Scoped negative result: partial K/M face bypass requires four carriers

research/partial-k-face-bypass/CLAIM.json

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+{
+  "track": "complex supplier",
+  "assignment_seed": 24,
+  "seed_source": "Python secrets.randbelow(100), OS randomness",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "started_utc": "2026-10-13T03:27:47Z",
+  "claimed_utc": "2026-10-13T03:34:48.843773+00:00",
+  "expected_finish_utc": "2026-10-13T04:07:47Z",
+  "time_budget_minutes": 40,
+  "orientation_limit_minutes": 8,
+  "verification_and_handoff_reserved_minutes": 10,
+  "object": "Partial raw-leaver bypass of face-copy helpers for mixed K/M coordinate pair (0,2) in the accepted K492/RAW504 construction lineage.",
+  "method": "Exact F2 frame-state scheduling with own reads allowed at arbitrary positions; both signs and nonempty deletion subsets of the two selected-source face copies. Price any feasible schedule including changed source accesses, later face formation, restoration and recursive children before promoting it.",
+  "seed_diversification": "Lexicographically sorted eight mixed pairs; 24 mod 8 selects (0,2). Start sign -1 from (-1,+1)[24 mod 2].",
+  "deliverable": "Scoped research note, reproducible exact checker and finite evidence; no new kappa unless a complete admitted construction is produced.",
+  "candidates_considered": [
+    {
+      "task": "Mixed K/M partial face bypass with movable own reads",
+      "decision": "selected; distinct from full triangles and first-own face/slot sharing"
+    },
+    {
+      "task": "Retired-row basis/gauge changes to free cold endpoints",
+      "decision": "not selected; substantial concurrent overlap with #645/#655/#659/#664"
+    },
+    {
+      "task": "Sharper fixed-dispatch paid-profile/owner ceiling",
+      "decision": "not selected; substantial overlap with #619/#639/#644 and later owner PRs"
+    }
+  ],
+  "coordination": "No pinned issues returned by GitHub GraphQL; the sole open issue was #650 (Discussions). Claim recorded locally; no reservation issue opened.",
+  "overlap_checked": {
+    "622": "accepted full K-triangle construction",
+    "626": "accepted owner repair",
+    "646": "whole signed-root triangle extension",
+    "651": "target/face sharing under own-read-first interface",
+    "645": "factory gauge44",
+    "665": "spectral split recursive interface, distinct"
+  },
+  "status": "completed",
+  "contributor": "Douglas R. Colkitt (@Mister-Meeseeks)",
+  "ai_assistance": "Substantial OpenAI Codex assistance in research, implementation, verification and prose.",
+  "scope_refinement": "The completed obstruction concerns deleting both selected-source face copies simultaneously. Partial one-face deletion masks were not investigated; their mention in the initial method is not a completed-coverage claim. Geometry covers all eight mixed pairs and both signs; bounded scheduling covers both signs of seed-selected (0,2).",
+  "evidence_driven_pivot": "The first relaxed schedule omitted the ordinary M consumer. Restoring its necessary frame cap changed the minimum remaining-packet carriers from two to four. The fully paid attaining control retains 492 helpers and loses at every 0<s<1.",
+  "completed_utc": "2026-10-13T03:57:46.442590+00:00",
+  "result": "Exact four-carrier lower bound for the fixed mixed two-face bypass at all 16 pair/sign cases; complete 2/3-carrier exhaustion for both signs of seed-selected (0,2); a full 492-helper paid control with strictly worse moment for all 0<s<1 and exact 716-column replay in both orientations. No new kappa.",
+  "result_link": "https://github.com/CrocSwap/integer-mult-bounds/tree/research/complex-seed24/research/partial-k-face-bypass",
+  "final_overlap_check": {
+    "open_pr_count": 500,
+    "through_pr": 680,
+    "origin_main": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+    "pinned_coordination_issues": 0,
+    "new_relevant_prs": {
+      "675": "Owner boundary audit, distinct; no production admission defect claimed.",
+      "679": "Selector-volume batching, distinct from fixed face/leaver delivery."
+    },
+    "conclusion": "No matching two-face raw-leaver scope found; #646 and #651 remain credited related work."
+  }
+}