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150, 486, 491, 503, 629 ] ] }, "distance": { "d": 35, "X": { "value": 92, "confidence": "upper_bound", "witness": [ 5, 6, 7, 25, 28, 33, 36, 56, 68, 72, 80, 90, 91, 94, 98, 109, 123, 127, 129, 137, 160, 167, 169, 170, 176, 186, 188, 189, 198, 209, 211, 216, 241, 242, 244, 251, 256, 258, 262, 266, 271, 273, 275, 284, 285, 298, 312, 323, 325, 338, 357, 365, 377, 380, 381, 397, 398, 399, 404, 405, 408, 410, 411, 414, 428, 437, 443, 447, 456, 459, 473, 483, 485, 490, 495, 506, 520, 524, 525, 527, 536, 554, 563, 570, 581, 582, 583, 586, 606, 609, 615, 623 ], "witness_provenance": { "found_by": [ "@FarLab" ], "date": "2026-10-17", "found_at_samples": 300, "survived_samples": 300, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 20 ] } }, "Z": { "value": 35, "confidence": "upper_bound", "witness": [ 5, 7, 24, 28, 45, 62, 108, 113, 119, 125, 131, 184, 201, 205, 210, 213, 222, 251, 257, 291, 296, 308, 364, 382, 416, 445, 447, 486, 496, 509, 520, 527, 549, 551, 566 ], "witness_provenance": { "found_by": [ "@FarLab" ], "date": "2026-10-17", "found_at_samples": 20000000, "survived_samples": 20000000, "tool": "research/kit/surrogate.distance_rand_witness (gf2_fast)", "seeds": [ 49148 ] } } }, "provenance": { "authors": [ "@FarLab" ], "construction": "Cyclic generalized-bicycle code over Z_315: H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with a = 1 + x^126 + x^138 + x^143 and b = x^164 + x^188 + x^206 + x^268; gcd(a, b, x^315 - 1) has degree 13 (x + 1 times an irreducible factor of degree 12), so k = 26 by design. Every check has weight 8.", "references": [], "date": "2026-10-17", "notes": "", "model": "Claude Fable 5.1", "origin": "submission", "search_budget": { "candidates_screened": 1528, "cpu_hours": 70, "tool": "gf2poly + surrogate (gf2_fast) from the research kit, on Brev n2d-highcpu-64", "ris_trials_per_side": 20000000 } }, "family": "generalized-bicycle" }