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127, 167, 205, 275, 461, 476, 532, 565 ], [ 6, 80, 222, 272, 462, 477, 533, 566 ], [ 25, 115, 171, 219, 463, 478, 534, 567 ], [ 10, 62, 112, 242, 464, 479, 535, 568 ], [ 29, 135, 153, 239, 465, 480, 536, 569 ], [ 66, 150, 280, 316, 466, 481, 537, 570 ], [ 139, 227, 299, 313, 467, 482, 538, 571 ], [ 120, 264, 284, 296, 450, 483, 539, 572 ], [ 193, 231, 247, 261, 451, 484, 522, 573 ] ] }, "distance": { "d": 71, "X": { "value": 71, "confidence": "upper_bound", "witness": [ 8, 10, 14, 27, 33, 46, 47, 58, 78, 79, 83, 89, 97, 102, 117, 119, 122, 138, 140, 146, 153, 157, 170, 177, 204, 207, 208, 216, 222, 225, 230, 238, 242, 248, 251, 255, 276, 310, 317, 324, 335, 337, 371, 375, 390, 396, 406, 413, 421, 426, 428, 448, 462, 465, 500, 505, 510, 517, 518, 558, 559, 581, 582, 584, 628, 632, 645, 647, 663, 678, 681 ], "witness_provenance": { "found_by": [ "@e-eight" ], "date": "2026-09-20", "found_at_samples": 8000000, "tool": "verify/gf2_fast distance_rand_witness, pair_depth 64", "seeds": [ 102 ] } }, "Z": { "value": 77, "confidence": "upper_bound", "witness": [ 7, 30, 31, 47, 57, 64, 76, 78, 87, 88, 89, 94, 95, 106, 107, 112, 116, 122, 125, 131, 135, 144, 149, 157, 160, 179, 198, 200, 217, 242, 250, 262, 268, 281, 292, 301, 316, 344, 346, 347, 350, 353, 355, 356, 364, 367, 376, 381, 385, 396, 397, 404, 417, 418, 423, 434, 440, 447, 464, 473, 477, 489, 491, 494, 501, 509, 513, 515, 562, 586, 599, 610, 612, 628, 638, 662, 670 ] } }, "family": "generalized-bicycle", "provenance": { "authors": [ "@edoaltamura" ], "origin": "submission", "novelty": "unknown", "construction": "Two-block group-algebra CSS code over Aff(F_19) = C_19 semidirect C_18 with action r=2, using H_X=[L(a)|R(b)] and H_Z=[R(b)^T|L(a)^T]. Element index is (x exponent)*18+(y exponent), with a=[182,323,322,217] and b=[176,208,142,68].", "references": [ "arXiv:2306.16400" ], "date": "2026-08-31", "model": "GPT-5 Codex", "notes": "Equivalence review: checked against the current board entries and their published construction data; not equivalent to an existing entry. The selected code was screened in a 3,500-candidate affine support-mutation run and then re-verified with independent RIS passes at 100,000 trials (pair depth 24), 1,000,000 trials (pair depths 32 and 48), and 2,000,000 trials (pair depths 48 and 64). The deepest X witness has weight 78 and the deepest Z witness has weight 77; both pass the opposite-kernel and non-stabilizer checks. Distance corrected from d=77 to d=71. Re-measured on fresh seeds with the bit-packed RIS, both Pauli sides searched jointly, at pair_depth 64: the accelerator's default depth of 10 searches a strictly smaller candidate set and returns 78-79 at this budget, leaving the claim looking healthy. The X side yields a weight-71 logical at 8,000,000 trials with seed 102. The witness lies in ker H_Z, raises the rank of H_X from 336 to 337 so it is outside the stabiliser group, and was re-checked independently of the search stack by a from-scratch GF(2) rank. The Z side is unchanged at 77 and is not refuted; d is the minimum over the two sides." } }