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"witness": [ 11, 22, 25, 38, 43, 53, 70, 72, 77, 78, 84, 87, 89, 91, 93, 120, 130, 139, 144, 151, 155, 157, 182, 194, 197, 209, 210, 217, 223, 255, 256, 266, 276, 292, 303, 306, 313, 316, 317, 323, 325, 328, 359, 366, 386, 388, 396, 405, 411, 412, 420, 435, 445, 450, 451, 474, 484, 495, 501, 507, 508, 512, 513, 514, 515, 528, 577, 578, 580, 604, 605, 612, 626, 633, 638, 641, 642, 652, 664, 665, 669 ], "witness_provenance": { "found_by": [ "@FarLab", "@vprusso" ], "date": "2026-09-07", "found_at_samples": 64000, "tool": "gf2_fast.distance_rand_witness, pair_depth 8", "seeds": [ 23 ] } } }, "provenance": { "authors": [ "@MathysRennela" ], "construction": "Two-block group algebra (2BGA) over the affine group of F_19: metacyclic(q, q-1, primitive_root) with left-support a=[294, 208, 142, 284] and right-support b=[6, 323, 76, 217]. Built via the research/kit group_algebra build_2bga sampler (sample_kasai_affine, seed=17).", "references": [ "arXiv:2601.08824", "arXiv:2604.20838" ], "origin": "submission", "date": "2026-07-18", "model": "Tencent Hy3", "notes": "Distance is an UPPER BOUND from randomized lightest-logical witness searches. The original d=100 claim (PR #224) was REFUTED by CI: the syndrome-decoder pass found a weight-97 X-logical and the accelerated RIS-fast pass (8M trials) found a weight-85 X-logical, both lighter than 100. This submission corrects the claim to the honest minimum found: d_X <= 85 (RIS-fast witness), d_Z <= 104 (original witness). d = min = 85. Both witnesses are validated against the pinned python stack (gf2.logical_basis / commutes / in_rowspace).\n\nDistance corrected from d=85 to d=81. A weight-81 Z-type logical exists. It was first reported by @FarLab on issue #896 (found at 64,000 trials with seed 23) and reproduced here independently at the same budget and seed. The witness lies in ker H_X, raises the rank of H_Z from 338 to 339 so it is outside the stabiliser group, and is nontrivial against the gf2 logical basis. Note that seed matters more than budget here: at 64,000 trials seeds 1, 2, 3, 7 and 11 return 96 to 101 while seed 23 returns 81, and an 8,000,000-trial run on a single seed returned only 84. Distance corrected from d=81 to d=63. The previous bound rested on one favourable seed: the weight-81 Z-logical was reported from a 64,000-trial run with seed 23, while this entry's own record notes that an 8,000,000-trial run returns only 84, and seeds 1, 2, 3, 7 and 11 return 96 to 101 at 64,000 trials. A fresh-seed random-information-set ladder at pair_depth 64 -- the accelerator's default of 10 searches a strictly smaller candidate set and reads 84 at 8,000,000 trials -- yields a weight-63 X-logical at 8,000,000 trials with seed 71, well below the claim. The witness lies in ker H_Z, raises the rank of H_X from 338 to 339 so it is outside the stabiliser group, and was re-checked independently of the search stack by a from-scratch GF(2) rank. The Z side is unchanged at 81 and is not refuted; d is the minimum over the two sides." } }