Independent verification: signed packed Gaussian convolution (no kappa claim)

research/gaussian-packed-convolution-audit/CLAIM.json

@@ -0,0 +1,55 @@
+{
+  "track": "independent verification",
+  "assignment_seed": 79,
+  "randomness": "Python secrets.randbelow(100), backed by OS randomness, drawn at session start; not redrawn",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "recorded_at_utc": "2026-10-13T03:59:28.387102+00:00",
+  "candidates": [
+    {
+      "object": "PR612 R420 B-XOR boundary identities",
+      "decision": "not selected; existing Lean/finite coverage and active R420 work"
+    },
+    {
+      "object": "PR489 equation (1), symbolic Gaussian inverse and determinant",
+      "decision": "selected; seed % 3 = 1; all-q integer-polynomial method differs from original rational samples"
+    },
+    {
+      "object": "PR628 prime-power inverse certificates",
+      "decision": "not selected; active neighboring PR666 and PR668 inverse/resultant work"
+    }
+  ],
+  "source_pr": 489,
+  "source_head": "8922e3b3f0fd7772b0fb42028eb2532984c3ab42",
+  "exact_object": "PR489 code/branchfree.py packed_lower: exact signed convolution digits, rounding toward zero, upper reversal",
+  "method": "Independent integer-dot-product and divmod oracle, exhaustive finite inputs, carry-boundary and mutation tests; no symbolic q identity duplication",
+  "domain": "n=1..4 all vector pairs over the declared ternary numerator alphabet at bits=0,1,3; 480 fixed stress pairs up to n=32 and 128-bit numerators; both orientations",
+  "stopping_rule": "Complete declared finite domain, all controls and proof of the radix invariant; no further pivot",
+  "expected_deliverable": "Independent verification of signed packed convolution, scoped arithmetic proof and deterministic replay receipt. No new kappa.",
+  "expected_finish": "this session; verification and handoff reserved after certificate construction",
+  "coordination": "No open sprint coordination issue found; only open non-PR issue #650. Claim recorded locally.",
+  "overlap_checked": "PR489 head/body/check.py and no comments; current inverse/convolution PR titles; central ledger labels #489 unreviewed. Original identities() tests n=1..12 at q=1/4,1/16,1/256.",
+  "status": "completed; submitted for independent review",
+  "pivot": {
+    "reason": "Five neighboring local claims already cover symbolic q Gaussian identities. Preserve their files and avoid duplicate work.",
+    "new_object": "PR489 packed_lower signed integer packing and completed-coordinate rounding; exhaustive tiny-domain plus adversarial carry/reversal tests",
+    "at_utc": "2026-10-13T04:01:08.626787+00:00"
+  },
+  "branch": "research/seed79-packed-convolution-8SHlWY",
+  "result": {
+    "vector_pairs": 22620,
+    "source_calls": 45240,
+    "output_coordinates": 183212,
+    "semantic_mutants_rejected": 8,
+    "admission_controls_rejected": 3,
+    "scope": "No source bug found in the declared finite domain. Independent written radix proof is not machine-formalized. No new kappa.",
+    "reproduce": "python3 -B research/gaussian-packed-convolution-audit/verify.py",
+    "expected": "PASS_INDEPENDENT_SIGNED_PACKED_CONVOLUTION",
+    "evidence": "EXPECTED.json",
+    "note": "README.md",
+    "last_overlap_pr": 687,
+    "completed_at_utc": "2026-10-13T04:11:37.179052+00:00",
+    "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/690",
+    "audited_contribution_commit": "b5ad6165f810b1e5ae10ef8d02a17fa386b185a2",
+    "post_submission_overlap": "PR689 appeared during submission; it concerns balanced ternary dirty echo composition, not signed packing. No dependency or duplication."
+  }
+}