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"orbit-fold (verify/heuristic_distance.py, PR #2902)" } }, "Z": { "value": 56, "confidence": "upper_bound", "witness": [ 24, 35, 36, 37, 52, 55, 63, 86, 91, 96, 114, 118, 125, 158, 172, 176, 179, 180, 203, 206, 210, 241, 252, 268, 284, 316, 331, 339, 361, 365, 372, 403, 405, 407, 408, 420, 434, 454, 465, 493, 498, 506, 526, 546, 559, 562, 577, 580, 582, 586, 594, 619, 637, 642, 652, 661 ], "witness_provenance": { "found_by": [ "@FarLab", "@vaibhav-baj" ], "date": "2026-10-09", "found_at_samples": 1000000, "seeds": [ 404 ], "tool": "orbit-fold (verify/heuristic_distance.py, PR #2902)" } } }, "provenance": { "authors": [ "@vaibhav-baj" ], "construction": "Cyclic generalized-bicycle code over Z_341: H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T], with a={11,66,73,99,110,154,220,223,286,290,316} (weight 11, invariant under j->32j mod 341: fixed points 11,66,99,110,154,220,286 and pair-orbits {73,290},{223,316}) and b=a(x^4)={4j mod 341 : j in a}={44,55,99,121,137,198,210,241,264,275,292}, a Frobenius image with the same zero set. Shared divisor one quintic * six full-order decics of x^341-1 (degree 65), so k=130; both check weights 11 (w=22). Found by the weight-11 sampler of the campaign behind codes/682-132-84.json (method in the note); 2M-trial RIS ladder bound 88, then 10,000,000 fresh-seed accelerated RIS trials (lightest logical: weight 86).", "origin": "submission", "date": "2026-10-07", "model": "Claude Fable 5.1 (Claude Code)", "search_budget": { "candidates_screened": 7, "ris_trials_per_side": 10000000, "cpu_hours": 22, "tool": "symmetric-word sampler with GF(1024) zero sets + gf2_fast accelerator" }, "notes": "Corrected to d <= 56 on 2026-10-09 by @FarLab with the orbit-fold search of PR #2902 (X: 86 -> 56; Z: 86 -> 56; see issue #2949). The entry was identified in the follow-up audit on issue #2899 (2026-10-08)." }, "family": "generalized-bicycle" }