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] }, "distance": { "d": 85, "X": { "value": 85, "confidence": "upper_bound", "witness": [ 6, 11, 15, 19, 47, 61, 71, 76, 80, 84, 112, 126, 136, 141, 145, 149, 177, 191, 201, 206, 210, 214, 242, 256, 266, 271, 275, 279, 307, 321, 327, 336, 341, 351, 355, 360, 363, 365, 370, 372, 386, 392, 401, 406, 416, 420, 425, 428, 430, 435, 437, 451, 457, 466, 471, 481, 485, 490, 493, 495, 500, 502, 516, 522, 531, 536, 546, 550, 555, 558, 560, 565, 567, 581, 587, 596, 601, 611, 615, 620, 623, 625, 630, 632, 646 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_65 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "Z": { "value": 85, "confidence": "upper_bound", "witness": [ 4, 18, 20, 25, 27, 30, 35, 39, 49, 54, 63, 69, 83, 85, 90, 92, 95, 100, 104, 114, 119, 128, 134, 148, 150, 155, 157, 160, 165, 169, 179, 184, 193, 199, 213, 215, 220, 222, 225, 230, 234, 244, 249, 258, 264, 278, 280, 285, 287, 290, 295, 299, 309, 314, 323, 329, 343, 371, 375, 379, 384, 394, 408, 436, 440, 444, 449, 459, 473, 501, 505, 509, 514, 524, 538, 566, 570, 574, 579, 589, 603, 631, 635, 639, 644 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_65 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Cyclic generalized-bicycle code on the ring x^325 - 1 with a(x) = x^28 + x^73 + x^95 + x^121 + x^129 + x^141 + x^224 + x^250 + x^274 + x^307, b(x) = x^34 + x^199 + x^205 + x^212 + x^224 + x^250; 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" }