Independent verification: P112 root-star floor via Weyl and maximal-clique replays

research/masked-star-frame-compatibility/CERTIFICATE.json

@@ -0,0 +1,164 @@
+{
+  "schema": "masked-star-frame-compatibility-v1",
+  "scope": "P112; exact C(alpha)/N(alpha) supports; ordinary complex transpose; arbitrary finite term count",
+  "lines": 120,
+  "live_lines": 112,
+  "label_rank": 9,
+  "roots_sha256": "499909f15616b21ed34b704054685a0c90c244fb81819ba458e076b8dd97308c",
+  "puncture": [
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+  "frames_sha256": "9f4794b9b10349aa5e4e095547b75fd08c4e895c08980db020c79c525a9a3924",
+  "frames_per_line": 90,
+  "orthogonal_pair_extension_histogram": {
+    "10": 2856,
+    "15": 448
+  },
+  "ordered_support_pairs": 57600,
+  "support_labels": 240,
+  "distinct_supports": 232,
+  "rank_histogram": {
+    "7": 7616,
+    "8": 37440,
+    "9": 12544
+  },
+  "ranks_sha256": "0ff8da9bad5e811a4daf04ea9b4e42111a2e43b6c5cab90602edfae14ad62866",
+  "rank7_live_normal_count_histogram": {
+    "1": 1792,
+    "2": 5824
+  },
+  "star_zero_frames_sha256": "cdd285f6a21e4871c6aaaf72d6d558a9e94c1adcb3085353c4f8c343c5899c65",
+  "nonorthogonal_clique_counts": {
+    "0": 1,
+    "1": 112,
+    "2": 2912,
+    "3": 25088,
+    "4": 88704,
+    "5": 161280,
+    "6": 145152,
+    "7": 55296,
+    "8": 4032
+  },
+  "maximum_nonorthogonal_clique": 8,
+  "maximum_clique_witness": [
+    2,
+    3,
+    13,
+    22,
+    44,
+    71,
+    80,
+    99
+  ],
+  "maximum_clique_root_vectors": [
+    [
+      0,
+      0,
+      0,
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+      0,
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+      0
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+    [
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+      1,
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+      -1,
+      -1,
+      1,
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+  ],
+  "coordinate_decoder_costs": [
+    8,
+    8,
+    8,
+    8,
+    8,
+    8,
+    8,
+    8
+  ],
+  "coordinate_decoder_entries": 12544,
+  "cost_floor": 64,
+  "controls": [
+    "changed_coordinate_coefficient_rejected",
+    "zero_decoder_rejected_by_diagonal",
+    "synthetic_K9_detected_without_depth_cutoff",
+    "rank_one_singleton_outside_star_family",
+    "repeated_normal_has_shared_zero_frame",
+    "orthogonal_normals_have_shared_zero_frame",
+    "free_odd_entry_patch_vanishes_on_every_frame"
+  ]
+}

research/masked-star-frame-compatibility/CLAIM.json

@@ -0,0 +1,47 @@
+{
+  "assignment_seed": 36,
+  "random_source": "Python secrets.randbelow(100), operating-system entropy",
+  "track": "complex supplier",
+  "base_commit": "49b3157d1d89adcef16df8be98445451672be5ba",
+  "task_id": "complex-masked-decoder",
+  "scope_status": "refined",
+  "object": "P112 masked root-star decoder with C(alpha) or N(alpha) supports and arbitrary complex coefficients",
+  "hypothesis": "Simultaneous orthogonal-frame constraints exclude a total copied-information cost below 64, closing the 63-cost case left by the scalar covering relaxation in PR1226.",
+  "method": "Reconstruct all E8 lines, all support-pair ranks, and all 1260 live frames; reduce nine rank-seven atoms to pairwise compatible live normal lines; exact clique census.",
+  "seed_diversification": "36 mod 3 = 0 selects simultaneous-frame compatibility before nonlinear ten-term synthesis or helper-boundary design; use cyclic vertex order offset 36 as one verification order.",
+  "candidates": [
+    {
+      "object": "P112 masked root-star rank-seven assembly",
+      "method": "simultaneous-frame compatibility; selected because PR1226 explicitly leaves its assembly gap open"
+    },
+    {
+      "object": "P120 ten-term decoder with one residual direction in each factor",
+      "method": "exact sparse-factor synthesis; rejected for this session because PR1224 already supplies a two-sided ten-term example and physical pricing is absent"
+    },
+    {
+      "object": "new helper boundary outside the 71-record provider catalogue",
+      "method": "derive a paid contract with shared restoration; deferred because no concrete legal boundary saving identified"
+    }
+  ],
+  "nearest_predecessor": {
+    "pr": 1226,
+    "author": "Navinor",
+    "head": "8b10989e4e45f0f9ce41004d7898a21a32f87e11"
+  },
+  "optimistic_budget": "Below cost 64, minimum per-term rank 7 and frame rank 8 restrict a candidate to eight or nine paid atoms. Free odd-entry singleton repairs vanish on every orthogonal frame. All omitted realization costs are nonnegative, so an obstruction already in this relaxation rules out savings in this family.",
+  "stopping_rule": "Stop once the finite compatibility obstruction is proved with witnesses and controls, or report the exact failed implication if false. No wider support search.",
+  "expected_deliverable": "One scoped negative result with written proof, exact finite certificate, independently implemented finite verification and meaningful mutation controls; no new kappa.",
+  "expected_finish_utc": "2026-10-13T21:21:00Z",
+  "coordination": "No pinned issue returned by the GitHub GraphQL pinnedIssues query; local claim as instructed. Read discussions including #1210 and its PR1226 result, open PR bodies and review ledger before this claim.",
+  "created_utc": "2026-10-13T20:45:22.648472+00:00",
+  "attribution": "Hanson Sun (@bbMisk), substantial OpenAI Codex assistance; predecessor credit retained; Apache-2.0.",
+  "result": {
+    "status": "completed independent verification",
+    "finding": "Exact support-family cost floor 64, independently corroborating concurrent PR1236. Both new checkers and the pinned PR1236 registered package pass on Python 3.12; no new kappa.",
+    "concurrent_result_pr": 1236,
+    "concurrent_result_head": "ee8437bd9879272094e20c024cd34a53c4e84cd8",
+    "distinct_evidence": "Weyl-reflection root generation, pivoted maximal-clique census, independent column-rank checks, and previously unreported Python 3.12 registered replay of PR1236.",
+    "result_url": "https://github.com/bbMisk/integer-mult-bounds/tree/research/p112-star-frame-verification-s36-20261013/research/masked-star-frame-compatibility",
+    "updated_utc": "2026-10-13T21:00:48.369867+00:00"
+  }
+}