Research: exact two-register CK coefficient frontier (no new kappa)

research/complex-restored-source29/CLAIM.json

@@ -0,0 +1,69 @@
+{
+  "track": "complex supplier",
+  "assignment_seed": 29,
+  "random_source": "Python secrets.randbelow(100), operating-system randomness; drawn once",
+  "started_utc": "2026-10-13T16:31:24Z",
+  "claimed_utc": "2026-10-13T16:40:34Z",
+  "base_commit": "2921874911956718fcaaaf9396fe8267b3cfa9f0",
+  "selected_at_base": {
+    "source_pr": 942,
+    "kappa": "1661960547713947/1000000000000000000",
+    "review": "docs/research/community-batch952-review.md",
+    "construction": "research/complex-t37-owners/PROOF.md"
+  },
+  "candidate_tasks": [
+    {
+      "task": "Relocate dyadic scales in the historical contracted coordinate-total factory",
+      "decision": "Excluded: complex-factory-scale-frontier27 already closes the fixed ADD-order scale class."
+    },
+    {
+      "task": "Share coefficient preparation across consecutive X4 reads",
+      "decision": "Excluded: PR945/975 and PR999 already cover nearby pair/four-source and bounded target-accumulation mechanisms."
+    },
+    {
+      "task": "Synthesize restored two-register CK scalar shears without using coefficient scratch",
+      "decision": "Chosen: extends PR883's two-register alphabet from one precondition block to CK's complete coefficient inventory; allows temporary source/target mutation and proves bounded word-metric minima without magnitude pruning."
+    }
+  ],
+  "scope": {
+    "provider": "Historical PR626 CK; seed odd selects CK rather than JP8",
+    "coefficients": "All 103 distinct positive absolute coefficients occurring in the two pinned CK programs; signs covered by conjugation and literal replay",
+    "alphabet": "Signed unit additions in both directions; negate, double, halve on either of T,S; no scratch, free swap, copy, or nonunit primitive",
+    "endpoint": "(T,S,W) -> (T+q*S,S,0); one private W clear is charged in addition to the two-register word",
+    "method": "Exact meet-in-the-middle search from the complete radius-six group ball, covering every word through length twelve; separate Fraction-matrix check",
+    "seed_use": "CK provider, cyclic gate traversal order, and selected diagnostic coefficient",
+    "stopping_rule": "Complete the fixed radius-six census and all source coefficients; no timeout-based claim or larger search restart",
+    "preflight": "A radius-four probe on the 37 coefficients with PR999 cost <=8 found candidate savings and established that exact enumeration is inexpensive; no optimality claim made from that probe.",
+    "diagnostic_coefficient": "29/8, from seed numerator 29; present in both CK orientations"
+  },
+  "comparators": [
+    696,
+    734,
+    837,
+    866,
+    882,
+    883,
+    999
+  ],
+  "coordination": "No pinned issue found via GitHub GraphQL; two open issues were unrelated. Local claim, no reservation issue opened. Open PR snapshot and targeted all-state searches inspected through PR1012.",
+  "expected_deliverable": "One exact finite circuit/negative-result package with source pins, shortest-word evidence, literal dirty-input replay, paid costs, precision scope, meaningful mutations, and one focused PR if useful.",
+  "expected_finish_utc": "2026-10-13T17:31:24Z",
+  "verification_reserve": "Final 15 minutes of the one-hour budget",
+  "attribution": "Hanson Sun (@bbMisk), substantial OpenAI Codex assistance; predecessor attribution retained",
+  "status": "completed",
+  "result": {
+    "coefficient_magnitudes": 103,
+    "ball_states": 30576,
+    "exact_minima": 77,
+    "unreached_through_length_12": 26,
+    "strict_improvement_magnitudes": [
+      2,
+      3
+    ],
+    "source_mutation_required_for_improvements": false,
+    "saved_real_primitives_per_ck_orientation": 3124,
+    "selected_frontier_changed": false,
+    "link": "https://github.com/bbMisk/integer-mult-bounds/tree/research/complex-restored-source-seed29",
+    "overlap_refresh_through_pr": 1026
+  }
+}