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"confidence": "upper_bound", "witness": [ 1, 2, 5, 7, 22, 35, 40, 43, 45, 57, 81, 92, 94, 123, 162, 182, 198, 217, 287 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-12", "found_at_samples": 2000, "survived_samples": 2000, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 1001 ] } } }, "provenance": { "authors": [ "Lee, Gideon" ], "construction": "Two-block group-algebra code C(a,b) over (C7 x C7) : C3 = SmallGroup(147, 4) (order 147), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 294; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 1, 2, 19, 62}, b = {0, 2, 3, 112} as element indices. Check weight 9. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race.", "references": [ "arXiv:2610.13880" ], "date": "2026-10-12", "notes": "Parameters and construction taken from the public database of arXiv:2610.13880v1. Distance is an upper bound certified by the witnesses attached here. The X witness is the database's own published logical operator rather than one this session's search produced; that side's witness_provenance records the difference. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race @ aed705a, CC BY 4.0; rebuilt here with the repo's own group data. Distance is an upper bound certified by the attached witnesses, not the paper's exact distance.", "origin": "baseline", "novelty": "known_parameters", "model": "Mimo-V2.6-Flash" }, "family": "2bga-nonabelian" }