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"found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_45 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "Z": { "value": 56, "confidence": "upper_bound", "witness": [ 3, 26, 31, 32, 42, 48, 71, 76, 77, 87, 93, 116, 121, 122, 132, 138, 161, 166, 167, 177, 183, 206, 211, 212, 222, 228, 251, 256, 257, 267, 273, 296, 301, 302, 312, 323, 330, 349, 368, 375, 394, 413, 420, 439, 458, 465, 484, 503, 510, 529, 548, 555, 574, 593, 600, 619 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_45 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^315 - 1 with a(x) = x^16 + x^38 + x^123 + x^208 + x^228 + x^270 + x^274 + x^287 + x^293, b(x) = x^39 + x^52 + x^54 + x^99 + x^167 + x^168 + x^186 + x^200 + x^206 + x^211 + x^225 + x^240 + x^262; 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" }