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166, 170, 288, 291, 334 ], [ 46, 123, 147, 167, 244, 264, 277, 335 ] ] }, "distance": { "d": 20, "X": { "value": 20, "confidence": "upper_bound", "witness": [ 52, 60, 93, 105, 111, 127, 136, 144, 171, 186, 187, 204, 219, 266, 281, 296, 312, 317, 325, 327 ] }, "Z": { "value": 20, "confidence": "upper_bound", "witness": [ 6, 46, 51, 69, 82, 84, 101, 118, 136, 144, 156, 163, 171, 193, 194, 219, 228, 274, 275, 309 ] } }, "provenance": { "authors": [ "@FarLab" ], "construction": "2BGA with supports a=[0, 88, 101, 111], b=[0, 9, 59, 98] on PSL(2,7) (order 168, the Klein-quartic/Hurwitz group) as permutations of the projective line P1(F7) with points ordered (0,...,6,inf), generated by T: z -> z+1 and S: z -> -1/z; elements enumerated by BFS closure (research/kit/group_algebra.perm_group, identity at index 0). H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T].", "references": [ "arXiv:2306.16400 (2BGA family)", "arXiv:2606.17268 (novelty check)", "arXiv:2606.24808 (novelty check)" ], "date": "2026-07-08", "notes": "Found by simulated annealing over weight-8 supports (identity pinned in both supports by shift equivalence; screen-then-confirm fitness). Claimed d is the lightest logical found by deep self-refutation: flat across 1M/4M/16M RIS trials/side on THREE independent seeds (discovery + 2 fresh), witness re-validated by the pinned python stack, BP+OSD (1M trials) found nothing lighter. Upper bound only. Novelty due diligence 2026-07-08: outside arXiv:2306.16400 (n<=200), arXiv:2606.17268 (n<=306, all even k), arXiv:2606.24808 (no PSL(2,7)); no [[336,20/19,*]] found; first qLDPC use of PSL(2,7) to our knowledge.", "model": "Claude Fable 5", "novelty": "new_parameters" }, "family": "generalized-bicycle" }