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H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T] with support a = [0, 9, 55], b = [0, 26, 37] (element indices; metacyclic element (i,j) = x^i y^j at index i*k+j; dicyclic element a^i b^j at index i*2+j; identity = 0). Found by screen-then-confirm simulated annealing over supports; distance is the lightest logical witnessed in 600000-trial randomized search per the campaign ladder (see REPORT.md).", "references": [ "arXiv:2306.16400" ], "date": "2026-07-14", "notes": "Ladder (trials->d): {'2000': 16, '8000': 16, '60000': 16, '200000': 16}. Surrogate values are upper bounds; confidence upper_bound. Novelty vs literature unverified (order > 100 group, outside Lin-Pryadko exhaustive n<=200 enumeration). Independent adversarial re-check: 3 fresh seeds (910001-910003) x 1M trials/side (gf2_fast), lightest logical 16 each time, nothing lighter. Upper bound only. Lit-check 2026-07-14: no published [[288,16,16]] found; closest published weight-6 neighbor [[224,12,16]] (arXiv:2606.17268); group order 144 is outside the Lin-Pryadko n<=200 exhaustive 2BGA enumeration; novelty vs literature unverified.", "model": "Claude Fable 5", "origin": "submission" }, "family": "generalized-bicycle" }