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473 ], [ 1, 23, 35, 47, 137, 202, 234, 287, 293, 330, 360, 380, 431, 474 ] ] }, "distance": { "d": 56, "X": { "value": 56, "confidence": "upper_bound", "witness": [ 11, 23, 29, 35, 42, 64, 69, 80, 94, 111, 127, 151, 163, 169, 175, 182, 204, 209, 220, 234, 251, 267, 286, 287, 299, 309, 316, 320, 340, 353, 356, 359, 362, 366, 368, 394, 396, 407, 413, 426, 427, 439, 449, 456, 460, 480, 493, 496, 499, 502, 506, 508, 534, 536, 547, 553 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-10-09", "found_at_samples": 1000000, "tool": "orbit-fold, 1M trials per fold, NERSC Perlmutter CPU", "seeds": [ 101 ] } }, "Z": { "value": 64, "confidence": "upper_bound", "witness": [ 1, 5, 14, 28, 34, 36, 40, 49, 63, 69, 71, 75, 84, 98, 104, 106, 110, 119, 133, 139, 141, 145, 154, 168, 174, 176, 180, 189, 203, 209, 211, 215, 224, 238, 244, 246, 250, 259, 273, 279, 283, 313, 314, 318, 348, 349, 353, 383, 384, 388, 418, 419, 423, 453, 454, 458, 488, 489, 493, 523, 524, 528, 558, 559 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^280 - 1 with a(x) = x^85 + x^128 + x^179 + x^199 + x^229 + x^266 + x^272, b(x) = x^45 + x^77 + x^142 + x^232 + x^244 + x^256 + x^278; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-10-04", "notes": "Found by a randomized sweep over sparse polynomial pairs, screened against the live board before any expensive work. Checked for single-block logicals via the ideal generated by (x^m - 1)/gcd(a, x^m - 1) before the distance was believed. Distance revision 2026-10-09 (Perlmutter refutation campaign, witnesses by @vprusso): X side 64 -> 56 (orbit-fold search (verify/heuristic_distance.orbit_fold_refute, PR #2902), 1,000,000 trials per folded code, seed 101)." }, "family": "generalized-bicycle" }