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"seeds": [ 2026 ] } }, "Z": { "value": 36, "confidence": "upper_bound", "witness": [ 8, 18, 29, 40, 50, 61, 72, 82, 93, 104, 114, 125, 136, 146, 157, 168, 178, 189, 200, 210, 221, 232, 242, 253, 264, 274, 285, 316, 348, 380, 412, 444, 476, 508, 540, 572 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-20", "found_at_samples": 300000000, "survived_samples": 300000000, "tool": "ris_gpu", "seeds": [ 2026 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Coset two-block group-algebra code (research/kit/coset.py build_coset). G = metacyclic C_36 x| C_24 with action r = 25 (kit group_algebra.metacyclic(36,24,25), element (i,j) at index i*24+j), H = subgroup with element indices [0, 8, 16] (order 3, non-normal, |N_G(H)/H| = 96), qubits indexed by the 288 left cosets G/H. a = [259, 398, 433, 696] (element indices in G), b = [294, 511, 589, 740] (element indices in N_G(H)). H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T].", "origin": "submission", "date": "2026-09-20", "model": "Claude Fable 5.1", "notes": "Distance is a witnessed upper bound from randomized information-set search; novelty vs the literature unverified.", "search_budget": { "candidates_screened": 1660, "ris_trials_per_side": 300000000, "wall_clock_hours": 1.0, "tool": "research/kit search funnel, gf2_fast RIS, verify/ris_gpu (A40)" } }, "family": "2bga-coset" }