ]
+  },
+  {
+    "group": "verify-tests",
+    "exit_code": 0,
+    "seconds": 126.88050974998623,
+    "command": [
+      "uv",
+      "run",
+      "--python",
+      "3.14",
+      "--with",
+      "sympy==1.14.0",
+      "--with",
+      "numpy==2.3.5",
+      "make",
+      "verify-tests"
+    ]
+  }
+]
Original file line number	Diff line number	Diff line change
		@@ -0,0 +1 @@
		[{"headRefOid":"eac6f7e378ab622dac50a2fd4b7ef6eab014de44","number":575,"title":"Conditional κ = 0.001600770286423653: joint prefixes in all 72 complex calls"},{"headRefOid":"f3e0af901f88f2fd3a213224ad3b59a16b5f4688","number":574,"title":"Conditional κ = 0.00160073442456167: PR568 eight-cold provider at PR571's nine plain calls"},{"headRefOid":"576e6ec9f442ed4c0e171821ff70f1856629778c","number":573,"title":"[Lean] Connect eight-tape parameter setup to the real ceiling logarithm"},{"headRefOid":"0c3a7d1b0d99dbc6a1cc5ec1675ddd74aa959586","number":572,"title":"Eight-cold / width-seven composition and cold replay: conditional κ = 0.001600535778621932"}]