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"distance": { "d": 57, "X": { "value": 57, "confidence": "upper_bound", "witness": [ 22, 26, 34, 42, 47, 65, 67, 69, 70, 99, 103, 111, 119, 124, 142, 144, 146, 147, 176, 180, 188, 196, 201, 219, 221, 223, 224, 233, 235, 242, 256, 262, 271, 291, 292, 294, 301, 310, 312, 319, 333, 339, 348, 368, 369, 371, 378, 387, 389, 396, 410, 416, 425, 445, 446, 448, 455 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_77 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "Z": { "value": 57, "confidence": "upper_bound", "witness": [ 7, 14, 16, 17, 37, 46, 52, 66, 73, 75, 84, 91, 93, 94, 114, 123, 129, 143, 150, 152, 161, 168, 170, 171, 191, 200, 206, 220, 227, 229, 238, 239, 241, 243, 261, 266, 274, 282, 286, 315, 316, 318, 320, 338, 343, 351, 359, 363, 392, 393, 395, 397, 415, 420, 428, 436, 440 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_77 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^231 - 1 with a(x) = x^41 + x^62 + x^68 + x^89 + x^90 + x^122 + x^128 + x^137 + x^146 + x^210, b(x) = x^23 + x^62 + x^95 + x^135 + x^146 + x^154 + x^161 + x^197 + x^207 + x^220; 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" }