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"seeds": [ 0 ] } }, "Z": { "value": 64, "confidence": "upper_bound", "witness": [ 1, 4, 17, 38, 39, 68, 69, 72, 74, 79, 86, 102, 104, 105, 117, 126, 130, 132, 135, 148, 169, 170, 199, 200, 203, 205, 210, 217, 233, 235, 236, 248, 257, 261, 279, 288, 290, 293, 295, 305, 324, 326, 331, 349, 369, 370, 371, 382, 390, 410, 419, 421, 424, 426, 436, 455, 457, 462, 480, 500, 501, 502, 513, 521 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_131 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^262 - 1 with a(x) = x^36 + x^96 + x^107 + x^157 + x^216 + x^254, b(x) = x^10 + x^27 + x^49 + x^70 + x^73 + x^93 + x^110 + x^112 + x^165 + x^191; 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" }