Mister-Meeseeks · Oct 16, 2026 · Oct 15, 2026
diff --git a/research/t74-pure44-kernel-composition/.gitattributes b/research/t74-pure44-kernel-composition/.gitattributes
@@ -0,0 +1,3 @@
+# Preserve exact imported bytes: their manifests include CRLF text sources.
+supplier/** -text -eol
+comparison/** -text -eol
diff --git a/research/t74-pure44-kernel-composition/OVERLAP.json b/research/t74-pure44-kernel-composition/OVERLAP.json
@@ -0,0 +1,161 @@
+{
+  "status": "POSSIBLE_OVERLAP_NOT_A_NOVELTY_CERTIFICATE",
+  "searched_at": "2026-10-15T12:22:05.730126+00:00",
+  "coverage": {
+    "open_prs": {
+      "fetched_at": "2026-10-15T12:19:30.601271+00:00",
+      "complete_pagination": true,
+      "records": 679
+    },
+    "discussions": {
+      "fetched_at": "2026-10-15T12:22:05.598083+00:00",
+      "complete_pagination": true,
+      "records": 1197
+    }
+  },
+  "warnings": [],
+  "limits": "Remote PR scope is open PRs including drafts. Closed work is searched through local READMEs, TASK metadata and ledger only. No code diffs or arbitrary package files are searched. Recheck relevant heads before submission.",
+  "terms": [
+    "pure44",
+    "alias619",
+    "2309",
+    "2302",
+    "2462"
+  ],
+  "nearest_work": [
+    {
+      "kind": "pr",
+      "number": 2474,
+      "title": "Conditional \u03ba = 0.001703676387993676: a fifth #2436 alias on the entrance-raised T74 words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2474",
+      "head": "5298f86c5193db65f869121eab3cac16d557196c",
+      "updated_at": "2026-10-15T12:00:00Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "2309",
+        "2302",
+        "2462"
+      ],
+      "score": 3,
+      "excerpt": "ec2e17315e49c758153f2cf1b8d100ea80dbff7`). This package adds a fifth PR2436 (tekuuu) alias to our PR2462 words: helper 637 borrows retired source register 31 (the PR2436 pair, with its G columns taken from PR2436's composed word), stacked on PR2436's four lifted-target aliases (helpers 640, 641, 642 and 644 borrowing from lenders 33, 55, 74 and 85, an A-phase prelude of 28 events, and the 4 centre COPY 8 to 7+1 splits) and on our entrance-raised words of PR2435/PR2447. The whole stack rests on P"
+    },
+    {
+      "kind": "pr",
+      "number": 2312,
+      "title": "Conditional \u03ba = 0.001696891067241618: helper width exchange on the borrowed T74 words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2312",
+      "head": "6a05b1bb39a95d1608db8522f40c2dcdbd6e4cf9",
+      "updated_at": "2026-10-15T05:29:06Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "2309",
+        "2302"
+      ],
+      "score": 2,
+      "excerpt": "ackoff 1e-3022, C the certified endpoint; outer/PROOF-GRID-MAX.md). It exceeds the current leader PR2309 (Dugongue, a concurrent independent pure 44th dirty alias with owner repacking) by 3.75943E-7, PR2302 (the previous package of this series) by 4.95301E-7 and PR2265 by 1.34785E-5 (63 strict inequalities: the 62 retained ones plus the explicit main-binding row gaussian_above_main, 17 rejecting controls). The single 3000-digit rejection moment of the strict assembly uses PR2168's exact-integer "
+    },
+    {
+      "kind": "pr",
+      "number": 2374,
+      "title": "Conditional \u03ba = 0.001697194950901770: exact owner fill on #2322's handoff construction",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2374",
+      "head": "5449da65da12bdfd94675dccc38731eaa91e93b6",
+      "updated_at": "2026-10-15T10:07:20Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "2309",
+        "2302"
+      ],
+      "score": 2,
+      "excerpt": "8 + 78 + 2 = 66826) with CLEAR charges, the warp routing reserve and the adapter bound, following PR2309 (Dugongue) and the audit PR2315 (thakrarsagar); (3) the supplier endpoints certified to 1e-3000 with the fixed-grid-maximum outer kappa C - 1/F - B (PR2180 / PR2161, dataisfire; exact-integer coarse exponential PR2168). Conditional final kappa = 0.0016971949509017704265940818773095411997\u2026(3046 digits) (supplier strict-assembly kappa 0.0016943193606376810384632624188834507488\u2026(2995 digits)). I"
+    },
+    {
+      "kind": "pr",
+      "number": 2435,
+      "title": "Conditional \u03ba = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2435",
+      "head": "324d7d3590dc21003940a44cb0cbdc32b3620f25",
+      "updated_at": "2026-10-15T11:12:24Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "2309",
+        "2302"
+      ],
+      "score": 2,
+      "excerpt": "dle {1:20824, 3:6695, 5:1, 48:25302}). Also carried: the private cleanup-buffer stock accounting (PR2309 Dugongue, PR2315 thakrarsagar; physical stock 66826), the pooled-slot time binding (PR2301, PR1959), and the supplier endpoints certified to 1e-3000 with the fixed-grid-maximum outer kappa C - 1/F - B (PR2180 / PR2161, dataisfire; PR2168). Conditional final kappa = 0.0016985113436976293290517338141877446308\u2026(3046 digits) (supplier strict-assembly kappa 0.00169563129470883767026399787085096882"
+    },
+    {
+      "kind": "pr",
+      "number": 2447,
+      "title": "Conditional \u03ba = 0.001698511924002761: optimal owner fill on #2435's entrance-raised words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2447",
+      "head": "805bbaddf664459c1eb92aa461645cd69764c86e",
+      "updated_at": "2026-10-15T11:46:41Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "2309",
+        "2302"
+      ],
+      "score": 2,
+      "excerpt": "ge rejects wrong per-call residual widths. Also carried: private cleanup-buffer stock accounting (PR2309, PR2315; physical stock 66826), the pooled-slot time binding (PR2301, PR1959) and the 1e-3000 endpoints with the fixed-grid-maximum outer kappa C - 1/F - B (PR2180 / PR2161; PR2168). Conditional final kappa = 0.0016985119240027614377579662622550277564\u2026(3046 digits) (supplier strict-assembly kappa 0.0016956318730476708322470897317373993996\u2026(2995 digits)). It exceeds PR2435 by 5.80305E-10 (exac"
+    },
+    {
+      "kind": "pr",
+      "number": 2462,
+      "title": "Conditional \u03ba = 0.001703552312979594: optimal owner fill for #2436's aliases on the entrance-raised T74 words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2462",
+      "head": "ef34071fee6dfb0286e9850a5cec4e36d9eb126d",
+      "updated_at": "2026-10-15T11:34:55Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "2309",
+        "2302"
+      ],
+      "score": 2,
+      "excerpt": "22 tamper controls on the four-alias edit. Also carried: private cleanup-buffer stock accounting (PR2309, PR2315), the pooled-slot time binding (PR2301, PR1959), the entrance-width binding stage and the 1e-3000 endpoints with the fixed-grid-maximum outer kappa C - 1/F - B (PR2180 / PR2161; PR2168). Conditional final kappa = 0.0017035523129795943854192668981419560041\u2026(3046 digits) (supplier strict-assembly kappa 0.0017006551579516851148133668144041309961\u2026(2995 digits)). It exceeds PR2436's exact "
+    },
+    {
+      "kind": "pr",
+      "number": 2322,
+      "title": "Improve conditional \u03ba to 0.001697060296258836 with coherent handoffs and retimed hosting",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2322",
+      "head": "002304ef01c4416a127916169ae6d94c1bee052b",
+      "updated_at": "2026-10-15T05:15:03Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "2309",
+        "2302"
+      ],
+      "score": 2,
+      "excerpt": "w exact fill and frame re-solve are Jeremy Kothe's PR2312 work. That source already contains the [PR2302](https://github.com/CrocSwap/integer-mult-bounds/pull/2302) kernels; they are not inserted twice. Dugongue's [PR2309](https://github.com/CrocSwap/integer-mult-bounds/pull/2309) is concurrent independent single-alias/repacking work. Our addition is the simultaneous four-role producer change and its own complete owner/schedule certificate. Fresh canonical-main and bounded live-overlap checks ar"
+    },
+    {
+      "kind": "pr",
+      "number": 2309,
+      "title": "Improve conditional \u03ba to 0.0016965151242727336 with a pure 44th dirty alias",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2309",
+      "head": "95aea1e24dede937f00545a4d8250caa02f60339",
+      "updated_at": "2026-10-15T04:34:00Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "2302"
+      ],
+      "score": 1,
+      "excerpt": "omplex endpoint 0.001696515124272733616036. This exceeds the latest competing claim reviewed in PR #2302 by about 1.19e-7 through an actual paid construction change.\n\nThe additional alias removes one width-4 helper without widening any other helper: 437 -> 436. All 666 complete calls use the cheaper extra provider. Deleting 666 literal hosted roles replaces paid ranks 1+4 by 5, and two further legal width-7 moves replace 7+7 by 14. The final 290376-role fill is reproduced from pinned inputs and "
+    }
+  ],
+  "conclusion": "No exact composed pure44+q518/506 artifact was identified. The later width-exchange/handoff lineage is stronger and already has both kernels and removes619. This is a distinct superseded construction, not an additive latest-frontier improvement.",
+  "additional_relevant_audit": {
+    "pr": 2478,
+    "head": "dc83994c2dda28064c902ee970ce47db602224ae",
+    "action": "Additive cut guard in bounded hook; both composed words pass. Complete fresh native replay also passes."
+  }
+}
diff --git a/research/t74-pure44-kernel-composition/README.md b/research/t74-pure44-kernel-composition/README.md
@@ -0,0 +1,140 @@
+# Pure44 alias and q518/506 kernel composition
+
+This is a **superseded finite conditional construction**, with modern
+κ = **0.00169659996105181924736999999999979966068000768963615052600000000004**.
+It composes Dugongue's PR2309 pure alias619→530 and owner fill with Jeremy
+Kothe's PR2302 q518/506 kernels and frame choices (the kernel shape is
+mdumitrean's PR1625). The full source and generators are preserved unchanged
+under [`supplier/`](supplier/README.md). Its manifest is
+`e1bcf65a27e52767e2f7f4c28b284ff21b4e4f991ba2a1a803617abe49ef3a9a` (479 files).
+
+The added result is their actual chronological composition: matching common
+gates, transporting eight insertions and two deletions into the pure44 word,
+preserving the alias-specific monomial map, transporting the other 43 warp
+frames, and deriving the entire inverse-reverse cleanup. The portable producer
+recovers both credited predecessor controls before auditing the new words.
+Matching rank profiles alone would not establish this compatibility.
+
+## Result and evidence
+
+Both providers have local paid profile `{1:2341,2:505,3:420,4:124,5:42,8:8}`,
+mass 5381, 436 public helpers and 76 private FULL cleanup buffers. All 666
+hosted calls use the extra provider. The complete global profile is
+`{1:1582416,2:336330,3:288393,4:82584,5:29451,7:148,8:5328,14:1,48:24479}`:
+mass 4,816,512, 66,304 live fields, 66,826 physical fields and 290,376 hosted
+roles. The row coefficient is 19,545 below the retained 20,161 guard.
+
+Relative to the pinned PR2309 invoice the profile changes by
+`+1332 C1 -2664 C2 +1332 C3`. Strict concavity gives `1+3^p < 2*2^p` for
+`0<p<1`; positive-child count and rank mass are unchanged, so the conservative
+per-child surcharge cancels. The modern κ improvement over that pinned claim
+is about `8.48368e-8`. Exact proof, values and inherited assumptions are in
+[`supplier/PROOF.md`](supplier/PROOF.md) and the frozen source.
+
+[`evidence/RESULT.json`](evidence/RESULT.json) records complete finite admission
+of this exact manifest. The accompanying release, supplier, native, assembly,
+invoice, hosted-owner and bootstrap receipts record their own coverage.
+The bounded hook freshly rebuilds both words and rejects eight targeted
+kernel/alias/cleanup mutations. A full cold replay separately checks native
+transport and phases, the literal owner invoice, strict supplier and modern
+outer admission, hosted-owner binding and the ordinary bootstrap.
+
+The frozen inner README predates the final runtime and deliberately treats its
+numbers as expectations; the source is not edited retroactively. The external
+receipts and this publication note supply the completed execution status.
+Predecessor receipts remain historical and do not admit the new words.
+
+## Latest-source comparison
+
+The submission review refreshed upstream main and searched all open PR bodies,
+including drafts, and paginated discussion bodies, comments and replies.
+[`OVERLAP.json`](OVERLAP.json) records coverage, exact heads and limitations.
+This is a bounded overlap review, not a novelty proof.
+
+[PR2312](https://github.com/CrocSwap/integer-mult-bounds/pull/2312) and its
+successors already claim stronger values using a different width exchange.
+[PR2474](https://github.com/CrocSwap/integer-mult-bounds/pull/2474), pinned at
+`5298f86c5193db65f869121eab3cac16d557196c`, claims approximately
+`0.001703676387993676489034`. Its actual words already contain the identical
+q518/506 gate edits; PR2322's coherent handoff has already removed helper619,
+and lender530 serves helper651. Applying our target deletion again cannot
+remove an additional helper. Our verified improvement must not be added to
+that claim. No universal obstruction to future rescheduling is asserted.
+
+The minimal pinned comparison inputs under `comparison/pr2474/` and
+`verify.py` reproduce these structural facts in both orientations. This is
+not complete verification or adoption of PR2474. The selected record is
+unchanged. The contribution preserves a distinct composition, its portable
+producer and reproducible evidence, without claiming a new leading bound.
+
+## Packing cap
+
+The paid-profile relaxation in
+`research/complex-local-word-ceiling/ceiling.py`, at dimension73, 66,304 live
+fields, 666 calls, centre mass64/call and idle rank≤51, gives
+`a < 0.001728266380383`. The modern outer satisfies `κ<a`, so this also bounds
+its κ and the composition realizes about **98.167735%** of that cap.
+[`evidence/PACKING-CAP.json`](evidence/PACKING-CAP.json) supplies the exact
+directed bracket and rational ratio. The tool's historical `a/(1+a)` conversion
+belongs to an older balanced outer reduction; it is not used for this modern
+outer. This cap fixes the local profile, coverage law and idle-rank guard.
+
+## Reproduction
+
+The bounded registered hook uses the Python3.12 standard library on Linux:
+
+```sh
+python3 scripts/research_package.py --package research/t74-pure44-kernel-composition --check-only
+python3.12 scripts/research_package.py --package research/t74-pure44-kernel-composition
+```
+
+It checks frozen bytes, receipt/value bindings, the latest-source structural
+comparison and exact cap, then freshly rebuilds and audits both composed words
+with meaningful rejecting controls. It also checks the additive centre-to-target
+cut guard from [PR2478](https://github.com/CrocSwap/integer-mult-bounds/pull/2478),
+with two rejecting cut mutations per provider. The full native replay also
+covers the interface that motivated that audit. The hook does not replace
+complete cold admission.
+
+Full replay from the repository root, with an external output path that does
+not already exist:
+
+```sh
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python -I -B \
+  research/t74-pure44-kernel-composition/supplier/verify_package.py \
+  --out /absolute/new/composition-cold
+```
+
+[`evidence/ENVIRONMENT.json`](evidence/ENVIRONMENT.json) records the tested
+Linux interpreter, dependencies, command and cold/reuse status. Native replay
+is fresh by default. Optional `--native-cache` reuse must pass the retained
+source-bound binder; it is not needed for the documented cold run. No historical
+selected-record suite was rerun because this PR changes no selected inputs.
+
+The all-size compiler, fixed-tape realization, precision, recovery, analytic
+transfer, bit-supplier and modern-outer interfaces remain inherited conditions.
+Finite certificate success is not an unconditional multiplication theorem,
+full Lean reflection, or independent human review.
+
+## Open next questions
+
+An independent review of the chronological transport and inherited physical
+hosting/outer interfaces would strengthen assurance; begin with the two exact
+rebuilt words, rejected mutations and source-bound native receipts. The blocker
+is independent mathematical review, rather than another numerical κ search.
+Any future attempt to improve the latest supplier must start from its actual
+handoffs and frame schedule and price a fresh complete invoice; helper619 and
+the q518/506 kernels cannot be counted twice. Structured details are in
+[`TASK.json`](TASK.json).
+
+## Credit
+
+Prepared for Marius-Paul Dumitrean (`mdumitrean`) with substantial OpenAI Codex
+assistance in construction, validation and writing. Dugongue/PR2309 supplies
+the pure44 alias, exact fill and private-buffer accounting; Jeremy Kothe/PR2302
+supplies the two kernels and frame refit, using mdumitrean/PR1625's kernel
+shape; Cinna Davis (`1337isnot1337`)/PR2226 supplies anticipatory dirty borrowing.
+The retained supplier, audit, outer and source-specific notices preserve the
+full predecessor attribution. Comparison excerpts credit Jeremy Kothe/PR2474,
+Vlado Vojdanovski/PR2322 and tekuuu/PR2436, with their retained NOTICE.
+New work is Apache-2.0; all retained source licenses continue to apply.