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"survived_samples": 1, "tool": "norm-word lift of a Z_91 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "Z": { "value": 66, "confidence": "upper_bound", "witness": [ 3, 9, 14, 26, 27, 36, 53, 58, 69, 71, 86, 88, 94, 100, 105, 117, 118, 127, 144, 149, 160, 162, 177, 179, 185, 191, 196, 208, 209, 218, 235, 240, 251, 253, 268, 270, 286, 293, 295, 297, 307, 321, 325, 340, 347, 359, 377, 384, 386, 388, 398, 412, 416, 431, 438, 450, 468, 475, 477, 479, 489, 503, 507, 522, 529, 541 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "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^66 + x^92 + x^94 + x^142 + x^146 + x^185 + x^193 + x^196 + x^250, b(x) = x^33 + x^45 + x^59 + x^92 + x^143 + x^172 + x^174 + x^254 + x^266; 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" }