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109, 132, 135, 151, 158, 162, 166, 168, 179, 193, 202, 212, 217, 218, 223, 230, 253, 255, 257, 264, 293, 304, 305, 318, 323, 331, 332, 334, 340, 346, 353, 354, 358, 365, 366, 371, 387, 393, 400, 410, 413, 414, 415, 416, 427, 431, 435, 448, 461, 476, 481, 499, 508, 512, 541, 544, 546, 555, 556, 578, 581, 588, 589, 593, 597, 600, 625, 627, 629, 645, 654 ], "witness_provenance": { "found_by": [ "@vaibhav-baj" ], "date": "2026-10-10", "found_at_samples": 3000000, "survived_samples": 10000000, "tool": "gf2_fast RIS, pair depth 8, fresh-seed 1M chunks", "seeds": [ 42002 ] } }, "Z": { "value": 84, "confidence": "upper_bound", "witness": [ 3, 18, 22, 34, 39, 55, 62, 70, 79, 80, 83, 102, 136, 149, 168, 171, 172, 180, 185, 197, 201, 202, 203, 207, 208, 238, 249, 257, 271, 280, 284, 294, 299, 300, 304, 315, 323, 329, 331, 332, 339, 342, 347, 350, 352, 355, 359, 361, 368, 376, 378, 380, 385, 388, 394, 403, 407, 416, 426, 438, 440, 462, 474, 486, 488, 492, 545, 548, 556, 557, 558, 566, 584, 591, 592, 605, 607, 614, 621, 629, 635, 640, 649, 661 ] } }, "provenance": { "authors": [ "@vaibhav-baj" ], "construction": "Cyclic generalized-bicycle code at prime length 331: H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T], with a={8,14,60,65,84,121,145,154,195,227,252,285,320,322} (weight 14) and b={28,75,89,114,136,152,220,224,252,264,292,296,298,300,312,328} (weight 16), random sparse multiples of a degree-61 divisor (x+1 times two degree-30 factors of x^331-1) found by Prange search in the ideal, with no multiplier relation between a and b and no rotation subgroup (prime length), so the verifier's orbit-fold search finds no symmetry (0 partitions). k=122, check weight 30. Structural single-block cap 94; RIS ladder 85; the submit tool's own 2M-trial pass found the weight-84 Z logical that is the submitted claim.", "origin": "submission", "date": "2026-10-10", "model": "Claude Opus 5.5 (Claude Code)", "search_budget": { "candidates_screened": 2, "ris_trials_per_side": 10000000, "cpu_hours": 15.0, "tool": "prime-length divisor-ideal sampler + gf2_fast accelerator" } }, "family": "generalized-bicycle" }