Research: Gaussian nonlinear message copy floor 40b under explicit width pricing

research/gaussian-nonlinear-copy-floor/CLAIM.json

@@ -0,0 +1,28 @@
+{
+  "track": "structural decoder research",
+  "os_random_seed": 44,
+  "base_commit": "f567884aeb8851b6e794af1184119a3bfbe1e631",
+  "started_utc": "2026-10-13T09:59:00Z",
+  "claimed_utc": "2026-10-13T10:01:50.923535+00:00",
+  "finish_utc": "2026-10-13T10:39:00Z",
+  "verification_start_utc": "2026-10-13T10:29:00Z",
+  "object": "Fixed-support deterministic zero-error nonlinear block messages on PR738 Gaussian E8 60-line geometry",
+  "method": "Conditional transcript injectivity on all 640 maximum nonorthogonal cliques; inherited exact flat-pair charge inequality; unequal independent bit demands",
+  "deliverable": "Scoped nonlinear copy floor C >= (2/3) sum b_t (40b uniform), finite nonlinear controls, source-pinned complete geometry replay, proof and handoff",
+  "candidates": [
+    "Gaussian nonlinear block-message extension of scalar floor40",
+    "Exact asymmetric-sink feasibility of P112 float screen",
+    "Higher-target signed-star puncture mechanisms"
+  ],
+  "selection": "Seed44 is even: choose Gaussian rather than Eisenstein/Hurwitz. Existing #785 and #814 cover those two geometries; #738 covers only scalar binary totals. No compute-only reopening of the existing decoder optimization search.",
+  "coordination": "Repository open-issue inventory contains only #650, no sprint coordination issue. Claim recorded locally. Live PR searches inspected decoder, puncture, star and nonlinear work through #884.",
+  "selected_kappa": "1661634653669567/1000000000000000000",
+  "workers": "One read-only predecessor/model reviewer; later bounded verification only.",
+  "result_update": {
+    "status": "completed mathematical/model result, verified locally; packaging and submission in progress",
+    "result": "C >= max(ceil(2 sum b_t/3), max_Q sum_Q b_t); uniform40b Gaussian/80b rational; inherited Dfc gives D/T <= 40b(s-3)",
+    "evidence": "Complete2,579,856 flat-pair replay;49,152 nonlinear receiver decodes;2,621,440 conditional projection assignments; explicit pricing, side-information and decoding controls",
+    "link": "README.md",
+    "verification": "All three focused package tests and selected-record integrity pass; separate AI-assisted proof/code review finds no actionable issue."
+  }
+}

research/gaussian-nonlinear-copy-floor/NOTICE.md

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+# Attribution and assistance
+
+Prepared for **@ToikY** with substantial **OpenAI Codex assistance** in task
+selection, proof composition, implementation, finite verification and writing.
+Separate AI workers supplied model/proof review and an independently written
+nonlinear truth-table checker. This is not independent human peer review.
+
+- **Sagar Thakrar / @thakrarsagar, PR738**: Gaussian E8 geometry, full flat-pair
+  weighted-clique certificate, floor40 and conditional three-stage budget.
+  Six files under vendor/pr738 are retained verbatim at
+  `9671c5d72f3119ba26f3774f40aa7130c67bcf77`, with their original metadata.
+- **Alexander Templeton / @azide0x37, PR785**: conditional transcript injection
+  and explicit per-bit nonlinear pricing model, originally for Hurwitz E8.
+- **Michael Fischler / @shiftybitshiftr, PR814**: the composition of that
+  argument with a general nonorthogonal clique certificate, unequal demands,
+  concentration inequality and nonlinear controls for Eisenstein E8.
+  The analogous composition here is credited and no method-priority claim is made.
+- **Joel Pulikkan / @GamingPuzzled, PR620**: Gaussian geometry and asymmetric
+  decoder question; **Douglas R. Colkitt / @Mister-Meeseeks, PR703**:
+  predecessor averaged-clique method; **DreamingOfClouds, PR446/PR595**:
+  pairing-rank and conditional deficit accounting. Their retained source credit
+  remains in PR738's original files.
+- **@chinmayarvind23, PR770** and **William Lawyer / @WilliamLawyer, PR868**:
+  distinct Gaussian clique-certificate ceilings. Their pending implementations
+  and ceilings are not dependencies or composed savings here.
+- The accepted construction remains **Jeremy Kothe's PR799**, **Chafik
+  Boukhalfa's PR741**, **DreamingOfClouds' PR589**, **eumemic's PR555** and their
+  retained source-gauge/compiler/analytic lineage.
+
+The original predecessor proof documents are retained under sources/ with
+exact source heads and hashes in SOURCES.json. New material and the retained
+PR files follow the repository's **Apache-2.0** license. No upstream/ file is
+changed. No literature-wide priority or official OpenAI endorsement is claimed.

research/gaussian-nonlinear-copy-floor/OVERLAP.json

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+{
+  "checked_utc": "2026-10-13 10:16:34 UTC",
+  "repository": "CrocSwap/integer-mult-bounds",
+  "base_commit": "f567884aeb8851b6e794af1184119a3bfbe1e631",
+  "pins": [
+    {
+      "pr": 738,
+      "title": "Scoped negative result: Gaussian E8 copy floor 40 excludes three stages",
+      "head": "9671c5d72f3119ba26f3774f40aa7130c67bcf77",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/738",
+      "role": "dependency"
+    },
+    {
+      "pr": 785,
+      "title": "Scoped negative result: Hurwitz copy floor for fixed-support nonlinear messages",
+      "head": "83e78085ae9c110a34bff87e71387292d85e47c0",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/785",
+      "role": "dependency"
+    },
+    {
+      "pr": 814,
+      "title": "Research: Eisenstein nonlinear message copy floor 22b under explicit width pricing",
+      "head": "d91c5152b314391406b0ec792b6765a5cf0af2f1",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/814",
+      "role": "dependency"
+    },
+    {
+      "pr": 770,
+      "title": "Research: Gaussian E8 weighted maximal-clique ceiling 40 and independent replay",
+      "head": "48d027a664288ea1d4e987de63cb79588b8b936b",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/770",
+      "role": "related, no code or numerical premise imported"
+    },
+    {
+      "pr": 868,
+      "title": "Research: Gaussian E8 all-clique certificate ceiling is 40 (no new kappa)",
+      "head": "54cbbea75b587bdf43a1c123e52220f936641d6f",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/868",
+      "role": "related, no code or numerical premise imported"
+    }
+  ],
+  "focused_query": "Gaussian nonlinear",
+  "focused_results": [
+    {
+      "pr": 785,
+      "title": "Scoped negative result: Hurwitz copy floor for fixed-support nonlinear messages"
+    },
+    {
+      "pr": 679,
+      "title": "Scoped negative result: volume-aware selector batching of complex children"
+    },
+    {
+      "pr": 508,
+      "title": "Conditional kappa 0.001372554837726243: coordinated gauge collapse with retimed asynchronous whole owners"
+    }
+  ],
+  "recent_open_prs": [
+    {
+      "pr": 887,
+      "title": "[Lean] Prove reserved-scratch echo bounds and equality family (no new kappa)"
+    },
+    {
+      "pr": 886,
+      "title": "Scoped negative result: PR589's bit word is exactly frame-optimal (no new kappa)"
+    },
+    {
+      "pr": 885,
+      "title": "[Lean] Prove the selected PR799 native Real moment bound"
+    },
+    {
+      "pr": 884,
+      "title": "Research construction: R439 frame-521 block, 47 to 31 ADDs (no new kappa)"
+    },
+    {
+      "pr": 882,
+      "title": "Research construction: seven grid-preserving JP8 circuits save 104 primitives per orientation (no new kappa)"
+    },
+    {
+      "pr": 883,
+      "title": "Research construction: four-primitive X4 preconditions save 784 per orientation (no new kappa)"
+    },
+    {
+      "pr": 669,
+      "title": "Research: prove higher-target star-code hierarchies and decoder geometry"
+    },
+    {
+      "pr": 881,
+      "title": "Independent verification: PR869's U8 word and \u03ba with a code-disjoint checker (no new kappa)"
+    },
+    {
+      "pr": 880,
+      "title": "Research/r439 block1 schedule seed8"
+    },
+    {
+      "pr": 879,
+      "title": "Independent verification: exact synthetic-transform physical layouts (no new kappa)"
+    },
+    {
+      "pr": 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"
+    },
+    {
+      "pr": 878,
+      "title": "[Lean] Verify selected PR589 B boundaries and XOR interfaces"
+    },
+    {
+      "pr": 877,
+      "title": "Research audit: quartic precision for balanced dirty cyclic inverses (no new kappa)"
+    },
+    {
+      "pr": 876,
+      "title": "Scoped negative result: simultaneous full pair/triple exchanges do not beat SW4 (seed 29)"
+    },
+    {
+      "pr": 860,
+      "title": "Research construction: signed CK reuse saves 926 primitives"
+    },
+    {
+      "pr": 875,
+      "title": "Scoped negative result: classify the E8 rank-five boundary at 36 punctures"
+    },
+    {
+      "pr": 874,
+      "title": "Research audit: X4 profile changes add, ideal exponent gains do not (no new kappa)"
+    },
+    {
+      "pr": 873,
+      "title": "Research construction: shorten R439 phase-B block 508 from 37 to 30 ADDs (no new kappa)"
+    },
+    {
+      "pr": 872,
+      "title": "[Lean] Packed Clifford representation bridge and a source-bound CK child"
+    },
+    {
+      "pr": 871,
+      "title": "Tooling: exact modular rank fast path for historical joint-frame verification"
+    },
+    {
+      "pr": 870,
+      "title": "Conditional \u03ba = 0.001661956299899884: PR858's sixteen-replica owner controller on the U8 word"
+    },
+    {
+      "pr": 869,
+      "title": "Conditional \u03ba = 0.001661948695165034: eight triangle-hybrid B deliveries in block 0 on PR799's word"
+    },
+    {
+      "pr": 868,
+      "title": "Research: Gaussian E8 all-clique certificate ceiling is 40 (no new kappa)"
+    },
+    {
+      "pr": 867,
+      "title": "Research consolidation: selected-source provenance gap map + 298-row vendored-source re-verification (no new kappa)"
+    },
+    {
+      "pr": 866,
+      "title": "Research audit: CK Horner reversal raises scalar-grid guard from 3 to 5 bits (no new kappa)"
+    }
+  ],
+  "open_issues": [
+    {
+      "issue": 650,
+      "title": "Can we turn on Discussions?"
+    }
+  ],
+  "conclusion": "No overlapping Gaussian nonlinear block-message contribution found in the focused results or most recent 25 open PRs through #887. PR738 is scalar; PR785 and PR814 address distinct Hurwitz and Eisenstein geometries. PR770/#868 optimize the clique-certificate method on scalar Gaussian geometry, not nonlinear block-message scope. This is a bounded metadata overlap check, not an exhaustive semantic audit of every open PR."
+}