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604, 653, 659, 671, 678, 681 ] ] }, "code_type": "CSS", "distance": { "X": { "confidence": "upper_bound", "value": 64, "witness": [ 0, 9, 25, 29, 46, 54, 56, 57, 60, 76, 79, 80, 87, 90, 99, 102, 108, 119, 140, 151, 155, 163, 164, 174, 175, 176, 178, 185, 186, 194, 200, 201, 202, 206, 207, 211, 212, 213, 216, 225, 227, 240, 242, 247, 250, 254, 256, 258, 263, 267, 268, 273, 274, 278, 288, 296, 299, 300, 307, 310, 312, 328, 331, 333 ], "witness_provenance": { "date": "2026-09-21", "found_at_samples": 400000, "found_by": [ "@DennisWayo" ], "seeds": [ 84929447858586164, 9218007 ], "survived_samples": 8000000, "tool": "gf2_fast circulant-GB structural gate" } }, "Z": { "confidence": "upper_bound", "value": 64, "witness": [ 341, 349, 351, 354, 370, 372, 375, 382, 383, 386, 394, 404, 408, 409, 414, 415, 419, 424, 426, 428, 432, 435, 440, 442, 455, 457, 466, 469, 470, 471, 475, 476, 480, 481, 482, 488, 496, 497, 504, 506, 507, 508, 518, 519, 527, 531, 542, 563, 574, 580, 583, 592, 595, 602, 603, 606, 622, 625, 626, 628, 636, 653, 657, 673 ], "witness_provenance": { "date": "2026-09-21", "found_at_samples": 400000, "found_by": [ "@DennisWayo" ], "seeds": [ 84929447858586164, 9218007 ], "survived_samples": 8000000, "tool": "GB involution mirror of gf2_fast structural witness" } }, "d": 64 }, "family": "generalized-bicycle", "k": 182, "n": 682, "name": "[[682,182,d<=64]] Z_341 cyclic-ideal generalized-bicycle code", "provenance": { "authors": [ "@DennisWayo" ], "construction": "Cyclic generalized-bicycle code over Z_341; a=[0, 3, 10, 22, 28, 77, 96, 106, 198, 214, 320, 323]; b=[10, 17, 20, 41, 64, 68, 119, 185, 192, 209, 265, 271]; 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/682-182-66.json and codes/682-182-66-b.json entries have d<=66 and maximum check weight 32; this distinct representation trades two distance points for a reduction to check weight 24 and remains Pareto non-dominated. This is an upper-bound claim, not an exact-distance certificate.", "novelty": "unknown", "origin": "submission", "references": [] }, "schema_version": "0.2" }