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65, 109, 120, 142, 149, 157, 208, 281, 298, 345, 351, 461, 500, 517, 527, 538, 548, 550, 581, 626, 648 ] ] }, "distance": { "d": 64, "X": { "value": 64, "confidence": "upper_bound", "witness": [ 8, 15, 28, 29, 42, 60, 69, 73, 80, 91, 95, 106, 125, 127, 139, 158, 162, 166, 173, 184, 197, 200, 201, 214, 215, 246, 249, 256, 262, 282, 290, 294, 312, 313, 321, 323, 370, 386, 401, 410, 412, 417, 431, 435, 441, 442, 445, 472, 475, 493, 503, 504, 537, 554, 556, 567, 573, 587, 600, 604, 606, 621, 637, 678 ], "witness_provenance": { "found_by": [ "@FarLab", "@MathysRennela", "@MicheldeMessieres" ], "date": "2026-10-09", "found_at_samples": 50000, "seeds": [ 101 ], "tool": "orbit-fold (verify/heuristic_distance.py, PR #2902)" } }, "Z": { "value": 64, "confidence": "upper_bound", "witness": [ 16, 23, 24, 27, 29, 46, 55, 57, 58, 61, 79, 85, 86, 88, 99, 117, 119, 122, 130, 139, 150, 172, 182, 184, 189, 202, 213, 244, 277, 278, 282, 286, 317, 337, 352, 365, 376, 377, 383, 389, 392, 413, 420, 431, 458, 469, 488, 501, 507, 513, 524, 544, 553, 561, 569, 592, 594, 606, 625, 630, 640, 643, 668, 677 ], "witness_provenance": { "found_by": [ "@FarLab", "@MathysRennela", "@MicheldeMessieres" ], "date": "2026-10-09", "found_at_samples": 50000, "seeds": [ 101 ], "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={33,55,100,131,133,143,154,164,181,220,330,336} (weight 12, invariant under j->32j mod 341: fixed points 33,55,143,154,220,330 and pair-orbits {100,131},{133,164},{181,336}) and b=a(x^4)={4j mod 341 : j in a}={42,59,132,183,191,198,220,231,275,297,315,321}, a Frobenius image with the same zero set. Shared divisor (x+1) * one quintic * six full-order decics of x^341-1 (degree 66), so k=132; both check weights 12 (w=24). Found by sampling symmetric weight-11/12/13 words (method in the note) with exact GF(1024) zero sets, screened by the constituent-code cap and a 1k->2M RIS ladder, then 10,000,000 fresh-seed accelerated RIS trials (lightest logical: weight 87); the CI gate's 8M-trial pass then found a weight-84 X logical, recorded as the X witness.", "origin": "submission", "date": "2026-10-07", "model": "Claude Fable 5.1 (Claude Code)", "search_budget": { "candidates_screened": 22, "ris_trials_per_side": 10000000, "cpu_hours": 50, "tool": "symmetric-word sampler with GF(1024) zero sets + gf2_fast accelerator" }, "notes": "Distance over-claim independently reported by @MathysRennela and @MicheldeMessieres on 2026-10-08 (see issue #2899); corrected to d <= 77 with a witness from the maintainers' orbit-restricted search. Tightened to d <= 64 on 2026-10-09 by @FarLab with the orbit-fold search of PR #2902 (50,000 trials per folded code) while landing correction PR #2937, whose merge had not reached main (issue #2949)." }, "family": "generalized-bicycle" }