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47, 48, 49, 54, 63, 64, 67, 82, 94, 95, 144, 145, 146, 152, 158, 160, 161, 164, 172, 181, 183, 199, 207, 211, 231, 241, 252, 254, 268, 308, 312, 314, 332, 338, 342, 348, 350, 353, 358, 363, 364, 367, 373, 375, 379, 383, 400, 403, 412, 414, 429, 434, 442, 448, 486, 493, 495, 500, 518, 525, 531, 534, 538, 540, 551, 564, 568, 569, 581, 595, 617, 642, 646, 657, 670 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-10-07", "found_at_samples": 300000000, "tool": "image of the X witness under the GB transpose automorphism", "seeds": [ 1 ] } } }, "provenance": { "authors": [ "@vprusso" ], "origin": "submission", "novelty": "new_parameters", "model": "Claude Fable 5.1 (Claude Code)", "date": "2026-10-07", "construction": "Cyclic generalized-bicycle code over Z_337: H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T], a = x^[39, 69, 99, 146, 157, 173, 189, 216, 238, 251, 260, 263, 273, 284, 308, 311], b = x^[2, 22, 47, 52, 62, 65, 78, 92, 96, 121, 135, 149, 181, 241, 251, 280], both sparse multiples of a designed divisor g of x^337 - 1 (hex 0x1b2e20f5df4de415d) of degree 64, so k = 2 deg g = 128 by construction. Found by the designed-divisor sampler (PR #2790 lineage) in the 2026-10-07 campaign.", "notes": "Readings: 200,000 trials 91; 2,000,000 trials 86 (seed 23); 10,000,000 trials 86 (Perlmutter CPU, seed 777) and 83 (laptop, seed 2026); 300,000,000 GPU trials per side (Perlmutter A100, seed 1): X 81, Z 82, both CPU-verified. Seed 2 at the same depth: X 82, Z 83. Annihilator attack 200,000 trials: nothing below 86. The board's [[674,128,80]] is a designed-divisor GB at the same lift with a different degree-64 divisor (a with 16 terms, b with 14, check weight 30), refuted from 87 to 80 at 1,000,000,000 trials per side; this entry's reading fell from 86 to 81 between 10M and 300M trials and has not been attacked at 1B. The Z witness is the image of the X witness under the GB transpose automorphism (block swap composed with i -> -i mod 337); the GPU read 82 on the Z side directly. Witnessed upper bound." }, "family": "generalized-bicycle" }