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"d": 66, "Z": { "value": 66, "confidence": "upper_bound", "witness": [ 6, 9, 14, 45, 62, 68, 75, 88, 97, 100, 105, 136, 153, 159, 166, 179, 188, 191, 196, 227, 244, 250, 257, 270, 274, 276, 279, 286, 287, 307, 318, 324, 333, 338, 343, 352, 354, 360, 365, 367, 370, 377, 378, 398, 409, 415, 424, 429, 434, 443, 445, 451, 456, 458, 461, 468, 469, 489, 500, 506, 515, 520, 525, 534, 536, 542 ], "witness_provenance": { "found_by": [ "@VedantMahadik-qc" ], "date": "2026-09-26", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_91 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "X": { "value": 72, "confidence": "upper_bound", "witness": [ 12, 23, 40, 43, 44, 55, 59, 68, 74, 79, 85, 88, 103, 114, 131, 134, 135, 146, 150, 159, 165, 170, 176, 179, 194, 205, 222, 225, 226, 237, 241, 250, 256, 261, 267, 270, 275, 278, 302, 305, 324, 331, 335, 337, 349, 350, 357, 360, 366, 369, 393, 396, 415, 422, 426, 428, 440, 441, 448, 451, 457, 460, 484, 487, 506, 513, 517, 519, 531, 532, 539, 542 ], "witness_provenance": { "found_by": [ "@VedantMahadik-qc" ], "date": "2026-09-26", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_91 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^273 - 1 with a(x) = x^50 + x^56 + x^89 + x^105 + x^106 + x^123 + x^258 + x^266 + x^272, b(x) = x^38 + x^45 + x^69 + x^70 + x^96 + x^127 + x^144 + x^146 + x^147 + x^234 + x^244 + x^249 + x^269; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].", "origin": "submission", "novelty": "known_parameters", "model": "Claude Opus 5", "date": "2026-09-23", "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 corrected from 84 to 82: the verifier found a weight-82 Z-logical. The X witness is its reflection under x -> x^-1, of equal weight for a cyclic generalized-bicycle code. Tightened 2026-09-26 by @VedantMahadik-qc: the Z_91 quotient code (both generator polynomials reduced modulo x^91 - 1, quotient dimension 6) has a weight-24 X logical and a weight-22 Z logical, and their norm-word lifts (multiplication by 1 + x^91 + x^182) are a weight-72 X logical and a weight-66 Z logical of the full code, so d <= 66. The code, checks, and authorship are unchanged; only the distance block and name are revised." }, "family": "generalized-bicycle" }