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229, 246, 251, 255, 260, 277, 282, 286, 291, 308, 313, 317, 322, 339, 341, 355, 372, 386, 403, 417, 434, 448, 465, 479, 496, 510, 527, 541, 558, 572, 589, 603, 620, 634, 651, 665 ], "witness_provenance": { "found_by": [ "@VedantMahadik-qc" ], "date": "2026-09-26", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_31 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "d": 66 }, "family": "generalized-bicycle", "k": 140, "n": 682, "name": "[[682,140,d<=66]] Z_341 cyclic-ideal generalized-bicycle code", "provenance": { "authors": [ "@DennisWayo" ], "construction": "Cyclic generalized-bicycle code over Z_341; a=[0, 1, 4, 27, 53, 79, 99, 137, 162, 223, 225, 294, 323, 331, 334]; b=[2, 122, 124, 131, 132, 134, 137, 168, 207, 220, 241, 268, 296, 297, 303, 308]; H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T].", "date": "2026-09-22", "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<=85 completed another 400000 structural trials, the Python RIS pass, and 8000000 RIS-fast trials without finding a logical lighter than 85; RIS-fast stopped at weight 86. Base-board validation reports no exact or WL duplicate. The current codes/682-140-82.json entry has d<=82 and maximum check weight 30; this distinct representation raises the witnessed distance to 85 at maximum check weight 31 and scores 1483.138. This is an upper-bound claim, not an exact-distance certificate. Tightened 2026-09-22 by @vprusso: a GPU random-information-set search (verify/ris_gpu.py, recover mode, k_sub 128, 80,000,000 trials per side, seed 1003) exhibits a weight-83 Z-type logical, so d <= 83; weight-84 X-type logicals were found at seeds 1002 (k_sub 64) and 1003 (k_sub 128), and 260,000,000 sketch trials per side over k_sub 32, 64, 128, and 256 plus 4,000,000 deep-kernel trials found nothing lighter than 83. The X witness is the original weight-85 operator, since the weight-84 X operators only lower a side value, not d. Every GPU operator was re-verified on the CPU with verify/gf2.py. Tightened 2026-09-26 by @VedantMahadik-qc: the Z_31 quotient code (both generator polynomials reduced modulo x^31 - 1) has a weight-6 logical on each side, and its norm-word lift (multiplication by 1 + x^31 + ... + x^310) is a weight-66 logical of the full code, so d <= 66. The code, checks, and authorship are unchanged; only the distance block and name are revised.", "novelty": "unknown", "origin": "submission", "references": [] }, "schema_version": "0.2" }