Research audit: CK Horner reversal raises scalar-grid guard from 3 to 5 bits (no new kappa)

research/dyadic-fractional-grid/CLAIM.json

@@ -0,0 +1,105 @@
+{
+  "assignment_seed": 60,
+  "drawn_at_utc": "2026-10-13T07:35:04.000978+00:00",
+  "claimed_at_utc": "2026-10-13T07:46:09.123523+00:00",
+  "track": "adversarial mathematical audit",
+  "base_commit": "f567884aeb8851b6e794af1184119a3bfbe1e631",
+  "candidate_selection": "60 modulo 3 = 0",
+  "candidates": [
+    {
+      "object": "Fixed-point fractional-grid transport for PR837 bidirectional Horner",
+      "method": "Exact 2-adic valuations of every coefficient and whole-program primitive prefix; integer-grid counterexamples",
+      "chosen": true
+    },
+    {
+      "object": "Numerical frame-search optimality in PR815",
+      "method": "Exact dual/interval proof audit",
+      "chosen": false,
+      "reason": "The source explicitly discloses missing exact dual certificates; a further solver audit would need a separate larger scope"
+    },
+    {
+      "object": "Global replica-prefix accounting",
+      "method": "Maximum-replica norm induction",
+      "chosen": false,
+      "reason": "PR821 already supplies this refinement"
+    }
+  ],
+  "statement": "Exact endpoint equality and positive magnitude-prefix bounds do not alone establish preservation of the old fixed-point fractional grid. Quantify the extra grid depth for the actual PR837 choices and all six pinned programs. This audits an explicitly unresolved precision obligation, not a claim of a defect in the selected construction.",
+  "method": "Prove the necessary/sufficient denominator-depth criterion for dyadic linear prefix maps. Census all 962 coefficients, replay all six original and replacement programs and produce exact integer-rounding witnesses with corrective guard bits.",
+  "domain": "The scalar primitive projections of fixed #626 CK/JP8 and #741 SW4 programs bound in PR837, both orientations, arbitrary native/private input columns. Fixed dyadic grids; exact intermediate representability, not physical frame/phase evaluation or all-size numerical stability.",
+  "stopping_rule": "Complete this finite census and replay; no compiler integration, exponent repricing or exploratory search beyond the stated domain",
+  "expected_finish": "Approximately 90 minutes from the claim; final quarter for validation and handoff",
+  "coordination": "Local claim; only issue #650 requested Discussions at previous refresh; no sprint coordination issue available.",
+  "related_prs": {
+    "837": {
+      "title": "Research: bidirectional Horner saves 312 SW4 primitives per orientation (no new kappa)",
+      "head": "0a2977195efc8fb2a918fbfb694ec8d294387f08",
+      "author": "bitplane"
+    },
+    "830": {
+      "title": "Research: transposed JP8 work saves 32,810 backward primitives (no new kappa)",
+      "head": "6a0b8d55bb8026f8b6d708ae07740453b41c872f",
+      "author": "Ryan-Haines"
+    },
+    "821": {
+      "title": "Research audit: 286-to-160-bit prefix estimate for pinned #626 (no new kappa)",
+      "head": "6b832a6ba4dce8dd6e2fb0897dd4543364b932f8",
+      "author": "Brodee042"
+    },
+    "815": {
+      "title": "Research: exact frame search certifies #741 and #626 providers frame-optimal (rediscovers #741; negative result)",
+      "head": "d8c8b40ab0a95b6d77389e6726d86dddb60fb53c",
+      "author": "Rohansguliani"
+    },
+    "764": {
+      "title": "Research: sharp inverse-square rounding bound for cyclic scans",
+      "head": "983d66f0f2e48ee500ec7eee2da9244c001c5064",
+      "author": "cbethin"
+    },
+    "751": {
+      "title": "Research: save 19,688 JP8 backward primitives with reverse Horner (no new kappa)",
+      "head": "7a1a3a319da359ec8b6e83230a7fcf7733fac8e5",
+      "author": "thakrarsagar"
+    },
+    "734": {
+      "title": "Research: prefix-bounded signed-Horner circuits for CK and JP8 (no new kappa)",
+      "head": "ba76ba3321d000c8996b0b254bcf0d7260e1bbb6",
+      "author": "AllStars101-sudo"
+    }
+  },
+  "initial_open_pr_count": 648,
+  "status": "submitted",
+  "final_overlap_check": {
+    "at_utc": "2026-10-13T08:30:13.943767+00:00",
+    "open_pr_count": 659,
+    "latest_number": 864,
+    "upstream_head": "f567884aeb8851b6e794af1184119a3bfbe1e631",
+    "pr837_head_unchanged": true,
+    "finding": "No overlapping fractional-grid audit found; new cyclic-inverse precision, signed CK reuse and X4 frame-optimality work has distinct scope."
+  },
+  "result": {
+    "statement": "CK forward scalar-projection fractional guard rises from 3 to 5 bits under PR837; shared forward/backward guards remain CK=8, JP8=27, SW4=19.",
+    "coefficient_count": 962,
+    "candidate_circuits_checked": 3842,
+    "extra_grid_coefficients": 18,
+    "complete_traces": 12,
+    "scalar_primitives_crosschecked": 1016110,
+    "local_undercharged_counterexamples": 24,
+    "whole_program_counterexample": "CK forward, native basis column 16: endpoint errors at guards 3 and 4, exact at guard 5.",
+    "new_kappa": false,
+    "precision_scope": "Fixed dyadic-grid representability of the scalar projection; physical frame/phase/recursive realizations and integer overflow outside scope."
+  },
+  "validation": {
+    "python_versions": [
+      "3.12.3",
+      "3.14.4"
+    ],
+    "unit_tests": 9,
+    "package_controls": 6,
+    "receipt": "EXPECTED.json",
+    "details": "VALIDATION.md",
+    "all_local_checks": "passed"
+  },
+  "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/866",
+  "submitted_at_utc": "2026-10-13T08:32:40.046289+00:00"
+}