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block, to research/kit/group_algebra.py build_2bga on the cyclic group Z_219 with supports a and b. k = 2 deg gcd(a, b, x^m - 1) = 18 by the designed common divisor.", "origin": "submission", "date": "2026-09-22", "model": "Claude Fable 5.1", "notes": "Found by a designed-divisor sweep over weight-3 pairs on Z_m sharing a common factor of x^m - 1 of degree at least 9 aimed at the weight-6 x unrestricted cell. Distance is a witness-backed upper bound; RIS ladder (verify/gf2_fast.cpp distance_rand_witness, pair depth 8): 2000 trials -> 12, 20000 -> 12, 200000 (seed 101) -> 12. Advances the weight-6 x unrestricted board; novelty vs the literature unverified. GPU RIS pass (verify/ris_gpu.py, 300,000,000 trials per side, seed 2026): lightest logical X 12, Z 12.", "search_budget": { "candidates_screened": 135, "ris_trials_per_side": 300000000, "wall_clock_hours": 1.0, "tool": "research/kit search funnel, gf2_fast RIS, verify/ris_gpu (A40)" } }, "family": "generalized-bicycle" }