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16, 63, 93, 166, 193, 195, 198, 334 ], [ 17, 64, 94, 167, 194, 196, 199, 335 ] ] }, "distance": { "d": 21, "X": { "value": 21, "confidence": "upper_bound", "witness": [ 8, 32, 56, 80, 104, 128, 152, 173, 176, 197, 200, 221, 224, 245, 248, 269, 272, 293, 296, 317, 320 ] }, "Z": { "value": 21, "confidence": "upper_bound", "witness": [ 6, 21, 30, 45, 54, 69, 78, 93, 102, 117, 126, 141, 150, 165, 174, 198, 222, 246, 270, 294, 318 ] } }, "provenance": { "authors": [ "@willzeng" ], "construction": "Coset two-block group-algebra code (research/kit/coset.build_coset). G = metacyclic(56,6,29) = C56 x| C6, twist r=29 (kit element order: (i,j) -> i*6+j). Non-normal H = (|H|=2, [G:H]=168, |N_G(H)|=168); qubits = 2*[G:H] cosets. H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T], a=[0, 225, 233, 239] (element indices in G), b=[0, 36, 134, 194] (subset of N_G(H)). Found by simulated annealing with correlated two-element moves; distance = lightest logical witnessed in randomized (RIS) self-refutation (4x190000 gf2_fast trials/side + 0 checkpointed-runner trials/side).", "references": [ "arXiv:2606.17268", "arXiv:2306.16400" ], "date": "2026-07-14", "notes": "Distance is an upper bound (witnessed). Advances the computed weight-8 unrestricted cell of THIS board; novelty vs literature unverified (arXiv:2606.17268 Appendix F / Table 6 could not be extracted -- manual check required before promotion). Independent adversarial re-check: 3 fresh seeds (940001-940003) x 2M trials/side single-run (gf2_fast), lightest logical 21 each time, nothing lighter (on top of ~2M aggregate trials/side over 10 seeds during the campaign ladder, flat from 8k). Upper bound only. Lit-check 2026-07-14: arXiv:2606.17268 Appendix F Table VI extracted in full and checked - no n=336 entries, max published w8 coset distance is <=20 ([[240,16,<=20]]); Lin-Pryadko enumeration covers only n<=200; novelty vs literature unverified.", "model": "Claude Fable 5", "origin": "submission" }, "family": "2bga-coset" }