Independent c2 numerical review: rational certification of all nine published output intervals

.github/workflows/c2-interval-audit.yml

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+name: Independent c2 interval audit
+
+'on':
+  pull_request:
+    paths:
+      - 'reviews/c2_interval_audit_20261001/**'
+      - '.github/workflows/c2-interval-audit.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  rational-and-source:
+    runs-on: ubuntu-latest
+    timeout-minutes: 10
+    steps:
+      - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262
+        with:
+          persist-credentials: false
+          fetch-depth: 0
+      - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065
+        with:
+          python-version: '3.11.16'
+      - name: Verify the frozen peer source and independent certificate
+        env:
+          PYTHONDONTWRITEBYTECODE: '1'
+          GIT_NO_REPLACE_OBJECTS: '1'
+        run: |
+          set -euo pipefail
+          git fetch --no-tags origin 59a06b65d138994119551059fa336919c07188bf
+          python -B -S reviews/c2_interval_audit_20261001/verify.py
+          cd reviews/c2_interval_audit_20261001
+          python -B -S -m unittest -v
+          python -B -O -S -m unittest -v
+          python -B -S oracle.py > "$RUNNER_TEMP/c2-normal.json"
+          python -B -O -S oracle.py > "$RUNNER_TEMP/c2-optimized.json"
+          cmp "$RUNNER_TEMP/c2-normal.json" "$RUNNER_TEMP/c2-optimized.json"
+          cmp RESULTS.json "$RUNNER_TEMP/c2-normal.json"
+          python -B -S verify.py
+          git diff --exit-code

reviews/c2_interval_audit_20261001/MANIFEST.json

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+{
+  "scientific_effect": "NONE",
+  "files": [
+    {
+      "path": "README.md",
+      "bytes": 1519,
+      "sha256": "f831e1fca62aaf745c1e8e8668679364e1dc1764340c6ee13e15d91e57c78146",
+      "git_blob": "9826f80b33d4bf605301f1b0a51f85490a62b009"
+    },
+    {
+      "path": "RESULTS.json",
+      "bytes": 3044,
+      "sha256": "27f91293c0ef8cc36975718eecfcd25c554022e2f8e12e41eda60bd77a1b4310",
+      "git_blob": "ea7cfd2064c72b973683e6a66f9d0a892b31c975"
+    },
+    {
+      "path": "REVIEW.md",
+      "bytes": 9655,
+      "sha256": "c808a02dfd2e8cea53985ceca7de8cb53d07db82b0bfbc368b6e37719239a5cf",
+      "git_blob": "008b017524e669c1496613c48988db170a3824e5"
+    },
+    {
+      "path": "SOURCE_BINDINGS.json",
+      "bytes": 920,
+      "sha256": "c467e8afa40067094344d017c9d0deff70c4af9c8c4a7b2a43e781d706befcdd",
+      "git_blob": "02d76b06977a77c509905458d34aeff6104f375e"
+    },
+    {
+      "path": "VALIDATION.md",
+      "bytes": 2266,
+      "sha256": "1f7868d47fdfc883589786c00e3dbc8f8e16b496c64e9f44504a84874ee6bfd6",
+      "git_blob": "94bca6d5a44a8e1fd74faa34b1fc909eae51e508"
+    },
+    {
+      "path": "oracle.py",
+      "bytes": 6375,
+      "sha256": "b462b1b24613f74abd66042e0f347f69423595e9a1aedf1c6b45197425afe075",
+      "git_blob": "094bdf84bc8be7aedb4e50e1b1b3732ce0e6f112"
+    },
+    {
+      "path": "test_bindings.py",
+      "bytes": 3459,
+      "sha256": "6fc688dfe38713345f07581dc01488589804946c81c360f33ad45d231a8a5ddd",
+      "git_blob": "4349b2113e5f8782bd4eacea79d643286c12334b"
+    },
+    {
+      "path": "test_oracle.py",
+      "bytes": 6087,
+      "sha256": "b9c18a8274874e8bba6161c82b35fb75cb03b031d1cfccef1e7de8b38267ff6b",
+      "git_blob": "f494bea76ece18538a222358067f462cd4dc9206"
+    },
+    {
+      "path": "verify.py",
+      "bytes": 4459,
+      "sha256": "df27846b1c3bf8a97918c543702ddfad1e0d9fdc4e9a63911e5a4d80d665daf8",
+      "git_blob": "c6fb38bf91bf76f07c171b0120eb86ed18028513"
+    }
+  ]
+}

reviews/c2_interval_audit_20261001/README.md

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+# Independent c/c2 numerical enclosure review
+
+Read REVIEW.md. This is the replay companion to numerical review5380714607 of
+Math-#223, not a new persistence theorem or a replacement for its author branch.
+
+A separate integer/Fraction evaluator certifies the nine supplied reference-kernel
+expressions for c, c2 and c2/c in dimensions1,2,3. Each exact rational result is
+strictly inside the original published interval. No floating numerical engine,
+Gamma library or quadrature is imported. Scientific effect NONE.
+
+## Replay
+
+    python -B -S -m unittest -v
+    python -B -O -S -m unittest -v
+    python -B -S oracle.py
+    python -B -S verify.py --local-only
+
+Full historical source authentication, in a checkout containing the pinned commit:
+
+    python -B -S reviews/c2_interval_audit_20261001/verify.py
+
+The last command verifies six exact source paths/blobs and checks that the copied
+published decimal intervals are exactly those in the source RESULTS.json.
+Local-only replay explicitly does not authenticate the upstream Git objects.
+
+The primary mathematical input beyond elementary interval operations and series
+is the positive-real log-Gamma Stirling remainder bound in NIST DLMF5.11(ii).
+The proof and explicit remainder terms are in REVIEW.md. No full parent theorem,
+finite-L c2 transfer, complex quadrature, full libm implementation or unused
+special-function branch is accepted by this record. Same-provider/source exposure
+and the corrected reviewer-cache test are recorded without rewriting history.

reviews/c2_interval_audit_20261001/RESULTS.json

@@ -0,0 +1,110 @@
+{
+  "Gamma_shift": 40,
+  "Gamma_terms": 20,
+  "binary_float_used": false,
+  "dyadic_bits": 240,
+  "scientific_effect": "NONE",
+  "scope": "independent numerical certification of the nine supplied closed forms only",
+  "source_analytic_derivation_revalidated": false,
+  "values": {
+    "1.c": {
+      "independent_rational_interval": [
+        "0.1101103789590514065452039444366610750264",
+        "0.1101103789590514065452039444366610750265"
+      ],
+      "published_interval": [
+        "0.1101103789590410",
+        "0.1101103789590625"
+      ],
+      "strictly_inside": true
+    },
+    "1.c2": {
+      "independent_rational_interval": [
+        "0.2300445802661749520884735424539552034425",
+        "0.2300445802661749520884735424539552034426"
+      ],
+      "published_interval": [
+        "0.2300445802661503",
+        "0.2300445802661998"
+      ],
+      "strictly_inside": true
+    },
+    "1.ratio": {
+      "independent_rational_interval": [
+        "2.0892179505778060085066669206919920101495",
+        "2.0892179505778060085066669206919920101496"
+      ],
+      "published_interval": [
+        "2.089217950577392",
+        "2.089217950578207"
+      ],
+      "strictly_inside": true
+    },
+    "2.c": {
+      "independent_rational_interval": [
+        "0.0734069193060342710301359629577740500176",
+        "0.0734069193060342710301359629577740500177"
+      ],
+      "published_interval": [
+        "0.07340691930602738",
+        "0.07340691930604167"
+      ],
+      "strictly_inside": true
+    },
+    "2.c2": {
+      "independent_rational_interval": [
+        "0.2215244106266869909000115594001050107224",
+        "0.2215244106266869909000115594001050107225"
+      ],
+      "published_interval": [
+        "0.2215244106266632",
+        "0.2215244106267110"
+      ],
+      "strictly_inside": true
+    },
+    "2.ratio": {
+      "independent_rational_interval": [
+        "3.0177592619457197900651855521106551257715",
+        "3.0177592619457197900651855521106551257716"
+      ],
+      "published_interval": [
+        "3.017759261945122",
+        "3.017759261946299"
+      ],
+      "strictly_inside": true
+    },
+    "3.c": {
+      "independent_rational_interval": [
+        "0.0417759318405983433429366654285755564666",
+        "0.0417759318405983433429366654285755564667"
+      ],
+      "published_interval": [
+        "0.04177593184059426",
+        "0.04177593184060272"
+      ],
+      "strictly_inside": true
+    },
+    "3.c2": {
+      "independent_rational_interval": [
+        "0.1612340491269627375475895156318002608686",
+        "0.1612340491269627375475895156318002608687"
+      ],
+      "published_interval": [
+        "0.1612340491269447",
+        "0.1612340491269810"
+      ],
+      "strictly_inside": true
+    },
+    "3.ratio": {
+      "independent_rational_interval": [
+        "3.8594961745478909155664511588764160940108",
+        "3.8594961745478909155664511588764160940109"
+      ],
+      "published_interval": [
+        "3.859496174547095",
+        "3.859496174548665"
+      ],
+      "strictly_inside": true
+    }
+  }
+}