Research: cubic arbitrary-stride inversion without a length admission (no new kappa)

.github/workflows/cyclic-stride-effective-depth.yml

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+name: Cyclic stride effective depth
+
+on:
+  workflow_dispatch:
+  pull_request:
+    paths:
+      - 'research/cyclic-stride-effective-depth/**'
+      - '.github/workflows/cyclic-stride-effective-depth.yml'
+  push:
+    branches: ['codex/stride-effective-depth-20261013']
+    paths:
+      - 'research/cyclic-stride-effective-depth/**'
+      - '.github/workflows/cyclic-stride-effective-depth.yml'
+
+permissions:
+  contents: read
+
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    timeout-minutes: 30
+    strategy:
+      fail-fast: false
+      matrix:
+        python: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python }}
+      - name: Effective depth, original and cubic kernels, and defect controls
+        run: python -I -O -B research/cyclic-stride-effective-depth/verify.py --out /tmp/stride-depth-math.json
+      - name: Package rejection controls and full read-only relocation
+        run: python -I -O -B research/cyclic-stride-effective-depth/test_package.py --out /tmp/stride-depth-package.json
+      - uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: stride-depth-python-${{ matrix.python }}
+          path: |
+            /tmp/stride-depth-math.json
+            /tmp/stride-depth-package.json

research/cyclic-stride-effective-depth-validation/LINUX314-PACKAGE.json

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+{
+  "controls": [
+    {
+      "name": "missing manifest",
+      "rejected": true,
+      "terminal": "ValueError: missing package manifest"
+    },
+    {
+      "name": "altered implementation",
+      "rejected": true,
+      "terminal": "ValueError: package hash: early.py"
+    },
+    {
+      "name": "extra file",
+      "rejected": true,
+      "terminal": "ValueError: package file coverage"
+    },
+    {
+      "name": "missing source",
+      "rejected": true,
+      "terminal": "ValueError: package file coverage"
+    },
+    {
+      "name": "source hash independent of manifest",
+      "rejected": true,
+      "terminal": "ValueError: source SHA256: vendor/pr846/PROOF.md"
+    },
+    {
+      "name": "source Git object independent of manifest",
+      "rejected": true,
+      "terminal": "ValueError: source Git blob: vendor/pr846/stride.py"
+    },
+    {
+      "name": "duplicate manifest key",
+      "rejected": true,
+      "terminal": "ValueError: duplicate JSON key: files"
+    },
+    {
+      "name": "symlink injection",
+      "rejected": true,
+      "terminal": "ValueError: package symlink"
+    },
+    {
+      "name": "preloaded module substitution",
+      "rejected": true,
+      "terminal": "ValueError: local module binding: common"
+    },
+    {
+      "name": "false receipt boolean integer confusion",
+      "rejected": true,
+      "terminal": "ValueError: mathematical receipt mismatch"
+    },
+    {
+      "name": "existing output preserved",
+      "rejected": true
+    },
+    {
+      "name": "full read-only isolated optimized relocation",
+      "passed": true,
+      "receipt_sha256": "f30ad0e119c9928f30e2fc97e1911e053fe347bc4fe3f2b328b295141bda1552"
+    }
+  ],
+  "full_readonly_replay": true,
+  "rejected": 11,
+  "status": "PASS_STRIDE_DEPTH_PACKAGE"
+}

research/cyclic-stride-effective-depth-validation/LINUX314-PLATFORM.json

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+{
+  "bytecode_disabled": true,
+  "isolated": true,
+  "machine": "aarch64",
+  "manifest_sha256": "0b40eccb5d47d2ac152ed7fe47c259eb71bc17d3c818a71c63e2bc026e9377e3",
+  "optimized": true,
+  "platform": "Linux-6.17.0-1032-nvidia-aarch64-with-glibc2.39",
+  "python": "3.14.8"
+}

research/cyclic-stride-effective-depth-validation/LINUX314-TERMINAL.json

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+{
+  "full_package_controls": true,
+  "manifest_sha256": "0b40eccb5d47d2ac152ed7fe47c259eb71bc17d3c818a71c63e2bc026e9377e3",
+  "math_sha256": "f30ad0e119c9928f30e2fc97e1911e053fe347bc4fe3f2b328b295141bda1552",
+  "status": "PASS_FROZEN_STRIDE_DEPTH_PACKAGE"
+}

research/cyclic-stride-effective-depth-validation/LINUX314.log.txt

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+PASS stride cases 423 scalar coefficient paths 90
+PASS depth controls 12 log boundaries 1545
+PASS cubic budget rows 216 identities 3
+PASS 300 original kernel cases with uniform depth admission
+PASS actual cubic stride radix 3 cumulative cases 16
+PASS actual cubic stride radix 4 cumulative cases 32
+PASS actual cubic stride radix 5 cumulative cases 48
+PASS actual cubic stride radix 7 cumulative cases 64
+PASS_CYCLIC_STRIDE_EFFECTIVE_DEPTH arrays=423 kernels=300 uniform=64 scalar_paths=90 budgets=216 kappa=unchanged
+PASS package control missing manifest
+PASS package control altered implementation
+PASS package control extra file
+PASS package control missing source
+PASS package control source hash independent of manifest
+PASS package control source Git object independent of manifest
+PASS package control duplicate manifest key
+PASS package control symlink injection
+PASS package control preloaded module substitution
+PASS package control false receipt boolean integer confusion
+PASS package control existing output preserved
+PASS full read-only isolated optimized relocation
+PASS_STRIDE_DEPTH_PACKAGE rejected=11 full_readonly_replay=True
+PASS_STRIDE_DEPTH_BINDINGS sources=12
+PASS_FROZEN_STRIDE_DEPTH_PACKAGE

research/cyclic-stride-effective-depth-validation/MACOS311-PACKAGE.json

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+{
+  "controls": [
+    {
+      "name": "missing manifest",
+      "rejected": true,
+      "terminal": "ValueError: missing package manifest"
+    },
+    {
+      "name": "altered implementation",
+      "rejected": true,
+      "terminal": "ValueError: package hash: early.py"
+    },
+    {
+      "name": "extra file",
+      "rejected": true,
+      "terminal": "ValueError: package file coverage"
+    },
+    {
+      "name": "missing source",
+      "rejected": true,
+      "terminal": "ValueError: package file coverage"
+    },
+    {
+      "name": "source hash independent of manifest",
+      "rejected": true,
+      "terminal": "ValueError: source SHA256: vendor/pr846/PROOF.md"
+    },
+    {
+      "name": "source Git object independent of manifest",
+      "rejected": true,
+      "terminal": "ValueError: source Git blob: vendor/pr846/stride.py"
+    },
+    {
+      "name": "duplicate manifest key",
+      "rejected": true,
+      "terminal": "ValueError: duplicate JSON key: files"
+    },
+    {
+      "name": "symlink injection",
+      "rejected": true,
+      "terminal": "ValueError: package symlink"
+    },
+    {
+      "name": "preloaded module substitution",
+      "rejected": true,
+      "terminal": "ValueError: local module binding: common"
+    },
+    {
+      "name": "false receipt boolean integer confusion",
+      "rejected": true,
+      "terminal": "ValueError: mathematical receipt mismatch"
+    },
+    {
+      "name": "existing output preserved",
+      "rejected": true
+    },
+    {
+      "name": "full read-only isolated optimized relocation",
+      "passed": true,
+      "receipt_sha256": "f30ad0e119c9928f30e2fc97e1911e053fe347bc4fe3f2b328b295141bda1552"
+    }
+  ],
+  "full_readonly_replay": true,
+  "rejected": 11,
+  "status": "PASS_STRIDE_DEPTH_PACKAGE"
+}

research/cyclic-stride-effective-depth-validation/MACOS311-PLATFORM.json

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+{
+  "bytecode_disabled": true,
+  "isolated": true,
+  "machine": "arm64",
+  "manifest_sha256": "0b40eccb5d47d2ac152ed7fe47c259eb71bc17d3c818a71c63e2bc026e9377e3",
+  "optimized": true,
+  "platform": "macOS-27.0.1-arm64-arm-64bit",
+  "python": "3.11.15"
+}

research/cyclic-stride-effective-depth-validation/MACOS311-TERMINAL.json

@@ -0,0 +1,6 @@
+{
+  "full_package_controls": true,
+  "manifest_sha256": "0b40eccb5d47d2ac152ed7fe47c259eb71bc17d3c818a71c63e2bc026e9377e3",
+  "math_sha256": "f30ad0e119c9928f30e2fc97e1911e053fe347bc4fe3f2b328b295141bda1552",
+  "status": "PASS_FROZEN_STRIDE_DEPTH_PACKAGE"
+}

research/cyclic-stride-effective-depth-validation/MACOS311.log.txt

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+PASS stride cases 423 scalar coefficient paths 90
+PASS depth controls 12 log boundaries 1545
+PASS cubic budget rows 216 identities 3
+PASS 300 original kernel cases with uniform depth admission
+PASS actual cubic stride radix 3 cumulative cases 16
+PASS actual cubic stride radix 4 cumulative cases 32
+PASS actual cubic stride radix 5 cumulative cases 48
+PASS actual cubic stride radix 7 cumulative cases 64
+PASS_CYCLIC_STRIDE_EFFECTIVE_DEPTH arrays=423 kernels=300 uniform=64 scalar_paths=90 budgets=216 kappa=unchanged
+PASS package control missing manifest
+PASS package control altered implementation
+PASS package control extra file
+PASS package control missing source
+PASS package control source hash independent of manifest
+PASS package control source Git object independent of manifest
+PASS package control duplicate manifest key
+PASS package control symlink injection
+PASS package control preloaded module substitution
+PASS package control false receipt boolean integer confusion
+PASS package control existing output preserved
+PASS full read-only isolated optimized relocation
+PASS_STRIDE_DEPTH_PACKAGE rejected=11 full_readonly_replay=True
+PASS_STRIDE_DEPTH_BINDINGS sources=12
+PASS_FROZEN_STRIDE_DEPTH_PACKAGE

research/cyclic-stride-effective-depth-validation/README.md

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+# Frozen stride-depth validation
+
+Complete macOS arm64 / Python 3.11.15 and Linux aarch64 / Python 3.14.8
+replays passed with isolation, optimization and bytecode disabled. Their
+full mathematical receipts are byte-identical to each other and to the
+decompressed `../cyclic-stride-effective-depth/EXPECTED.json.gz`.
+
+Frozen package manifest SHA256:
+`0b40eccb5d47d2ac152ed7fe47c259eb71bc17d3c818a71c63e2bc026e9377e3`.
+Complete mathematical receipt SHA256:
+`f30ad0e119c9928f30e2fc97e1911e053fe347bc4fe3f2b328b295141bda1552`.
+
+Each platform recomputed the full mathematics three times: default replay,
+rejection of an altered expected receipt, and a read-only relocated replay
+in a path containing spaces. Eleven package rejection controls passed on
+each platform. Linux also began with the supplied package read-only, outside
+a Git checkout, under a durable supervisor that recorded exit status zero.
+
+The full `*-MATH.json.gz` receipts, package controls, platform information,
+terminal records and logs are retained here. Compare decompressed receipt
+bytes; container compression identity is not required. `VALIDATION.json`
+records their hashes. All 12 retained source files match their pinned Git
+objects and SHA256 hashes, as recorded in `SOURCE-GIT-CHECK.json`.
+
+Evidence includes 423 array cases, 90 scalar coefficient paths, all 300
+original PR846 kernel cases, 64 actual cubic-width kernel executions,
+216 integer budgets, three exact nonnegative polynomial identities,
+54 admission checks, 1,545 logarithm boundaries, 12 new mathematical
+controls and four inherited controls, 12 zero-base checks and 33 traffic
+cases through length 131,072. Scalar paths are not huge-array executions.
+Original and early-exit outputs agree exactly; the two traffic bills are
+40L and 44L respectively, with the additional head returns charged.
+
+The source record preserves preparation base
+`007664306fff84fbb1c9a1b4053b69f439764034`. Before publication the branch was
+fast-forwarded to `bbc600db2fc15007b7c914f4f2b2ed55fa909c87`, without changing
+any frozen package byte. Selected-record consistency passed there at
+`1661960547713947/1000000000000000000`; staged whitespace and byte checks
+also passed. Only two new research directories and their workflow are added.
+The full repository suite and hosted CI are separate from these local
+prepublication records. The scoped workflow repeats both Python versions.
+
+Finite exact checks support the written universal argument; they are not
+independent human review or proof-assistant verification. Clean scratch,
+phase access and remaining transform obligations remain explicit. No new
+kappa or bit-reversible/borrowed-array implementation is claimed.