Scoped negative result: three-mode P112 COPY64 despite four span-loss exceptions

research/p112-three-mode-seed40/CLAIM.json

@@ -0,0 +1,42 @@
+{
+  "track": "structural decoder research",
+  "assignment_seed": 40,
+  "randomness": "secrets.randbelow(100), OS-backed; drawn 2026-10-14T01:35:00.768397+00:00",
+  "base_commit": "ef5f39403610d231a0c27e8a6b4f08c10209bcd6",
+  "started_at": "2026-10-14T01:35:00Z",
+  "expected_finish": "2026-10-14T02:35:00Z",
+  "claim_recorded_at": "2026-10-14T01:40:41.509794+00:00",
+  "posting": "Local claim: pinnedIssues returned zero pinned issues; no reservation issue created. Live discussions and open PRs read.",
+  "candidates": [
+    {
+      "question": "One arbitrary free rectangle mixed with three P112 coordinate modes by GL(4,C).",
+      "decision": "Selected: explicit open extension in PR1473; new projected rank-three support strata. Seed 40 chooses lexicographic triple number 40, namely (2,4,5)."
+    },
+    {
+      "question": "Nine-normal sparse-dependency P112 decoder with arbitrary row shifts.",
+      "decision": "Not selected: PR1325 and PR1224 already cover nearby structural questions."
+    },
+    {
+      "question": "Rank-eight rigidity on deeper P108 punctures.",
+      "decision": "Not selected: active extensive PR1474/1469/1425 coverage."
+    }
+  ],
+  "scope": "Classify all supports of nonzero complex combinations of fixed coordinate modes (2,4,5), then test two-anchor erasure/span bounds relevant to one free rank-one correction. Extend by symmetry only if certified.",
+  "method": "Exact rational arrangement flats and binary pairing ranks; arbitrary amplitudes via support containment and GL(4,C) projected identity.",
+  "optimistic_budget": "Other five modes cost 40. To help, four replacement terms must have sum <24 or power sum <3*8^q for some 0<q<=1, even granting zero preparation, source access, frame changes, restoration and other recursive costs.",
+  "stop_rule": "At most 12 minutes orientation; stop construction effort if a proved lower bound rules out the optimistic COPY bill; reserve final 15 minutes for verification and handoff. One evidence-driven pivot only.",
+  "expected_deliverable": "One scoped proof or concrete obstruction with exact finite certificate, independent finite-premise implementation, controls, replay and source pins; no selected frontier change.",
+  "overlap": {
+    "fetched_at": "2026-10-14T01:39:11.016707+00:00",
+    "open_prs": 745,
+    "discussions": 174,
+    "complete_pagination": true,
+    "closest": {
+      "1473": "ea2f6bf0940580dfaeb393ec0786abc8f7bbb7b4",
+      "1432": "4bcc49e3f4041018b0607da46a87d8928a6e0fd0",
+      "1325": "ba2d1cae64738891dd530b3526fb8ae3b25541aa"
+    }
+  },
+  "author": "Hanson Sun (@bbMisk)",
+  "ai_assistance": "Substantial OpenAI Codex assistance."
+}

research/p112-three-mode-seed40/INDEPENDENT.json

@@ -0,0 +1,194 @@
+{
+  "anchor_pairs": 6216,
+  "controls": [
+    "rank-two-dependent-triangle",
+    "false-span-preservation-has-four-counterexamples",
+    "every-proper-exceptional-deletion-restores-span",
+    "singleton-premise-boundary",
+    "omitted-compensation-changes-constrained-entry"
+  ],
+  "exceptional_pairing_checks": 156,
+  "exceptions": [
+    {
+      "anchors": [
+        8,
+        16
+      ],
+      "erasure": [
+        4,
+        5,
+        6,
+        7,
+        26,
+        33,
+        40,
+        41,
+        42,
+        43,
+        60,
+        61,
+        62,
+        63,
+        72,
+        73,
+        74,
+        75,
+        92,
+        93,
+        94,
+        95,
+        102,
+        109
+      ],
+      "stratum": 8
+    },
+    {
+      "anchors": [
+        9,
+        17
+      ],
+      "erasure": [
+        0,
+        1,
+        2,
+        3,
+        27,
+        32,
+        38,
+        39,
+        42,
+        43,
+        60,
+        61,
+        64,
+        65,
+        70,
+        71,
+        74,
+        75,
+        92,
+        93,
+        96,
+        97,
+        103,
+        108
+      ],
+      "stratum": 10
+    },
+    {
+      "anchors": [
+        14,
+        22
+      ],
+      "erasure": [
+        0,
+        1,
+        2,
+        3,
+        27,
+        32,
+        36,
+        37,
+        40,
+        41,
+        62,
+        63,
+        66,
+        67,
+        68,
+        69,
+        72,
+        73,
+        94,
+        95,
+        98,
+        99,
+        103,
+        108
+      ],
+      "stratum": 16
+    },
+    {
+      "anchors": [
+        15,
+        23
+      ],
+      "erasure": [
+        4,
+        5,
+        6,
+        7,
+        26,
+        33,
+        36,
+        37,
+        38,
+        39,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        96,
+        97,
+        98,
+        99,
+        102,
+        109
+      ],
+      "stratum": 18
+    }
+  ],
+  "flat_dimension_counts": {
+    "0": 1,
+    "1": 13,
+    "2": 25
+  },
+  "geometry_sha256": "384dd5b48cfd306667deafa09f58255f39a8099e609122dc695fe4ce416b2115",
+  "integer_fixture": {
+    "entries": 12544,
+    "omission_first_failure": [
+      4,
+      9
+    ],
+    "ranks": [
+      8,
+      8,
+      8,
+      6
+    ]
+  },
+  "maximal_erasure_size_counts": {
+    "20": 168,
+    "22": 2688,
+    "24": 672,
+    "26": 2688
+  },
+  "original_pairing_checks": 1521,
+  "proper_flats": 39,
+  "schema_version": 1,
+  "scope": "Finite geometric premises independently recomputed; quantified GL(4,C) theorem is written mathematics.",
+  "single_row_restoration_checks": 96,
+  "span_checks": 242424,
+  "span_dimensions": [
+    [
+      8,
+      8,
+      18648
+    ],
+    [
+      9,
+      8,
+      4
+    ],
+    [
+      9,
+      9,
+      223772
+    ]
+  ],
+  "transport_pairing_entries": 702464
+}