Finite bit construction: coupled R439 helper triples save 140 further ADDs (no new kappa)

research/r439-helper-triples/CLAIM.json

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+{
+  "track": "Bit supplier",
+  "assignment_seed": 12,
+  "random_source": "Python secrets.randbelow(100), operating system randomness",
+  "draw_note": "Earlier unsaved draw output was truncated before inspection; 12 is the recorded assignment draw.",
+  "base_commit": "007664306fff84fbb1c9a1b4053b69f439764034",
+  "claimed_at_utc": "2026-10-13T14:48:47.842229+00:00",
+  "expected_finish_utc": "2026-10-13T15:24:37Z",
+  "expected_verification_start_utc": "2026-10-13T15:14:37Z",
+  "coordination": "GitHub GraphQL pinnedIssues returned an empty list; local claim. Open issues 650 and 913 are not sprint coordination issues.",
+  "candidates": [
+    {
+      "task": "Replace a PR926 helper pair plus an unmatched helper by a coupled GL(3,2) basis",
+      "decision": "chosen; overlapping helper changes are outside the PR941 disjoint-pair floor"
+    },
+    {
+      "task": "Full hosted adoption of PR926 semantic compensation",
+      "decision": "too broad for this bounded run"
+    },
+    {
+      "task": "R439 phase-B frame factorization",
+      "decision": "overlaps PRs 884, 891, 904, 908, 914, 923, 925, 936, 952"
+    }
+  ],
+  "object": "Frozen PR915 target basis inside PR926 R439 D compensation, keeping the remaining word fixed",
+  "method": "BFS all 168 GL(3,2) maps under six directed CNOT generators. For each of 192 PR926 helper pairs and 55 unmatched helpers, score every shortest representative with both preparation and restoration. One seed-12 ordered greedy disjoint pass, with literal positive-envelope guards. No restart or general optimum claim.",
+  "deliverable": "One finite circuit candidate or scoped negative result, reproducible census, exact all-column boundaries and negative controls",
+  "overlap": "713 open PRs scanned; PR941 certifies disjoint helper matching, excluding overlapping bases. PR952 synthesizes phase-A six-wire prefixes. No helper-triple compensation claim found.",
+  "selected_kappa": "1661957774647029/1000000000000000000",
+  "selected_source": "PR890, with unchanged PR589 bit supplier",
+  "result": {
+    "status": "finite bit construction, no new kappa",
+    "completed_at_utc": "2026-10-13T15:05:08.697112+00:00",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/965",
+    "implementation_commit": "82f2b20fff8ecc869dd0994721b77652c6c5063a",
+    "complete_ADDs": 11840,
+    "saved_beyond_PR926": 140,
+    "accepted_triples": 40,
+    "scores": 1774080,
+    "verification": "Full receipt equality, independent group/census, arbitrary-input restoration, owning checks, native legality and 5/9/11-stage replay passed; 144 bridge controls rejected. Selected-record check passed.",
+    "remaining": "Semantic D supplier admission, complete hosted emission/audit and invoices, outer assembly; inherited theorem assumptions remain.",
+    "overlap_refresh": "Queue through PR962 plus exact helper-triples search with zero matches before submission; no pinned coordination issue.",
+    "labels": "codex and codex-automation are not available in the upstream label catalog."
+  },
+  "verification_began_utc": "2026-10-13T14:55:12Z",
+  "negative_result_review": [
+    "research/experiment-log/negative-searches/factored-retiming/README.md: different word and retiming objective",
+    "research/experiment-log/campaign-100/algebraic-word-construction.md entry 45: proposal not evidenced"
+  ]
+}