Scoped negative result: coupled partial read exchanges on P6k4

.github/workflows/complex-read-exchange.yml

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+name: Coupled partial read-exchange checks
+on:
+  pull_request:
+    paths:
+      - 'research/complex-read-exchange/**'
+      - '.github/workflows/complex-read-exchange.yml'
+  workflow_dispatch:
+permissions:
+  contents: read
+jobs:
+  exact-replay:
+    runs-on: ubuntu-latest
+    timeout-minutes: 20
+    strategy:
+      matrix:
+        python: ['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 }}'
+      - name: Re-enumerate both domains and independently check every refusal
+        run: python -B -I -O research/complex-read-exchange/verify.py
+      - name: Confirm verification leaves tracked files unchanged
+        run: git diff --exit-code

research/complex-read-exchange/CLAIM.md

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+# Complex-supplier research claim: coupled read exchanges
+
+Prepared for Jason Willems (@at1as) with substantial OpenAI Codex assistance.
+
+- Base: `66849e1475c930fd7732b1a0067ffee7e1e95f60`.
+- Separate branch: `research/complex-kappa-seed21`; completed PR #666 is unchanged.
+- Track: complex-supplier improvement, deliberately selected following the user's
+  request to try improving kappa. Diversification seed **21** was drawn once from
+  20..39 using operating-system randomness, not from the gist's unrestricted
+  0..99 track lottery. This choice is recorded explicitly.
+- Claim recorded: 2026-10-13 04:58 UTC (2026-10-12 America/Los_Angeles).
+- Initial bounded session: aim to finish by 06:15 UTC, reserving at least the final
+  quarter for validation and handoff; do not assume an improvement exists.
+- Object: two simultaneous partial entering-copy read-set exchanges on the
+  promoted P6k4 input to PR #699, retaining its fixed helper boundaries and
+  owner map. Compare with its four-exchange output, not merely with old #626.
+- Dependency: #699 at `03e8d7ca494a083e5053cd6b1228f66b98414479`, plus its
+  pinned #635 source. The main selected result remains #626/#543. #699 and
+  #589 are pending/conditional dependencies, not newly accepted frontiers.
+- Hypothesis: moves individually rejected by target-frame containment might
+  become legal together because one shrinks a frame needed by the other.
+  A complete paid-profile reduction at unchanged widths can improve the complex
+  moment while preserving the owner assignment and unchanged #589 bit headroom.
+- Method: enumerate entering-copy candidates from the literal word, test
+  simultaneous choices with exact binary frame arithmetic, and check arbitrary
+  input scalar equality for legal candidates. Price the full paid profile,
+  including sources, targets, centers, tails, helper ends and idle owners.
+- Deliverable: a verified improving construction if found; otherwise a precisely
+  bounded completed search and reproducible evidence, with no impossibility claim
+  outside its enumerated class. No unsupported new kappa claim.
+
+## Candidate selection and overlap
+
+Three narrow candidates: (0) coupled partial entering-copy exchanges;
+(1) mixed-beta nine-term decoders on P112; (2) joint A/cleanup regrouping.
+Seed 21 modulo 3 selects candidate 0, after checking that its scope is open.
+Candidate 1 has larger potential but requires a new decoder/factory interface;
+candidate 2 is less sharply bounded and borders earlier failed regrouping searches.
+
+Read CONTRIBUTING.md, the selected certificate, current status, PR ledger,
+#626 construction/review, and retained negative-search summaries. Refreshed **551
+open PRs through #732**. No pinned coordination issue exists, so this claim is local.
+#699's `construction/sw4/NOTES.md` explicitly reports 602 single-pair candidates
+and says cross-pair partial combinations were not enumerated. #698 fixes the
+scalar word and gate order, #687 moves one read in one raw K-triangle, and #651
+fixes role and delivery rules; these do not close the present simultaneous class.
+Owner packing, existing entrance promotions and single-pair exchanges are not
+claimed as new work. Scalar primitive reductions alone do not improve kappa.
+
+Search domain, stopping rule, source hashes, completed coverage and any pivot
+will be recorded with the experiment. Delegated work is limited to reproducing
+this pinned baseline and reviewing this specific rewrite and its complete cost.
+
+## Evidence-driven follow-up
+
+The complete two-pair domain contained 175,456 joint choices across all 1,431
+pairs, requiring both selected masks to be nonempty and at least one partial.
+All were rejected by target caps. A preceding shared-direct-target subdomain
+covered 5,840 of those choices. The direct-target overlap graph on the 54 eligible
+pairs has 16 connected components of size three and six isolated vertices.
+One bounded follow-up therefore tests all simultaneous nonempty choices in
+those 16 three-pair components, still requiring at least one partial and keeping
+known SW4 moves on untouched pairs. This tests a possible three-way repair
+without reopening arbitrary gate permutations or unrestricted multi-pair search.
+
+## Completed result and handoff
+
+Completed this claim in [PR #775](https://github.com/CrocSwap/integer-mult-bounds/pull/775).
+The two-pair domain rejected all 175,456 parameterized cases; the bounded
+three-pair follow-up rejected all 27,344 cases in the 16 connected triples.
+These are case counts, not counts of distinct completed rewrites. Both independent
+engines agreed on every first-refusal digest and the finite coverage. The public
+optimized Python 3.13 replay passed, including the exact 728-column SW4 scalar
+control and all 13 focused tests; Python 3.11 checks also passed.
+
+No legal improving candidate was found and no kappa improvement is claimed.
+The exclusion applies only to the pinned word and the documented eligibility,
+insertion, boundary and frame-floor rules. The direct-target graph does not prove
+circuit independence, and arbitrary triples and larger combinations remain open.
+The final overlap refresh covered 586 open PRs through #767; #741's frame-growth
+construction is credited as a separate approach. This bounded experiment is
+complete. Further search classes belong in a separate research claim.

research/complex-read-exchange/EXPECTED.json

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+{
+  "input_sha256": "0390ec65dc4d47df1887aabdc2ec5b6ddea3cfc8e65582873fdfeba81d100073",
+  "comparison_sha256": "d232183f233899961bf55cac67a18545ed33548d9a7ca7078990d1a83d557c59",
+  "domains": {
+    "two_pairs": {
+      "arity": 2,
+      "domain": "all",
+      "eligible_pairs": 54,
+      "groups": 1431,
+      "counts": {
+        "single_total": 602,
+        "single_cap": 564,
+        "single_legal": 38,
+        "coupled_total": 175456,
+        "coupled_cap": 175456
+      },
+      "failure_site_sha256": "fe76c61059ebeb274e91233cf1cc250ebb8d2b6d97fd98c0bf43e92edeaef916",
+      "failure_witness_sha256": "44f7dc3e0d6d1f498aaaefab7600e9096f5a067cf2baeed4cc1113da5c937e66",
+      "exact_baseline_columns": 728
+    },
+    "connected_triples": {
+      "arity": 3,
+      "domain": "shared-targets",
+      "eligible_pairs": 54,
+      "groups": 16,
+      "counts": {
+        "single_total": 602,
+        "single_cap": 564,
+        "single_legal": 38,
+        "coupled_total": 27344,
+        "coupled_cap": 27344
+      },
+      "failure_site_sha256": "c238beff39b56afd1a1cbcfd5bd0e5f23ec335bdb248c3ff85d02de2da83446d",
+      "failure_witness_sha256": "d7d1b65c87927cd8fc20bb950804cc53fad13af0c00c15c52fdfbf85f1ae2444",
+      "exact_baseline_columns": 728
+    }
+  }
+}

research/complex-read-exchange/NOTICE.md

@@ -0,0 +1,44 @@
+# Attribution and scope
+
+Prepared for Jason Willems (@at1as), with substantial OpenAI Codex assistance in
+selecting this experiment, writing its search and independent checker, rebuilding
+pinned inputs, executing checks, and reviewing scope. Separate Codex agents
+reviewed the construction and implementation. No independent human review or
+literature-priority claim is made.
+
+Jeremy Kothe (@jeremykothe2), PR #699 at
+`03e8d7ca494a083e5053cd6b1228f66b98414479`, provides the P6k4 supplier, SW4
+read-exchange mechanism, deterministic recipe and admitted comparison profile.
+Its `construction/sw4/NOTES.md` explicitly leaves cross-pair partial combinations
+open. BRoute is the construction attribution used in that source package; we do
+not infer a separate human identity from it. Our scripts implement a new joint
+search and an independent checker; the rewrite semantics and frame-floor policy
+are inherited, not claimed as new.
+
+The supplier retains icekylinx's gauge44 factory, Jeremy Kothe's no-triangle,
+layered, cold-end and entrance-promotion work, Chafik Boukhalfa's #685 owner map,
+eumemic's #589 bit supplier, and the DreamingOfClouds, Rohan Arun, Dominik Scholz,
+Jeremy Diviney, jaymosley07 and other upstream contributions credited in the
+retained notices. #635 at `a6895a69f8ad98ab45777b03e9e6f48888c39f6f` is the
+pinned construction-code dependency used during reconstruction. No new supplier
+or kappa improvement is claimed here.
+
+The input word is a freshly reconstructed artifact with its decompressed content
+matched to #699's pin. SW4-RECIPE.json is copied unchanged from its committed
+recipe. `inputs/PR699-NOTICE.md`, `inputs/UPSTREAM-NOTICE.md` and `inputs/LICENSE`
+preserve its notices and license. SOURCE.json gives exact identities.
+
+Related #698's fixed-word frame bound, #687's single-triangle relocation result,
+#651's delivery restrictions and #717's format limits informed scope selection;
+none is imported as a proof of this result. PR #666 is our separate completed
+analytic/certificate contribution and is not a dependency.
+
+New code and documentation: Apache-2.0, as in this repository. The underlying
+all-size compilation, realization, hosting, precision/tape and analytic contracts
+remain conditional. An independently implemented finite checker does not mean
+independent human authorship or full theorem formalization.
+
+Chafik Boukhalfa's concurrent #741, pinned at
+`e516b1463606840a15f80aac1995d64ce0092e89` during final overlap review, changes
+eight frames after the full SW4 recipe and claims a stronger conditional bound.
+It is credited as distinct progress, not used as a dependency or ruled out here.

research/complex-read-exchange/OVERLAP.json

@@ -0,0 +1,80 @@
+{
+  "base": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "open_count": 551,
+  "highest_pr": 732,
+  "relevant": [
+    {
+      "headRefOid": "67e9e846d9e8814b2dd01133251bb83fafa8f5b6",
+      "number": 717,
+      "title": "Format limits part 2 (no \u03ba claim): erratum to #595, exact invoice prices, frontier-word censuses, decoder floors, spec requirements, centre and fragmentation walls",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/717"
+    },
+    {
+      "headRefOid": "03e8d7ca494a083e5053cd6b1228f66b98414479",
+      "number": 699,
+      "title": "Conditional \u03ba = 0.001660666354374641: four entrance promotions, six dim-8 ends and a width-neutral B read exchange on the PR659 word",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/699"
+    },
+    {
+      "headRefOid": "ab78f797cffcbeddbb17a7eb069741085ffe3351",
+      "number": 698,
+      "title": "Scoped negative result: selected CK B frames are optimal at fixed boundaries",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/698"
+    },
+    {
+      "headRefOid": "82bbb9c3ac34540f196410d137ebc59d9c2c43a9",
+      "number": 687,
+      "title": "Scoped negative result: certify one K-triangle relocation neighborhood",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/687"
+    },
+    {
+      "headRefOid": "5fc2a0c4e10558f09f03a8e42559dcf8e381e57e",
+      "number": 685,
+      "title": "Conditional \u03ba = 0.001660339298410333: four entrance promotions and 72 cold ends",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/685"
+    },
+    {
+      "headRefOid": "cbf30fdb56126d8cb7594f32e4d9a74ea7cd80a7",
+      "number": 683,
+      "title": "Scoped negative result: partial K/M face bypass requires four carriers",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/683"
+    },
+    {
+      "headRefOid": "4982f0ca66ffe0960b5a6451deb5b66b1039326b",
+      "number": 659,
+      "title": "Conditional \u03ba = 0.001656193765416678: gauge44 without K-triangles (56 cold ends), with layered ends",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/659"
+    },
+    {
+      "headRefOid": "df5b9c41fcea749242af886646dfebb9d86319a7",
+      "number": 651,
+      "title": "Research: the complex delivery layer is rigid \u2014 target hosting and raw-face sharing closed exactly",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/651"
+    },
+    {
+      "headRefOid": "638a5171dd1aca89ff50d07dcbe288b567769804",
+      "number": 645,
+      "title": "Gauge44 factory and whole-family assignment for conditional \u03ba = 0.001649483702558979",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/645"
+    }
+  ],
+  "final_refresh": {
+    "open_count": 586,
+    "highest_pr": 767,
+    "relevant": [
+      {
+        "number": 741,
+        "title": "Conditional \u03ba = 0.001661202643272239: eight B-frame coalescences after SW4",
+        "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/741",
+        "headRefOid": "e516b1463606840a15f80aac1995d64ce0092e89"
+      },
+      {
+        "number": 699,
+        "title": "Conditional \u03ba = 0.001660666354374641: four entrance promotions, six dim-8 ends and a width-neutral B read exchange on the PR659 word",
+        "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/699",
+        "headRefOid": "f042731cb332359166e8215839f9a3da28c46c5b"
+      }
+    ],
+    "conclusion": "PR741 raises eight gate frames after the full SW4 exchanges; it does not enumerate the partial-exchange domains here. PR699 advanced by a README/MANIFEST-only commit; construction inputs remain at the pinned bytes."
+  }
+}