Research audit: quartic precision for balanced dirty cyclic inverses (no new kappa)

research/dirty-prefix-precision/CLAIM.json

@@ -0,0 +1,84 @@
+{
+  "pass": 6,
+  "assignment_seed": 63,
+  "drawn_at_utc": "2026-10-13T08:36:24.867393+00:00",
+  "track": "adversarial mathematical audit",
+  "base": "f567884aeb8851b6e794af1184119a3bfbe1e631",
+  "status": "submitted",
+  "branch": "research/pass06-audit-seed63",
+  "claimed_at_utc": "2026-10-13T08:46:31.924453+00:00",
+  "candidate_selection": "63 modulo 3 = 0",
+  "candidates": [
+    {
+      "object": "Uniform precision growth in PR628 balanced dirty commutators",
+      "method": "Bound ideal prefixes and their inverses through recursive restoration, then sum perturbed leaf errors",
+      "chosen": true
+    },
+    {
+      "object": "Minimum all-dirty echo call count at fixed scratch",
+      "method": "Exact tree recurrence audit",
+      "chosen": false,
+      "reason": "PR730 and PR744 already supply complementary exact optimization and independent coverage"
+    },
+    {
+      "object": "Restored-source precision at arbitrary cyclic stride",
+      "method": "Audit PR846 FIFO recursion under a borrowed-array contract",
+      "chosen": false,
+      "reason": "PR846 explicitly leaves dirty-array realization open; resolving it needs a new construction beyond this bounded audit"
+    }
+  ],
+  "statement": "Audit whether the N-leaf trajectory growth used in PR628 DIRTY-PROOF.md is necessary for balanced binary commutators. Establish a uniform ideal-prefix and inverse-prefix bound and a complete rounding-error budget, retaining arbitrary initial dirty arrays and the unchanged leaves.",
+  "expected_deliverable": "Written proof, exact prefix and error-propagation evidence, source-bound integer budget comparison and actual rounded-leaf/kernel replay; no new kappa.",
+  "domain": "PR628 balanced binary product-shear tree, every n>=1 and arbitrary composable bounded linear factor maps. Numerical evidence uses pinned cyclic leaves and nonaliased immutable phases. Higher fanout, different allocation, clean storage and physical supplier integration outside scope.",
+  "stopping_rule": "Complete this one prefix-bound/error recurrence and its declared deterministic validation; no optimizer or supplier construction",
+  "expected_finish": "Approximately 90 minutes; reserve final quarter for validation and handoff",
+  "coordination": "Only open non-PR issue #650 requests Discussions. No coordination issue exists; this claim is local.",
+  "related_prs": {
+    "628": "Original rounded leaf, dirty composition and conservative N-step precision bound",
+    "663": "Exact balanced binary leaf count and independent nonlinear restoration audit",
+    "673": "Multiway echo and phase-alias repair; same conservative per-leaf growth technique",
+    "730": "Ordered mixed-tree cost optimization, different scope",
+    "744": "Ternary fixed-space verification, different scope",
+    "862": "Cubic precision with owned widened words; explicitly excludes arbitrary dirty-bit restoration"
+  },
+  "initial_open_pr_count": 660,
+  "latest_pr_at_claim": 867,
+  "final_overlap_check": {
+    "at_utc": "2026-10-13T09:16:19.773721+00:00",
+    "open_pr_count": 669,
+    "latest_number": 876,
+    "upstream_head": "f567884aeb8851b6e794af1184119a3bfbe1e631",
+    "pr628_head": "0768f97d06c623b8211e651543c66135796b62bf",
+    "finding": "No overlapping balanced dirty-prefix precision audit found. Concurrent PR862 has an owned-widened-storage contract; new PR868-876 concerns other geometry, supplier or verification work."
+  },
+  "result": {
+    "statement": "The unchanged balanced binary dirty commutator has a sufficient O(p+d+r^4) word-size bound, improving its inherited O(p+d+r^5) budget; no new kappa.",
+    "prefix_exponent": "E(1)=1; E(n)=n+max(floor(n/2)+E(ceil(n/2)),ceil(n/2)+E(floor(n/2))) <= 4n-3",
+    "radix64_example": {
+      "target_bits": 128,
+      "initial_magnitude_bits": 20,
+      "old_exact_count_bits": 516978511,
+      "new_prefix_bits": 73245212,
+      "leaf_calls": 4000,
+      "dirty_arrays": 6
+    },
+    "small_radix_limit": "The old bound can be tighter; no optimal guard claim."
+  },
+  "validation": {
+    "python_versions": [
+      "3.12.3",
+      "3.14.4"
+    ],
+    "uniform_budgets": 1740,
+    "dense_prefix_traces": 18,
+    "rounded_generic": 48,
+    "rounded_kernels": 40,
+    "mathematical_controls": 10,
+    "unit_tests": 4,
+    "package_mutation_controls": 6,
+    "minimal_isolated_optimized_replay": "passed",
+    "details": "VALIDATION.md"
+  },
+  "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/877",
+  "submitted_at_utc": "2026-10-13T09:20:21.110701+00:00"
+}