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291, 336, 350, 452, 475, 494, 533, 635 ], [ 15, 30, 178, 223, 277, 278, 292, 337, 351, 453, 476, 495, 534, 636 ] ] }, "distance": { "d": 110, "X": { "value": 110, "confidence": "upper_bound", "witness": [ 22, 26, 30, 53, 57, 61, 84, 88, 92, 115, 119, 123, 146, 150, 154, 177, 181, 185, 208, 212, 216, 239, 243, 247, 270, 274, 278, 301, 305, 309, 332, 336, 340, 343, 345, 348, 353, 354, 360, 363, 374, 376, 379, 384, 385, 391, 394, 405, 407, 410, 415, 416, 422, 425, 436, 438, 441, 446, 447, 453, 456, 467, 469, 472, 477, 478, 484, 487, 498, 500, 503, 508, 509, 515, 518, 529, 531, 534, 539, 540, 546, 549, 560, 562, 565, 570, 571, 577, 580, 591, 593, 596, 601, 602, 608, 611, 622, 624, 627, 632, 633, 639, 642, 653, 655, 658, 663, 664, 670, 673 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_31 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "Z": { "value": 110, "confidence": "upper_bound", "witness": [ 9, 12, 18, 19, 24, 27, 29, 40, 43, 49, 50, 55, 58, 60, 71, 74, 80, 81, 86, 89, 91, 102, 105, 111, 112, 117, 120, 122, 133, 136, 142, 143, 148, 151, 153, 164, 167, 173, 174, 179, 182, 184, 195, 198, 204, 205, 210, 213, 215, 226, 229, 235, 236, 241, 244, 246, 257, 260, 266, 267, 272, 275, 277, 288, 291, 297, 298, 303, 306, 308, 319, 322, 328, 329, 334, 337, 339, 342, 346, 350, 373, 377, 381, 404, 408, 412, 435, 439, 443, 466, 470, 474, 497, 501, 505, 528, 532, 536, 559, 563, 567, 590, 594, 598, 621, 625, 629, 652, 656, 660 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_31 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^341 - 1 with a(x) = x^45 + x^147 + x^186 + x^205 + x^228 + x^330, b(x) = x^3 + x^48 + x^62 + x^63 + x^117 + x^162 + x^310 + x^325; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-24", "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." }, "family": "generalized-bicycle" }