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"found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_58 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "Z": { "value": 75, "confidence": "upper_bound", "witness": [ 19, 23, 28, 32, 33, 37, 47, 48, 53, 54, 56, 77, 81, 86, 90, 91, 95, 105, 106, 111, 112, 114, 135, 139, 144, 148, 149, 153, 163, 164, 169, 170, 172, 193, 197, 202, 206, 207, 211, 221, 222, 227, 228, 230, 251, 255, 260, 264, 265, 269, 279, 280, 285, 286, 288, 297, 308, 310, 327, 355, 366, 368, 385, 413, 424, 426, 443, 471, 482, 484, 501, 529, 540, 542, 559 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_58 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^290 - 1 with a(x) = x^3 + x^63 + x^66 + x^84 + x^101 + x^102 + x^123 + x^164 + x^180 + x^233 + x^265 + x^284, b(x) = x^11 + x^142 + x^147 + x^164 + x^170 + x^175 + x^194 + x^211 + x^231 + x^249 + x^258 + x^271; 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." }, "family": "generalized-bicycle" }