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"value": 94, "confidence": "upper_bound", "witness": [ 6, 13, 30, 40, 53, 57, 84, 97, 100, 106, 115, 117, 122, 136, 141, 146, 147, 167, 183, 186, 210, 214, 218, 225, 227, 229, 240, 245, 266, 270, 277, 279, 293, 301, 303, 306, 307, 315, 318, 328, 334, 336, 350, 351, 355, 357, 358, 367, 368, 376, 379, 387, 392, 396, 401, 405, 408, 414, 439, 445, 448, 451, 456, 475, 481, 482, 483, 502, 503, 506, 516, 520, 530, 541, 552, 556, 559, 561, 576, 584, 587, 595, 606, 609, 612, 625, 640, 654, 657, 664, 666, 667, 673, 678 ] } }, "family": "2bga-coset", "provenance": { "authors": [ "@edoaltamura" ], "construction": "Two-block group-algebra CSS code over the affine group Aff(F_19)=C_19 semidirect C_18 with action r=2: H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T], with a=[182,323,76,217] and b=[294,208,142,82]. The group has order 342, so n=684 and every check has weight 8.", "references": [ "arXiv:2306.16400" ], "origin": "submission", "date": "2026-08-30", "model": "GPT-5.6 Luna", "notes": "Equivalence check: checked against the current board entries and their published construction data; not equivalent to an existing entry. Screening used 100 RIS trials over 3,000 one- and two-support mutations around the affine [[684,8,85]] point, followed by 2,000-trial confirmation of 80 finalists. Deep re-verification used three independent 1,000,000-trial RIS passes with pair depths 24, 32, and 48; the minimum returned was 73. The X witness of weight 73 and the Z witness of weight 94 were independently checked in the opposite-check kernels and outside the stabilizer row spaces.\n\nDistance corrected from d=73 to d=70. An 8,000,000-trial refutation search (verify/heuristic_distance.py --fast-trials 8000000 --seed 1) found a weight-70 X-type logical, replacing the previous weight-73 X witness. The replacement was checked independently of that tool: it lies in ker H_Z, it raises the rank of H_X from 336 to 337 so it is outside the stabiliser group, and it is nontrivial against the gf2 logical basis. Found by @vprusso, 2026-09-06." } }