Research: dirty arbitrary-stride cyclic inverse on two tapes (no new kappa)

.github/workflows/dirty-stride-source-reuse.yml

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+name: Dirty stride source reuse
+on:
+  pull_request:
+    paths:
+      - 'research/dirty-stride-source-reuse/**'
+      - '.github/workflows/dirty-stride-source-reuse.yml'
+  push:
+    paths:
+      - 'research/dirty-stride-source-reuse/**'
+      - '.github/workflows/dirty-stride-source-reuse.yml'
+  workflow_dispatch:
+permissions:
+  contents: read
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    timeout-minutes: 45
+    strategy:
+      matrix:
+        python: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python }}
+      - run: python -I -O -B research/dirty-stride-source-reuse/test_package.py

research/dirty-stride-source-reuse/CLAIM.json

@@ -0,0 +1,80 @@
+{
+  "seed": 36,
+  "scope_override": "User explicitly selected the dirty-array solver remaining in PR846",
+  "base": "47481c89fd30a43f8f882eb4b391e89c29273fd0",
+  "head846": "4bdb3e755ea7118170a7a34764df955880dec282",
+  "track": "Complex supplier / explicit user-selected dirty recursive interface",
+  "candidates": [
+    {
+      "object": "Direct cycle walk of PR628 dirty leaf",
+      "decision": "Not selected: known arbitrary-stride route does not remove sorting."
+    },
+    {
+      "object": "Dirty two-stack FIFO for PR846",
+      "decision": "Not selected: requires a new storage and movement proof."
+    },
+    {
+      "object": "Reuse the source prefix for the recursive closure target",
+      "decision": "Selected: two closure calls, no additional dirty array per leaf, exact restoration."
+    }
+  ],
+  "method": "Exact two-tape trace, independent geometric and dense rational oracles, complete restoration and precision checks, malformed-package controls.",
+  "deliverable": "One isolated research construction with executable solver, full recurrence, exact receipts, controls and scope limits.",
+  "finish": "2026-10-13 15:55 UTC",
+  "coordination": "No pinned sprint issue returned by GitHub GraphQL; claim is local.",
+  "overlap": [
+    628,
+    744,
+    764,
+    805,
+    846,
+    862,
+    877,
+    905,
+    929,
+    951,
+    977,
+    982
+  ],
+  "hypothesis": "Source-prefix reuse gives a dirty arbitrary-stride additive solver with O(L) rounded arithmetic, O(1) clean arithmetic registers and no extra dirty array; fixed-tape linearity is not assumed.",
+  "inspected_heads": {
+    "628": "0768f97d06c623b8211e651543c66135796b62bf",
+    "663": "e0e546fd01b396478c68b6b6c5a16d87515983ba",
+    "673": "0b4f514c60d9bc7786415d7cbc24754f24d6dc3b",
+    "744": "302383e0c1ec71c50860362d3f394f85664c2445",
+    "764": "983d66f0f2e48ee500ec7eee2da9244c001c5064",
+    "805": "ef34bd5b32fcf2d5640dae90b5b8f28488738d5a",
+    "846": "4bdb3e755ea7118170a7a34764df955880dec282",
+    "862": "57e0659150d323b784580110b36aa64a2dca2a33",
+    "877": "80a60c0da2b916798167deb0ce3a5ef22fda147a",
+    "905": "aab6c0b8f4574cb36285ab5dab3fcfad0cd2b69e",
+    "929": "85a1d11adbbd7610d269cfeb3e477cf7d457f2eb",
+    "951": "de0c8641dcf1a4cd0abde9b897fa946de2bede49",
+    "977": "2846af720af190cb75b45ebddbb0357dec1121ec",
+    "982": "5eca5b435d2ce172edf6ffb85694c7efa31bf114"
+  },
+  "orientation_minutes": 14,
+  "coverage_rule": "Construct and prove the specified leaf. Exhaust the declared finite domains. No parameter search or optimality claim.",
+  "scope_limit": "Constant coefficients and supplied unit gauges only. No variable site phases, complete transform, physical supplier, or multiplication reduction.",
+  "evidence_driven_pivot": {
+    "initial": "The indexed source-prefix word restores correctly, but its direct movement is quadratic. The length-2378 stride-856 fixture needed 21388833 record moves before final head returns.",
+    "new_mechanism": "Use reversible block swaps with the dirty target as carrier, a causal conjugation for the seed expansion, and physical staging of child targets. Route all kernel arrays over two tapes.",
+    "preserved": "The first indexed implementation, proof, and receipts remain in the local research archive.",
+    "hypothesis": "The complete data movement obeys a two-child Euclidean recurrence and is linear in L."
+  },
+  "overlap_refresh_max_pr": 983,
+  "status": "verified research construction; ready for submission",
+  "overlap_refresh_utc": "2026-10-13T15:50:23.096008+00:00",
+  "overlap_result": "PR977 improves the precision of PR846 and keeps its clean scratch tape model. PR982 borrows outputs for a fanout interface. Neither supplies the dirty arbitrary-stride leaf constructed here. PR951 remains a different clean-scalar and arithmetic contract.",
+  "submission_context": {
+    "kappa": "1661960547713947/1000000000000000000",
+    "certificate": "research/community-frontier942-audit/ASSEMBLY.json",
+    "certificate_sha256": "4b2894956e594e408e111d806c842f2ed2c32aefcadff93fad69ff0b46f1991a",
+    "review": "docs/research/community-batch952-review.md",
+    "reproduce": "make frontier942-verify",
+    "main": "407d52ff15b2217b6e22bce44728b4c3907b6515",
+    "note": "Context refresh only. The experimental base and source pins remain unchanged."
+  },
+  "completed_at_utc": "2026-10-13T15:57:06.516658+00:00",
+  "result": "Dirty constant-coefficient inverse with source-prefix reuse and reversible transport on two tapes. Complete finite replay, exact restoration, ten package controls, and read-only receipt regeneration pass. No new kappa."
+}