Research: all-puncture E8 star decoder exclusion and p=56 classification (seed 49, no new kappa)

research/e8-star-all-punctures-seed49/CLAIM.json

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+{
+  "track": "40-49: Structural decoder research",
+  "seed": 49,
+  "base_commit": "ce7ad1b6ab09452c3478723a2e96ed5ff212dc08",
+  "candidate_tasks_evaluated": [
+    {
+      "candidate_index": 1,
+      "selected": true,
+      "selection_rule": "seed 49 -> 49 % 3 == 1 (1-indexed)",
+      "description": "All-puncture (0 <= p <= 119) E8 star label-decoder ratio exclusion, exact p=56 two-orbit dimension-loss classification, and sharp k-reader subspace support-union hierarchy U_1..U_9 = (56,84,100,108,112,116,118,119,120), extending PR #631, PR #875, and PR #939."
+    },
+    {
+      "candidate_index": 2,
+      "selected": false,
+      "description": "Coded coordinate-star factorizations for the five-port quadratic decoder at p=6 (v=192), extending PR #958 and PR #1046."
+    },
+    {
+      "candidate_index": 3,
+      "selected": false,
+      "description": "First cost-six puncture threshold for orthogonal E8 root pairs in the B14 model, complementing PR #1020."
+    }
+  ],
+  "investigated_object": "Real E8 root-only star label-decoder cost C_star(P)/(120-p) across all puncture sizes 0 <= p <= 119 and the 255 weight-56 dimension-loss puncture sets at p=56",
+  "method": "Live-quotient matroid rank reduction on C/K_P, W(E8) two-orbit classification of the 255 weight-56 codewords, 5-orbit k=3 subspace union census, k=4 hyperplane-incidence inequality, k=5..9 annihilator affine-hyperplane bound, and exact optimization over all 24,310 sorted 9-rank profiles across 0 <= p <= 119",
+  "deliverable": "research/e8-star-all-punctures-seed49/ with verify.py, independent_check.py, test_package.py, CERTIFICATE.json, PROOF.md, README.md, SOURCES.json, OVERLAP.json, NOTICE.md, and VALIDATION.md",
+  "status": "completed",
+  "pr": 1171,
+  "pr_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1171",
+  "result_summary": "Proved C_star^live(P)/(120-p) = C_star(P)/(120-p) >= 63/111 for all 0 <= p <= 119 (equality only at p=9), classified the 255 p=56 dimension-loss puncture sets into two W(E8) orbits of exact star costs 57/64 (size 135) and 50/64 (size 120), and certified the sharp subspace support-union hierarchy U_1..U_9 = (56,84,100,108,112,116,118,119,120). No new kappa claimed."
+}

research/e8-star-all-punctures-seed49/NOTICE.md

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+# Notice, Attribution, and AI Assistance Disclosure
+
+## License
+
+This package (`research/e8-star-all-punctures-seed49/`) is licensed under the **Apache License, Version 2.0**, matching the upstream `CrocSwap/integer-mult-bounds` repository.
+
+## Predecessor Attribution
+
+This work builds directly on and retains byte-identical copies of predecessor artifacts in `sources/` (verified by SHA-256 and Git blob SHA-1 in `SOURCES.json`):
+
+1. **Chi Zhao** (`@chizhao`, PR #631, commit `fb893b5ee1317c2da3b297e6fe78eca0857d1a76`):
+   - Retained files: `sources/pr631/README.md`, `sources/pr631/verify.py`.
+   - Established the $120$ positive $E_8$ root lines, the $9$-dimensional binary reader code $C \subset \mathbb{F}_2^{120}$, the $256$ standard parabolic flats, the single-reader puncture thresholds $\delta_d$, and the exclusion of star ratio $< 63/111$ for $0 \le p \le 35$.
+2. **Philipp** (`@mightyOil`, PR #875, commit `7f334e4c749fd83d03feb6c1de4e4cda9534c9dc`, `research/e8-rank5-boundary`):
+   - Retained file: `sources/pr875/README.md`.
+   - Established the two-reader support-union bound $|\operatorname{supp}(c_a) \cup \operatorname{supp}(c_b)| \ge 84$ resolving the $p = 36$ rank-5 boundary.
+3. **Ross Richardson** (`@RossRichardson`, PR #939, commit `3a8ec54d62fb8824c658dc7ed356f99423cac8cf`, merged as `c9b187382b2d370e21e866fa4070a7bfceaf86ad`, `research/e8-joint-reader-bound`):
+   - Retained files: `sources/pr939/README.md`, `sources/pr939/PROOF.md`.
+   - Generalized the pairwise joint-reader capacity inequality $M_a + M_b \ge 84 - p$ to $0 \le p \le 55$ and identified the $p = 56$ binary label dimension-loss boundary.
+
+## Disclosure of Substantial AI Assistance
+
+This research note, mathematical proof, primary verifier (`verify.py`), independent checker (`independent_check.py`), package test suite (`test_package.py`), and certificate (`CERTIFICATE.json`) were prepared by `@3xcalibur-tech` with substantial AI assistance from **Antigravity (Google DeepMind / Gemini)**.

research/e8-star-all-punctures-seed49/OVERLAP.json

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+{
+  "base_commit": "ce7ad1b6ab09452c3478723a2e96ed5ff212dc08",
+  "checked_through_open_pr": 1169,
+  "coordination_issues_checked": [
+    650,
+    913
+  ],
+  "related_merged_prs": [
+    {
+      "pr": 631,
+      "author": "Chi Zhao (@chizhao)",
+      "commit": "fb893b5ee1317c2da3b297e6fe78eca0857d1a76",
+      "scope": "E8 parabolic flat census and single-reader puncture thresholds for 0 <= p <= 35",
+      "relationship": "Extended here from p <= 35 (and p <= 55 in PR #939) to all 0 <= p <= 119; retained in sources/pr631/ and replayed in test_package.py."
+    },
+    {
+      "pr": 875,
+      "author": "Philipp (@mightyOil)",
+      "commit": "7f334e4c749fd83d03feb6c1de4e4cda9534c9dc",
+      "scope": "Pairwise reader support union >= 84 at the p = 36 rank-5 boundary",
+      "relationship": "Generalized here to the sharp all-dimension subspace support-union hierarchy U_1..U_9 = (56,84,100,108,112,116,118,119,120)."
+    },
+    {
+      "pr": 939,
+      "author": "Ross Richardson (@RossRichardson)",
+      "commit": "3a8ec54d62fb8824c658dc7ed356f99423cac8cf",
+      "merge_commit": "c9b187382b2d370e21e866fa4070a7bfceaf86ad",
+      "scope": "Pairwise joint-reader capacity bound M_a + M_b >= 84 - p for 0 <= p <= 55, stopping at the p = 56 rank-loss boundary",
+      "relationship": "Directly resolves PR #939's p = 56 stopping boundary (complete two-orbit classification of all 255 weight-56 puncture sets, exact costs 57/64 and 50/64) and extends the 63/111 exclusion across the remaining range 56 <= p <= 119 where k <= 2 alone fails at 43 budgets."
+    }
+  ],
+  "related_open_prs_checked": [
+    {
+      "pr": 1139,
+      "title": "Research: sharp ten-coordinate threshold for doubly degenerate triple shared nodes",
+      "overlap": "none (concerns doubly degenerate triple shared nodes in complex/leaver geometry, not E8 star label-decoder punctures)"
+    }
+  ],
+  "overlap_status": "no_overlap_found"
+}