[Lean] Prove nonlinear dirty-commutator restoration and ordered products (no new kappa)

research/lean-nonlinear-commutator/CLAIM.json

@@ -0,0 +1,178 @@
+{
+  "pass": 8,
+  "assignment_seed": 83,
+  "drawn_at_utc": "2026-10-13T10:18:13.485465+00:00",
+  "track": "independent verification or formalization",
+  "base": "f567884aeb8851b6e794af1184119a3bfbe1e631",
+  "status": "submitted",
+  "branch": "research/pass08-verification-seed83",
+  "claimed_at_utc": "2026-10-13T10:26:20.672476+00:00",
+  "candidate_selection": "83 modulo 3 = 2; fresh draw coincidentally equals the preceding seed, but the proof obligation is different",
+  "candidates": [
+    {
+      "object": "Formal fractional-grid admission criterion for dyadic scalar prefixes",
+      "chosen": false,
+      "reason": "A complete rational/program bridge would require a larger arithmetic-library setup; the existing exact finite audit already isolates the immediate guard change"
+    },
+    {
+      "object": "Formal exact balanced-tree leaf-count formula from PR663",
+      "chosen": false,
+      "reason": "Useful arithmetic, but it leaves the more consequential nonlinear restoration interface untouched"
+    },
+    {
+      "object": "All-tree nonlinear dirty commutator semantics and ordered additive-map product",
+      "chosen": true,
+      "method": "Lean 4 core/Std, finite integer-array values of arbitrary width, indexed disjoint scratch pools; pin the original dispatcher and PR663 argument"
+    }
+  ],
+  "statement": "Prove by structural induction that every binary dirty commutator restores arbitrary borrowed arrays, has a target-independent increment and an exact reverse-word inverse for arbitrary fixed deterministic nonlinear leaves. Under leaf additivity, prove the ordered composite independent of initial dirt. Bind the abstract semantics to the pinned PR628 dispatcher by bounded trace and execution checks.",
+  "domain": "Binary reserved-scratch trees; fixed-point arrays represented as integer vectors of arbitrary finite width; leaves assumed to restore their source and add a fixed function of that source to a distinct target. Fixed, nonaliased external data.",
+  "stopping_rule": "One scoped semantics formalization plus explicit bounded source correspondence; no rounded leaf accuracy proof, alias-guard repair, multiway/connector reuse, resource optimum, physical supplier or new kappa.",
+  "expected_finish": "Approximately 120 minutes from claim; reserve final quarter for validation and handoff",
+  "coordination": "Only open issue #650 asks for Discussions; no coordination claim channel exists. Claim recorded locally.",
+  "initial_open_pr_count": 679,
+  "latest_pr_at_claim": 887,
+  "related_prs": {
+    "628": "Subject binary dispatcher and inherited leaf contract",
+    "663": "Written all-n nonlinear induction and free-term finite audit; this adds a kernel proof",
+    "673": "Multiway extension and phase-alias repair, outside scope",
+    "784": "Reserved-scratch resource theorem",
+    "887": "Previous pass formalizes resource counts, not execution semantics",
+    "878": "Selected XOR boundary semantics, different circuit and model",
+    "877": "Precision bound retaining the nonlinear restoration hypothesis",
+    "889": "Concurrent common-factor multi-output batch; different recursive interface, no imported dependency"
+  },
+  "bounded_correspondence": {
+    "all_binary_trees_by_leaves_1_to_7": [
+      1,
+      1,
+      2,
+      5,
+      14,
+      42,
+      132
+    ],
+    "all_binary_trees_total": 197,
+    "generated_lean_sha256": "35d6a7bed4b0b0350e539c71a5f58a5a9f54ad4abc02bd436c7c0985b34455bc",
+    "lean_trace_equalities": 34,
+    "source_execution_cases": 1170,
+    "source_execution_leaf_calls_including_inverse": 3722940,
+    "source_factor_counts": [
+      1,
+      2,
+      3,
+      4,
+      5,
+      6,
+      7,
+      8,
+      9,
+      10,
+      11,
+      12,
+      13,
+      14,
+      15,
+      16,
+      17,
+      18,
+      19,
+      20,
+      21,
+      22,
+      23,
+      24,
+      25,
+      26,
+      27,
+      28,
+      29,
+      30,
+      31,
+      32,
+      33,
+      34,
+      35,
+      36,
+      37,
+      38,
+      39,
+      40,
+      41,
+      42,
+      43,
+      44,
+      45,
+      46,
+      47,
+      48,
+      49,
+      50,
+      51,
+      52,
+      53,
+      54,
+      55,
+      56,
+      57,
+      58,
+      59,
+      60,
+      61,
+      62,
+      63,
+      64,
+      83
+    ],
+    "source_trace_instructions": 206830,
+    "source_words": 130,
+    "tree_execution_cases": 2364,
+    "array_widths": [
+      1,
+      2,
+      3
+    ],
+    "leaf_families": [
+      "integer floor with nonzero offset",
+      "bounded square modulo 97",
+      "noncommuting integer shears"
+    ],
+    "formal_trace_factor_counts": [
+      1,
+      2,
+      3,
+      4,
+      5,
+      6,
+      7,
+      8,
+      9,
+      10,
+      11,
+      12,
+      13,
+      14,
+      15,
+      16,
+      83
+    ],
+    "controls": 13
+  },
+  "overlap_refresh": {
+    "open_prs": 686,
+    "through_pr": 894,
+    "upstream_head": "f567884aeb8851b6e794af1184119a3bfbe1e631",
+    "subject_and_audit_heads_unchanged": true,
+    "related_new_work": "PR889 batches multiple outputs sharing a common factor and gives different query-count evidence. It does not formalize this binary-tree nonlinear contract. PR893 audits historical Lean evidence rather than this mathematical obligation."
+  },
+  "completed_at_utc": "2026-10-13T10:57:03.649998+00:00",
+  "pr": 896,
+  "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/896",
+  "mathematical_commit": "238f0bbca6271441e365d3dca4af00a39382dfd4",
+  "result": "Lean 4.21.0 proves the typed binary evaluator restores arbitrary dirt, has target-independent nonlinear increments and exact inverses; additive leaves give the ordered product. Twelve formal statements, 34 source trace equalities, 1170 source and 2364 tree executions, and 13 controls pass. Leaf correctness and all-size address/Python correspondence remain separate. No new kappa.",
+  "validation": "Complete ordinary Python 3.14.4 and isolated optimized read-only Python 3.12.3 replays agree. Source/receipt/overwrite controls, selected-record integrity and staged scope/whitespace pass; hosted CI tracked separately.",
+  "immediate_pre_submission_check": {
+    "through_pr": 895,
+    "new_arrival": "PR895 screens BW16 as a decoder unit; no overlap with nonlinear restoration semantics"
+  }
+}