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1, 5, 20, 24, 54, 58, 82, 86, 93, 97, 142, 148, 151, 157, 183, 189, 215, 219, 230, 236 ] }, "Z": { "value": 16, "confidence": "upper_bound", "witness": [ 50, 73, 98, 109, 164, 173, 198, 215, 334, 369, 428, 480, 511, 516, 545, 603 ] } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Two-block group algebra (2BGA) code on the metacyclic group C_33 semidirect_29 C_10 (order 330): H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] from the left and right regular representations, which commute for any group (arXiv:2306.16400). Element (i,j) = x^i y^j at index i*10+j with (i1,j1)(i2,j2) = (i1 + i2*29^j1 mod 33, j1+j2 mod 10), identity at index 0 (research/kit/group_algebra.py: metacyclic(33,10,29) then build_2bga(mul, a, b)). a = [0, 234, 100], b = [0, 289, 128].", "origin": "submission", "date": "2026-09-20", "model": "Claude Fable 5.1", "notes": "Weight-6 metacyclic 2BGA sweep (a sweep script kept with the search run (not committed; method in the research note)): 21,000 random identity-normalized weight-3 support pairs over 1,560 presentations C_n x| C_m with 150 <= nm <= 350, k >= 18 kept, screened at 300 gf2_fast RIS trials. Ladder for this code (gf2_fast RIS, trials -> lightest logical): 300 -> 18, 2k -> 16, 20k -> 16, 200k -> 16, 1M -> 16. Upper-bound confidence; d = 16 is the lightest logical witnessed. Advances the weight-6 x unrestricted board cell if the gate agrees; novelty vs the literature unverified.", "search_budget": { "candidates_screened": 21000, "ris_trials_per_side": 1000000, "wall_clock_hours": 1.0, "tool": "research/kit search funnel, gf2_fast RIS" } }, "family": "generalized-bicycle" }