Audit retained-helper independence in scatter parity

research/retained-alias-parity-audit/CLAIM.json

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+{
+  "track": "adversarial mathematical audit",
+  "assignment_seed": 62,
+  "randomness": "Python secrets.randbelow(100), backed by operating-system randomness",
+  "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a",
+  "selected_kappa": "836330098538459/500000000000000000",
+  "candidates": [
+    {
+      "task": "Retained-slot independence in PR3004's exact scatter-parity necessity claim",
+      "decision": "Selected: the prior coefficient census treats retained slots as independent; the actual checker permits aliases of one helper."
+    },
+    {
+      "task": "Cold-helper last-touch implication",
+      "decision": "Excluded: existing PR702/712/729 and current helper checks already cover the obvious lifetime mutations."
+    },
+    {
+      "task": "Prime-power inverse nonunit-root lemma",
+      "decision": "Excluded: PR796 gives a different exact Newton-polygon audit, in addition to PR621/668 review."
+    }
+  ],
+  "scope": "Correct the exact scatter-agreement criterion when the ret list repeats a helper, and test an accepted symbolic fixture against the unchanged exporter on all 661 dirty-input columns.",
+  "method": "Group coefficient discrepancies by physical retained helper; prove independence of distinct register rows under the reversible prefix. Seed chooses retained index 8 and the first cyclic target at or after 62 omitting that index (row 64). Append alias slot 9 and paired occurrences of slots 8 and 9.",
+  "domain": "One selected PR589 baseline and bounded alias/odd-multiplicity controls; exhaustive small alias maps and rows as specified in the final receipt.",
+  "stopping_rule": "Stop after deciding this one necessity claim, testing the selected-byte positive control and distinct-source negative controls. No supplier search or native/full multiplication admission.",
+  "expected_deliverable": "Scoped audit note, deterministic exact receipt, source pins and independently implemented scalar/record replay.",
+  "expected_finish_utc": "2026-10-17T03:29:00Z",
+  "coordination": "Live GraphQL pinnedIssues query returned no pinned issue. Claim recorded locally as instructed. Read discussion 1166 through 2026-10-17T02:50Z; current centre-demand claim is disjoint.",
+  "overlap": "Read PR2977/2992/3004/3099/3100 and their canonical discussion2976. Targeted live PR searches for retained alias and duplicate retained, plus cached/local-note search; no direct alias-parity audit identified. The local overlap tool had no usable remote cache; no exhaustive novelty claim.",
+  "attribution": "theon199, with substantial OpenAI Codex assistance; no independent human review claimed",
+  "status": "completed",
+  "result": "Written exact alias-group criterion and minimal four-entry witness. The balanced alias passes full H1-H5 and all 661 input columns in both representations; unpaired/distinct-helper controls diverge. Exhaustive 23 alias patterns / 87641 rows, six behavioral groups, registered replay and selected-source bindings pass. No new kappa.",
+  "result_url": "https://github.com/theon199/integer-mult-bounds/tree/research/seed62-mathematical-audit/research/retained-alias-parity-audit",
+  "overlap_refresh": "2026-10-17T03:04Z: canonical main unchanged at exact base; PR3004 head unchanged; new PR3116 batching and PR3117 R439 disjoint-helper optimum are disjoint. No targeted retained-alias-parity match. Latest discussion1166 claim concerns complex centre-demand coupling, not bit scatter slot aliases."
+}