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194, 206, 218, 232, 241, 259, 276, 288, 290, 311, 333, 339, 346, 366, 370 ] ] }, "distance": { "d": 36, "X": { "value": 36, "confidence": "upper_bound", "witness": [ 6, 15, 27, 36, 48, 57, 69, 78, 90, 99, 111, 120, 132, 141, 153, 162, 174, 183, 190, 201, 211, 222, 232, 243, 253, 264, 274, 285, 295, 306, 316, 327, 337, 348, 358, 369 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_21 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "Z": { "value": 36, "confidence": "upper_bound", "witness": [ 4, 25, 46, 67, 88, 109, 130, 151, 172, 189, 199, 200, 210, 220, 221, 231, 241, 242, 252, 262, 263, 273, 283, 284, 294, 304, 305, 315, 325, 326, 336, 346, 347, 357, 367, 368 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_21 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^189 - 1 with a(x) = x^7 + x^11 + x^31 + x^38 + x^44 + x^66 + x^87 + x^89 + x^101 + x^118 + x^136 + x^145 + x^159 + x^171 + x^183, b(x) = x^6 + x^10 + x^24 + x^38 + x^46 + x^54 + x^57 + x^98 + x^103 + x^108 + x^150 + x^152 + x^161 + x^168 + x^170; 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" }