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147, 151, 155, 176, 184, 199, 210, 229, 230, 237, 255, 277, 286, 303, 307, 310, 312, 320, 323, 339, 343, 356, 360, 367, 373, 376, 388, 390, 397, 398, 415, 419, 422, 434, 435, 437, 454, 468, 471, 475, 495, 526, 527, 533, 539, 544, 546, 551, 559, 569, 574, 578, 585, 596, 603, 611, 629, 630, 644, 654, 655, 661, 662, 665, 668 ] } }, "provenance": { "authors": [ "@kessler-frost" ], "origin": "submission", "novelty": "unknown", "construction": "Generalized bicycle code over the cyclic group Z_337: H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T], with a = x^[55, 60, 62, 79, 128, 135, 136, 190, 212, 276] and b = x^[63, 105, 112, 144, 215, 241, 253, 267, 276, 300, 312, 316, 317, 320] (exponents modulo 337). The designed-divisor search retained the 14-term b polynomial from @vprusso's [[674,86,92]] submission and searched new 10-term a polynomials while preserving k = 2 deg gcd(a, b, x^337 - 1) = 86.", "model": "GPT 5.6 Sol", "references": [ "https://github.com/unitaryfoundation/qldpc-challenge/blob/96d7bca0385b8ab40575bec4b8445a27b6e08bfb/codes/674-86-92.json", "https://github.com/unitaryfoundation/qldpc-challenge/pull/560", "https://github.com/unitaryfoundation/qldpc-challenge/blob/928cedb93aeeaa768dfb7f93db2d31d54e38e9f0/fieldnotes/2026-07-14-designed-divisor-and-odd-k.md", "https://quantum-journal.org/papers/q-2021-11-22-585/", "https://arxiv.org/abs/2203.17216", "https://arxiv.org/abs/2608.09115" ], "date": "2026-08-16", "notes": "Submitted by @kessler-frost, who designed and ran the candidate search. The retained b polynomial is credited to @vprusso and the pinned source above; the a polynomial was found in the new search. The original d <= 95 submission was refuted by public CI seed 147873169, whose RIS-fast pass found the retained weight-89 Z logical. This revision therefore makes only the corrected witness-backed claims d_X <= 98, d_Z <= 89, and d <= 89; no lower bound or exact-distance claim is made. No exact or WL-equivalent current-board entry was found, but no exhaustive literature classification is known, so novelty is unknown. X-side bound revised 2026-08-19 by GPU deep refutation. Random-ISD runs with the sqetch GPU kernels (Muzhou Ma, MIT) on an NVIDIA L40S: a 50M-trial x 3-seed triage per side, then a 1,000,000,000-trial recovery ladder per side (seed 77000003 for X, 77000004 for Z), committed a weight-92 X logical, re-verified on the CPU with the repo's GF(2) arithmetic and recorded here as the new X witness, tightening dX<=98 to dX<=92. The same budget found no Z logical lighter than weight 90, so the claimed dZ<=89 and the overall d<=89 stand unchanged (the deep run corroborates rather than refutes the headline distance; score unchanged at 86*89^2/674 = 1010.55). All distances remain witness-backed upper bounds, not exact-distance claims. @kessler-frost constructed the code; @FarLab is added as an author for the bound revision, following the board's precedent for refutation contributions. Migrated 2026-08-19 (issue #611): refutation credit moved from provenance.authors to witness_provenance on the refuted side(s); authors again lists only the constructor." }, "family": "generalized-bicycle" }