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405, 486, 504, 515, 537, 610 ], [ 45, 74, 128, 189, 202, 229, 246, 374, 406, 487, 505, 516, 538, 611 ], [ 46, 75, 129, 190, 203, 230, 247, 375, 407, 488, 506, 517, 539, 612 ], [ 47, 76, 130, 191, 204, 231, 248, 376, 408, 489, 507, 518, 540, 613 ] ] }, "distance": { "d": 66, "X": { "value": 66, "confidence": "upper_bound", "witness": [ 10, 26, 30, 34, 39, 55, 77, 83, 94, 98, 115, 131, 135, 139, 144, 160, 182, 188, 199, 203, 220, 236, 240, 244, 249, 265, 287, 293, 304, 308, 320, 324, 326, 330, 331, 370, 371, 391, 397, 398, 399, 402, 425, 429, 431, 435, 436, 475, 476, 496, 502, 503, 504, 507, 530, 534, 536, 540, 541, 580, 581, 601, 607, 608, 609, 612 ], "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": 72, "confidence": "upper_bound", "witness": [ 3, 11, 17, 28, 29, 38, 46, 52, 63, 64, 73, 81, 87, 98, 99, 108, 116, 122, 133, 134, 143, 151, 157, 168, 169, 178, 186, 192, 203, 204, 213, 221, 227, 238, 239, 248, 256, 262, 273, 274, 283, 291, 297, 308, 309, 321, 326, 348, 356, 361, 383, 391, 396, 418, 426, 431, 453, 461, 466, 488, 496, 501, 523, 531, 536, 558, 566, 571, 593, 601, 606, 628 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^315 - 1 with a(x) = x^16 + x^89 + x^111 + x^122 + x^140 + x^221 + x^253, b(x) = x^66 + x^83 + x^110 + x^123 + x^184 + x^238 + x^267; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-10-02", "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 72 -> 66 (orbit-fold search (verify/heuristic_distance.orbit_fold_refute, PR #2902), 1,000,000 trials per folded code, seed 101)." }, "family": "generalized-bicycle" }