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502, 564, 577, 583, 635, 672, 673 ] ] }, "code_type": "CSS", "distance": { "X": { "confidence": "upper_bound", "value": 64, "witness": [ 1, 7, 20, 32, 41, 54, 56, 58, 70, 73, 77, 82, 86, 91, 93, 101, 105, 110, 114, 118, 127, 128, 132, 151, 154, 163, 168, 173, 177, 180, 185, 186, 190, 205, 208, 217, 221, 223, 226, 228, 238, 240, 242, 245, 246, 255, 261, 262, 264, 267, 271, 283, 285, 286, 295, 299, 301, 304, 306, 309, 311, 312, 318, 332 ], "witness_provenance": { "date": "2026-09-21", "found_at_samples": 400000, "found_by": [ "@DennisWayo" ], "seeds": [ 135703970552456684, 9218007 ], "survived_samples": 8000000, "tool": "gf2_fast circulant-GB structural gate" } }, "Z": { "confidence": "upper_bound", "value": 64, "witness": [ 342, 356, 362, 363, 365, 368, 370, 373, 375, 379, 388, 389, 391, 403, 407, 410, 412, 413, 419, 428, 429, 432, 434, 436, 446, 448, 451, 453, 457, 466, 469, 484, 488, 489, 494, 497, 501, 506, 511, 520, 523, 542, 546, 547, 556, 560, 564, 569, 573, 581, 583, 588, 592, 597, 601, 604, 616, 618, 620, 633, 642, 654, 667, 673 ], "witness_provenance": { "date": "2026-09-21", "found_at_samples": 400000, "found_by": [ "@DennisWayo" ], "seeds": [ 135703970552456684, 9218007 ], "survived_samples": 8000000, "tool": "GB involution mirror of gf2_fast structural witness" } }, "d": 64 }, "family": "generalized-bicycle", "k": 170, "n": 674, "name": "[[674,170,d<=64]] Z_337 cyclic-ideal generalized-bicycle code", "provenance": { "authors": [ "@DennisWayo" ], "construction": "Cyclic generalized-bicycle code over Z_337; a=[0, 1, 38, 90, 96, 109, 171, 237, 253, 255, 265, 296]; b=[85, 98, 124, 156, 179, 205, 226, 242, 244, 308, 318, 329]; H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T].", "date": "2026-09-21", "model": "OpenAI GPT-5 (Codex)", "notes": "Recovered from a collapsed-candidate bank and retained by a live-board Pareto filter on (n,k,d,max check weight). A 400000-trial circulant-GB structural search found the submitted X witness; the Z witness is its independently verified GB block-swap/index-reversal image. A final local CI-style pass at d<=64 completed another 400000 structural trials, the Python RIS pass, and 8000000 RIS-fast trials without finding a logical lighter than 64. Base-board validation reports no exact or WL duplicate. The current codes/674-170-76.json entry also has effective d<=64 but maximum check weight 28; this distinct representation lowers that axis to 24. This is an upper-bound claim, not an exact-distance certificate.", "novelty": "unknown", "origin": "submission", "references": [] }, "schema_version": "0.2" }