Scoped negative result: scratch-free CK/JP8 boundaries need extra primitives

.github/workflows/complex-scratch-free-boundaries.yml

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+name: Complex scratch-free boundary certificate
+
+on:
+  pull_request:
+    paths:
+      - 'research/complex-scratch-free-boundaries/**'
+      - 'research/complex-swap-runs-seed37/**'
+      - 'research/complex-dyadic-lowering/lower.py'
+      - 'research/community-k492-audit/pr626/replay/mixed-global/base/providers/**'
+      - '.github/workflows/complex-scratch-free-boundaries.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  finite-boundary-check:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 5
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Exact quotient, source census, witnesses and controls
+        run: |
+          python3 -I -O -B research/complex-scratch-free-boundaries/verify.py
+          python3 -I -O -B research/complex-scratch-free-boundaries/test_package.py
+          git diff --exit-code

research/complex-scratch-free-boundaries/CLAIM.md

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+# Sprint claim
+
+- Track: complex supplier. OS assignment seed **24**, drawn with Python `secrets.randbelow(100)` and persisted before selection. An earlier unpersisted draw was lost in truncated tool output and was not used for task selection.
+- Exact base: `ba82555c64e1879e4b7decce28186f208fcb8262`.
+- Current accepted selection: PR1042, kappa `1672188119205421/10^18`; selected manifest, assembly, actual gauge44-slots-t16 construction and batch1047 review inspected. No selected-frontier change proposed.
+- Three candidates: CK coefficient-grid synthesis (overlaps PR1118); restored CK helper butterflies (overlaps PR1116); scratch-free permutation boundaries (selected).
+- Object: PR971's 168 historical CK/JP8 deferred-swap boundaries, especially the 2+3-cycle boundary. Permit arbitrary mixed intermediate rows on exactly the moved coordinates, with the complete invertible PR696 real primitive alphabet and no work register or borrowed fixed coordinate.
+- Hypothesis/method: reducing exact dyadic words modulo 3 permits an exhaustive meet-in-the-middle exclusion of words through length eight. Independently replay exact witnesses and classify the actual boundaries. Seed 24 fixes coordinate/generator presentation, not sampled coverage.
+- Deliverable: one finite cost/scratch result with complete search domain, exact replay, meaningful adverse controls and a source-bound boundary census. No multiplication theorem or new kappa claim.
+- Stopping rule: complete radius-four modular balls for dimensions 2, 3 and 5; permit one evidence-driven refinement only if needed. No unbounded circuit search.
+- Expected finish: 2026-10-13 19:14 UTC; final verification/handoff starts by 19:06 UTC.
+- Coordination: GitHub pinned-issue query immediately before claim returned none. Local claim used. Open queue read through PR1127; targeted scratch/permutation searches and PR1095 head `1db482a6cb63ae49cf156357ef98b8e4b676fcd9` inspected. PR1095's monomial-prefix class is distinct and credited. No workers delegated.
+
+## Result and handoff — 2026-10-13 19:05 UTC
+
+Submitted [PR1145](https://github.com/CrocSwap/integer-mult-bounds/pull/1145), a scoped negative result. Complete independent radius-four balls agree on 509,157 matrices/distances. The scratch-free two-/three-cycle minima are 4/6; the disjoint 2+3-cycle minimum lies in [9,10], compared with the existing 8-operation scratch witness. All 168 historical boundaries are source-bound; exactly-moved-coordinate elimination costs at least 28 additional real primitives per orientation. Nine versus ten, borrowed fixed registers and full supplier integration remain unresolved.
+
+Research base is unchanged; submission rebased to `ce7ad1b6ab09452c3478723a2e96ed5ff212dc08`, which now selects PR1094. All seven input blobs remain identical. Tested implementation commit: `07e119dc44edf2bfa546f7212b5d60b0b9f44f12`. Full replay and ten test groups pass on CPython 3.14.6 and 3.9.6, with exact receipt regeneration, 37 gate omissions, source/receipt corruption and minimal relocation. Current selected-record integrity and five selected tests pass. Only this claim closeout changes after that tested implementation.
+
+Final overlap refresh through PR1142 and title searches for scratch-free/permutation work found no duplicate; PR1095's exact head stayed unchanged. No pinned coordination issue exists, so this is the single local claim update. Upstream has neither `codex` nor `codex-automation` label. Hosted CI remains separate from the completed local checks. No merge, selected-frontier edit or upstream source edit.