Scoped negative result: E8 star-copy ratio cannot improve through 55 punctures (no new kappa)

research/e8-joint-reader-bound/CLAIM.json

@@ -0,0 +1,48 @@
+{
+  "track": "Structural decoder research",
+  "assignment_seed": 46,
+  "random_source": "Python secrets.randbelow(100), operating-system randomness; one draw",
+  "base_commit": "91a2094f2e022930069e8cfdc810a3ea1b81cd09",
+  "started_utc": "2026-10-13T13:26:04.736633+00:00",
+  "claimed_utc": "2026-10-13T13:29:33.805011+00:00",
+  "expected_finish_utc": "2026-10-13T14:06:00+00:00",
+  "time_budget_minutes": 40,
+  "orientation_limit_minutes": 8,
+  "verification_reserved_minutes": 10,
+  "coordination": "No pinned issues returned by GitHub GraphQL; two open issues are unrelated. Claim recorded locally.",
+  "candidates": [
+    {
+      "task": "E8 joint-reader support-union obstruction to simultaneously cheap star readers",
+      "decision": "Chosen: analytic compatibility bound, distinct from single-reader thresholds and the 36-puncture equality census."
+    },
+    {
+      "task": "Adaptive nonlinear Gaussian decoder routing with priced metadata",
+      "decision": "Not chosen: substantial conceptual overlap with PR912 adaptive Hurwitz routing."
+    },
+    {
+      "task": "Higher-target proper-star puncture classification",
+      "decision": "Not chosen: active broad work in PR669 and PR772."
+    }
+  ],
+  "object": "120 real E8 root lines, 9-dimensional binary star reader space; simultaneous rank-constrained reader supports",
+  "hypothesis": "The minimum support union of independent readers and root-flat capacity bounds strengthen the single-reader puncture exclusion.",
+  "method": "Exact root/code census plus a written pair-union inequality; small complete rank-invoice optimization, no random annealing.",
+  "expected_deliverable": "Self-contained scoped structural negative result, exact certificates, independent arithmetic check and negative controls; no kappa claim.",
+  "stopping_rule": "Complete pair inequality and all puncture budgets below reader-space rank loss (56); stop or report narrower valid bound if it fails.",
+  "predecessors": {
+    "631": "fb893b5ee1317c2da3b297e6fe78eca0857d1a76",
+    "875": "7f334e4c749fd83d03feb6c1de4e4cda9534c9dc"
+  },
+  "overlap": "Inspected open PRs through 934 and relevant decoder PRs; PR875 is exact 36-deletion equality/orbit, PR631 single-reader bounds, PR669 proper stars, PR912 nonlinear routing. No matching pair-union claim seen.",
+  "result_update": {
+    "completed_utc": "2026-10-13T13:43:50.758470+00:00",
+    "status": "Submitted scoped structural negative result; no new kappa",
+    "pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/939",
+    "result": "Shared-deletion pair-union constraints extend the real E8 star copy-ratio exclusion to all puncture sets of size at most 55. Necessary relaxed cost bounds are 53 for 36..43, 45 for 44..51, and 44 for 52..55; no attainability claim.",
+    "coverage": "256 parabolic flats, 511 nonzero readers, 130305 distinct pairs, 56 budgets; independent 486200 sorted profile visits; five package tests and predecessor controls pass.",
+    "scope": "Root-only fixed binary labels and additive star copy rank; 56+ punctures and general pairing-rank/nonlinear decoders are outside scope.",
+    "upstream_at_submission": "47481c89fd30a43f8f882eb4b391e89c29273fd0",
+    "upstream_selected_kappa": "1661957774647029/1000000000000000000",
+    "handoff": "README.md gives the single-command replay; PROOF.md supplies exhaustive coverage arguments; VALIDATION.md records independent and inherited checks."
+  }
+}

research/e8-joint-reader-bound/NOTICE.md

@@ -0,0 +1,28 @@
+# Attribution and license
+
+Prepared for Ross Richardson (@RossRichardson), with substantial OpenAI
+Codex assistance in mathematical development, implementation, independent
+computation, proof review and documentation. The independent checker and
+separate review were also AI-assisted; no independent human review is claimed.
+
+New files follow the repository's Apache-2.0 license in ../../LICENSE.
+Retained sources under sources/ are unchanged, with their original author
+and assistance notices. Their exact commits, paths and hashes appear in
+SOURCES.json.
+
+- Chi Zhao / @vectorsss, PR631: the E8 reader model, Weyl/parabolic coverage,
+  exact single-reader thresholds, small-puncture identity and <=35 theorem.
+  His README and verifier are preserved verbatim.
+- Philipp / @mightyOil, PR875: the 36-puncture rank-five equality census,
+  exact orbit and cost. Its README is retained for attribution and scope;
+  our joint-reader inequality does not depend on its implementation.
+- Joel Pulikkan / GamingPuzzled, PR620: the star minimum-basis accounting
+  and earlier decoder/puncture research.
+- DreamingOfClouds, PR595/PR602: corrected format-limit context.
+- eumemic, PR543 and subsequent punctured suppliers: E8 bit construction
+  context, with the earlier community and OpenAI #109 lineage credited
+  by the repository's contributor and upstream notices.
+
+The new contribution is the shared-puncture reader-union constraint,
+its exact root-capacity invoice relaxation and the resulting <=55
+star-ratio exclusion. No literature-wide priority is asserted.

research/e8-joint-reader-bound/OVERLAP.json

@@ -0,0 +1,99 @@
+{
+  "initial_open_count": 724,
+  "submission_open_count": 706,
+  "highest_pr_number_seen": 934,
+  "checked_utc": "2026-10-13T13:39:43.255795+00:00",
+  "pinned_coordination_issue": null,
+  "related_prs": [
+    {
+      "number": 631,
+      "title": "Prove E8 star-decoder puncture thresholds through 35 deleted lines",
+      "headRefOid": "fb893b5ee1317c2da3b297e6fe78eca0857d1a76",
+      "updatedAt": "2026-10-12T23:12:30Z"
+    },
+    {
+      "number": 875,
+      "title": "Scoped negative result: classify the E8 rank-five boundary at 36 punctures",
+      "headRefOid": "7f334e4c749fd83d03feb6c1de4e4cda9534c9dc",
+      "updatedAt": "2026-10-13T09:00:22Z"
+    },
+    {
+      "number": 620,
+      "title": "Research notes (no \u03ba claim): E8 decoder floors are tight; #615 levers exhausted; +1.1e-7 \u03ba owner-map headroom on #617",
+      "headRefOid": "e9cf03bbdf7094b5a83f6dbd1d74bfd77a05fb87",
+      "updatedAt": "2026-10-13T02:36:29Z"
+    },
+    {
+      "number": 669,
+      "title": "Research: prove higher-target star-code hierarchies and decoder geometry",
+      "headRefOid": "7d526020fc368ce4157cd436995c2f4fcf683318",
+      "updatedAt": "2026-10-13T09:34:35Z"
+    },
+    {
+      "number": 715,
+      "title": "Scoped negative result: minimal E8 mixed-port extension is saturated",
+      "headRefOid": "d8ed5c6cf2781d6efa0062a2636e1a2644f96c85",
+      "updatedAt": "2026-10-13T04:41:15Z"
+    },
+    {
+      "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",
+      "headRefOid": "4a97676294f9fa413b65986e9984fddeda71e4cc",
+      "updatedAt": "2026-10-13T09:29:47Z"
+    },
+    {
+      "number": 725,
+      "title": "Scoped negative result: sharp global-star punctures and 67 attaining patterns",
+      "headRefOid": "6eadc4eb4ebc355b13fa36a3138d97a583ea7f37",
+      "updatedAt": "2026-10-13T04:52:28Z"
+    },
+    {
+      "number": 732,
+      "title": "Research note: sharp off-target proper-star puncture threshold",
+      "headRefOid": "80431a74c31e807581f5c2258c87abe2084caacd",
+      "updatedAt": "2026-10-13T04:59:10Z"
+    },
+    {
+      "number": 747,
+      "title": "Research: classify 240-port optimal punctures and certify the all-target threshold",
+      "headRefOid": "aeaf0899179a14644b412e838ede14db967c765e",
+      "updatedAt": "2026-10-13T05:03:15Z"
+    },
+    {
+      "number": 765,
+      "title": "Scoped negative result: tensor E8 basis mixing cannot lower 72^d copy rank",
+      "headRefOid": "d8eaa3db32f76111b39db9b930f347ef30118a28",
+      "updatedAt": "2026-10-13T05:18:29Z"
+    },
+    {
+      "number": 772,
+      "title": "Research: uniform proper-star ranks and all-target puncture thresholds",
+      "headRefOid": "02b59e553649c333072b5dd4dfb97e43942efa14",
+      "updatedAt": "2026-10-13T05:26:08Z"
+    },
+    {
+      "number": 912,
+      "title": "Research/seed42 decoder",
+      "headRefOid": "945b3da1f1dd87cebd456b3a0459601b15f7ea8b",
+      "updatedAt": "2026-10-13T12:00:26Z"
+    }
+  ],
+  "finding": "No matching shared-puncture pair-union extension was found in the complete open PR metadata. PR631 and PR875 pins are unchanged. PR669 studies proper-star observation codes; PR912 studies adaptive Hurwitz routing. PR875 retains the exact rank-five equality classification which this bound does not supply.",
+  "immediate_submission_refresh": {
+    "checked_utc": "2026-10-13T13:42:19.024786+00:00",
+    "highest_pr": 937,
+    "new_since_full_inventory": [
+      {
+        "headRefOid": "b303fed6dfe2066dcd78c0d8ed74d2a3b153ba72",
+        "number": 937,
+        "title": "Finite complex construction: two center shears save 5,562 primitives per invocation (no new kappa)"
+      },
+      {
+        "headRefOid": "0679fb6e1e4c91f573ae07ab1d0ea273b13c74e3",
+        "number": 936,
+        "title": "Finite bit construction: five-wire prefixes save 340 further ADDs beyond PR904 (no new kappa)"
+      }
+    ],
+    "finding": "New bit and complex circuit contributions do not overlap the root-only joint-reader theorem."
+  }
+}