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213, 216, 241, 242, 249, 252, 253, 265, 273, 284, 285, 288, 318, 319, 326, 329, 330, 342, 350, 361, 362, 365, 395, 396, 403, 406, 407, 419, 427, 438, 439, 442 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_77 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "Z": { "value": 54, "confidence": "upper_bound", "witness": [ 11, 14, 15, 26, 34, 46, 47, 50, 57, 58, 88, 91, 92, 103, 111, 123, 124, 127, 134, 135, 165, 168, 169, 180, 188, 200, 201, 204, 211, 212, 237, 240, 242, 251, 253, 258, 267, 285, 314, 317, 319, 328, 330, 335, 344, 362, 391, 394, 396, 405, 407, 412, 421, 439 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_77 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^231 - 1 with a(x) = x^10 + x^32 + x^49 + x^61 + x^74 + x^106 + x^122 + x^127 + x^136 + x^179 + x^195 + x^211 + x^212, b(x) = x^10 + x^26 + x^35 + x^47 + x^68 + x^93 + x^163 + x^172 + x^177 + x^195 + x^218; 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" }