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"date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_51 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "Z": { "value": 65, "confidence": "upper_bound", "witness": [ 7, 20, 24, 34, 58, 71, 75, 85, 109, 122, 126, 136, 160, 173, 177, 187, 211, 224, 228, 238, 257, 259, 274, 279, 287, 291, 293, 299, 301, 308, 310, 325, 330, 338, 342, 344, 350, 352, 359, 361, 376, 381, 389, 393, 395, 401, 403, 410, 412, 427, 432, 440, 444, 446, 452, 454, 461, 463, 478, 483, 491, 495, 497, 503, 505 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_51 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^255 - 1 with a(x) = x^4 + x^52 + x^87 + x^119 + x^139 + x^152 + x^154 + x^200 + x^230 + x^239 + x^253, b(x) = x^20 + x^31 + x^76 + x^85 + x^188 + x^225 + x^226 + x^243; 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" }