Research consolidation: exact rational numerator and residue contracts

research/rational-residue-scope/CLAIM.json

@@ -0,0 +1,47 @@
+{
+  "task_id": "pass22-consolidation99-exact-rational-residue-scope",
+  "seed": 99,
+  "track": "research consolidation",
+  "catalogue_card": "scope-navigation",
+  "base_commit": "1b59b624d21924f8e3537cdc1ac52d3be6eda2fe",
+  "claimed_at_utc": "2026-10-13T20:01:17.007812+00:00",
+  "expires_at_utc": "2026-10-13T22:01:17.007812+00:00",
+  "instruction_revision": "6d8cffe3dcb0680b68ae8a9d79b98e6e719f1f34",
+  "selection_note": "The legacy seed99 draw preceded detection of the updated gist. Keep the already assigned consolidation task; use current repository coordination and scope guidance.",
+  "candidates": [
+    {
+      "question": "Reconcile PR1135 rational numerator width with PR1159 binary residue backend",
+      "decision": "chosen: explicit unit-denominator/integral-output boundary, with a source-bound application and failure witnesses"
+    },
+    {
+      "question": "Retained PR1015 B-block attribution",
+      "decision": "defer: PR1181 already supplies the retention receipt"
+    },
+    {
+      "question": "PR279 parent-source inventory",
+      "decision": "defer: PR1190 already supplies the complete Git-tree reconstruction"
+    }
+  ],
+  "predecessors": {
+    "PR1057": "78a062df1dcab2bffea5ff4d8243f3da6e465414",
+    "PR1135": "4c35687d7c0da8e6cf33f17e418ecf31c95ff3ad",
+    "PR1159": "f38bfe5da0bed21f42ce5251d23491a56519d7c4"
+  },
+  "scope": "Compare three exact contracts: arbitrary additive rational echo, common-denominator numerator storage, and quotient-register storage. Extend only the algebraic interpretation of PR1159 to reduced odd-denominator rational matrices whose completed output is integral and has a strict signed bound. Rounded leaves and nonintegral output decoding are explicitly excluded; even reduced denominators are not units modulo 2^w.",
+  "method": "Prove the localization homomorphism and source-bound applicability table; run a centrally rescaled rational version of the frozen 52-factor PR1159 program with alternating 1/3 and3 factors, unchanged integral full product, and all literal modular primitives. Independent Fraction-prefix and dirty-basis replay; exact residue inverses and full additional coefficient-preparation invoice. Bounded small odd-denominator/matrix cases, failures for nonunit denominator, false integrality, wrapping, rounded substitution and bad inverses.",
+  "budget": "About 70 minutes from19:54 UTC; at least final25% validation/packaging; no broad rational reconstruction or rounded repair search. Stop on a failed homomorphism or unpaid interface; at most one bounded pivot.",
+  "optimistic_complete_cost": "Inherited1376 calls, five length-two data arrays and four private work registers. If all coefficient denominators are units, the kernel stays52292 commands and56-bit data for the same integer endpoint bound. Price inverse preparation, every coefficient conversion, checks, input/output conversion, control, routing and all original descriptor storage separately. No q^D initialization for residue data; no claim it removes PR1135 cost for its different exact numerator representation.",
+  "coordination": "Read Discussions1163/1166/1167 and all active threads; no overlapping claim. Open PRs through1190, including1159/1135/1164 and1181/1190. Public scoped claim authorized by updated user gist.",
+  "status": "completed; submitted",
+  "attribution": "Gareth Davidson with substantial OpenAI Codex assistance; Ali Romman PR1135, Davidson PR1057/1159 and their credited source lineage; modular localization is classical, no priority claim.",
+  "completed_at_utc": "2026-10-13T20:38:24.272420+00:00",
+  "submission_base": "49b3157d1d89adcef16df8be98445451672be5ba",
+  "mathematical_head": "7961d6ab49181a0cfd5813daccdae89ea904ece6",
+  "pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/1229",
+  "discussion": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1202",
+  "scope_status": "changed; executable comparison broader than original navigation card",
+  "result": "52 rational factors,1376 unchanged calls; exact least prefix denominator9;94-bit sufficient common-numerator data versus56-bit residue data, neither numerator minimum nor runtime comparison;2406 paid preparation commands plus52292 kernel commands; rounded and nonintegral output boundaries excluded; no kappa.",
+  "validation": "Complete Python3.14 and read-only isolated optimized3.12 replay receipts agree. Registered metadata/replay pass;8 package tests and25 selected/source-binding tests pass;12 mathematical/admission/price controls.",
+  "receipt_sha256": "2c63ba9c68e4537a49815af076b9097ae49c3f5a7ca66229710455b9d3aed6e2",
+  "final_overlap": "20:35 UTC;836 open PRs through1228,6 Discussion threads and comments,324 local records; complete pagination,no warnings. Relevant predecessor heads unchanged; declared search coverage is not a novelty certificate."
+}