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432, 440, 448, 453, 459 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_116 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "Z": { "value": 60, "confidence": "upper_bound", "witness": [ 5, 11, 16, 24, 32, 36, 45, 59, 65, 79, 83, 87, 96, 110, 121, 127, 132, 140, 148, 152, 161, 175, 181, 195, 199, 203, 212, 226, 237, 240, 248, 252, 275, 279, 282, 292, 300, 306, 317, 325, 331, 334, 335, 347, 353, 356, 364, 368, 391, 395, 398, 408, 416, 422, 433, 441, 447, 450, 451, 463 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_116 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^232 - 1 with a(x) = x^0 + x^43 + x^44 + x^50 + x^68 + x^91 + x^168 + x^171 + x^180 + x^218, b(x) = x^34 + x^43 + x^52 + x^55 + x^56 + x^58 + x^68 + x^105 + x^127 + x^222 + x^225 + x^227; 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" }