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"found_at_samples": 5000, "survived_samples": 5000, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 4242 ] } }, "Z": { "value": 19, "confidence": "upper_bound", "witness": [ 7, 31, 67, 79, 92, 128, 140, 160, 164, 165, 184, 195, 200, 220, 231, 245, 256, 281, 292 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-12", "found_at_samples": 2000, "survived_samples": 2000, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 1006 ] } } }, "provenance": { "authors": [ "Lee, Gideon" ], "construction": "Two-block group-algebra code C(a,b) over C51 x C3 = SmallGroup(153, 2) (order 153), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 306; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 32, 91, 124}, b = {0, 19, 31, 56} as element indices. Check weight 8. 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": "generalized-bicycle" }