Finite bit construction: certify R439 matching floor and save 31 further ADDs

research/r439-helper-matching/CERTIFICATE.json

@@ -0,0 +1,21 @@
+{
+  "B": 10548832,
+  "D_adds": 5729,
+  "F": 70083,
+  "baseline_sha256": "5642fd0e35a1acc11acff8d0c08350c1617e95f310d4d35ad63a651f9eeeba0b",
+  "candidate_sha256": "06808b6a98689bba6095fd96c0602fa585dc114bf33073f30acce34b1fdff18d",
+  "floor_word_sha256": "8948c509341735070c46de5ecb723f8e4294c22b14470ad7c3140875ab10971f",
+  "format": "r439-helper-matching/1",
+  "greedy_sha256": "fdb1a0dfafe5392e01fb87f5813737db0f15682c5cb98fc224d4d4cdbc806dd2",
+  "helper_pairs": 199,
+  "middle_weight": 4719,
+  "native_ADDs": 11949,
+  "nine_stage_prefix_bits": 192,
+  "nomination_sha256": "cc74c21e757542d73ffb82b2a58a69a31dbfa4260916426f52dc998dbb527ca4",
+  "parent_sha256": "6aec2c6f91c87a7440af10cdeb90b8814501224a86de14d4033ae3ffa00899da",
+  "payload_bits": 101,
+  "saved_beyond_greedy": 31,
+  "saved_beyond_parent": 1259,
+  "seed": 4,
+  "target_shears": 306
+}

research/r439-helper-matching/CLAIM.json

@@ -0,0 +1,84 @@
+{
+  "assignment_seed": 4,
+  "drawn_at_utc": "2026-10-13T13:11:39.515987+00:00",
+  "track": "bit supplier",
+  "source": "secrets.randbelow(100), OS randomness",
+  "pass": 12,
+  "base": "91a2094f2e022930069e8cfdc810a3ea1b81cd09",
+  "branch": "research/pass12-bit-seed04",
+  "status": "submitted",
+  "claimed_at_utc": "2026-10-13T13:17:36.187221+00:00",
+  "candidate_selection": "Seed 4 modulo 3 selects candidate 1. Seed 4 fixes secondary nomination ordering.",
+  "candidates": [
+    {
+      "object": "Restored decoder stars in the selected R439 full-frame A totals",
+      "chosen": false,
+      "reason": "PR708/753 cover the predecessor mechanism; a new R439 transplant is less informative than closing the exact matching gap."
+    },
+    {
+      "object": "Exact disjoint helper matching around the fixed PR915 target basis, including the 192-bit prefix budget",
+      "chosen": true,
+      "method": "Certify the unrestricted pairing cost with integer vertex/odd-set prices; nominate one seed-4 matching and one lexicographic forward-cost matching, then exhaust all one-pair deletions of nominated optima if needed."
+    },
+    {
+      "object": "Reduce the selected frame267 fixed positive-transfer circuit",
+      "chosen": false,
+      "reason": "Fresh PR925 supplies a complete 12-ADD minimum in that class; larger computation alone would reopen a closed search."
+    }
+  ],
+  "statement": "Improve and bound the disjoint helper-pair class around the exact frozen PR915 target basis. Compare selected PR589, PR915, PR926 and the new fully charged candidate separately.",
+  "domain": "All 439*438/2 = 96,141 unordered helper pairs, both orientations; 1,885 positive undirected edges. At most three maximum-weight matching nominations total, including the completed lexicographic calibration, followed by all one-pair deletions of those nominations. No target-basis changes or overlapping helper shears.",
+  "optimistic_complete_cost": "The preliminary maximum-weight pairing saves 1,260 ADDs beyond PR915, giving D=5,728 and a complete word of 11,948. It has F=73,603, B=10,518,760 and a 193-bit nine-stage bound, so it is not admitted. PR926 costs 11,980 and has a 192-bit bound.",
+  "admission": "Recompute every combined word. Require 64*F^3*B^2 < 2^104 and 2^18*F^5*B^4 < 2^192. No inherited parent bound, free restoration or addition of standalone savings.",
+  "stopping_rule": "Complete the matching certificate and the declared bounded nomination/deletion family. If no admitted improvement exists, retain the exact floor and explicit budget obstruction as scoped evidence; do not claim global precision-constrained optimality.",
+  "expected_finish": "Approximately 90 minutes, with the final quarter reserved for verification and handoff.",
+  "coordination": "No pinned sprint coordination issue exists; open non-PR issues are #650 and #913. Claim recorded locally.",
+  "overlap": {
+    "open_prs": 720,
+    "through_pr": 929,
+    "related": "PR716 and PR817 certify R420 target matchings; PR926 uses a greedy R439 helper matching and explicitly leaves matching optimality open. PR923/925 concern separate phase-A/B blocks. No matching certificate for this frozen R439 matrix was found."
+  },
+  "predecessors": {
+    "915": "e9daefe320a0043000bd9746664ed02c3287d056",
+    "926": "0f216a345c37bc71cc0e22030ef11ec31b26a69e",
+    "817": "3147cac35c659152d36db1e0e60b9ce4b152c008",
+    "716": "afeb452f58ff0cbf109172335e2ba282aac3dcde"
+  },
+  "scope": "Finite bit construction and exact restricted pairing bound. Semantic D acceptance and full hosted reconstruction/invoice remain integration obligations. No new kappa, unrestricted optimum or measured runtime claim.",
+  "completed_at_utc": "2026-10-13T13:50:49.944418+00:00",
+  "publication_base": "47481c89fd30a43f8f882eb4b391e89c29273fd0",
+  "result": {
+    "pr": 941,
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/941",
+    "mathematical_head": "34f7eff4e2d4ab7c249a6505bc04a2d6aa41dea9",
+    "complete_ADDs": {
+      "selected_PR589": 24305,
+      "fixed_PR915": 13208,
+      "greedy_PR926": 11980,
+      "candidate": 11949,
+      "arithmetic_floor": 11948
+    },
+    "D_ADDs": 5729,
+    "helper_pairs": 199,
+    "middle_weight": 4719,
+    "saving_beyond_greedy": 31,
+    "F": 70083,
+    "B": 10548832,
+    "local_payload_bits": 101,
+    "nine_stage_prefix_bits": 192,
+    "exact_bound": "439 doubled vertex prices and 19 odd-set prices cover all 96,141 edges; primal and dual saving equal 1,260. The precision-constrained class minimum lies in [11,948, 11,949].",
+    "bounded_search": "Three arithmetic optima fail the nine-stage cap. All 598 single-pair deletions are priced; 17 of 601 total words fit. No exclusion of every arithmetic optimum is claimed.",
+    "validation": "Complete receipts match on ordinary CPython 3.14.4 and isolated optimized read-only CPython 3.12.3. All five words pass original endpoints and native 5/9/11-stage local checks; 240 bridge controls, 19 local controls, 8 package tests pass. The floor calibration separately fails the nine-stage cap. Optional nomination reproduces every field.",
+    "integration": "Requires semantic D acceptance, changed whole-hosted emission/audit, complete finite/precision invoices and outer assembly. No new kappa or unrestricted optimum.",
+    "hosted_CI": "Separate from local validation; no hosted success claimed."
+  },
+  "final_refresh": {
+    "upstream": "47481c89fd30a43f8f882eb4b391e89c29273fd0",
+    "open_prs": 708,
+    "through_pr": 937,
+    "gist_revision": "4180bf0d4045ffdcd12d75bb1fec91c234420162",
+    "source_preservation": "All 14 consumed source files match the new main byte for byte; selected-record checks pass before and after rebase.",
+    "selection": "Main advanced to PR890, kappa 0.001661957774647029, retaining PR589. This contribution does not claim that improvement.",
+    "overlap": "PR933 concerns gate order/reframing with fixed D; PR936 extends phase-A prefix synthesis. Neither is composed here."
+  }
+}