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"confidence": "upper_bound", "witness": [ 13, 32, 38, 133, 152, 158, 253, 272, 278, 374, 390, 394, 396, 422, 442, 446, 464, 468, 494, 510, 514, 516, 542, 562, 566, 584, 588, 614, 630, 634, 636, 662, 682, 686, 704, 708 ], "witness_provenance": { "found_by": [ "@MicheldeMessieres" ], "date": "2026-10-08", "found_at_samples": 100000, "survived_samples": 300000, "tool": "bit-packed RIS (sym-restricted, then plain)" } }, "Z": { "value": 36, "confidence": "upper_bound", "witness": [ 21, 47, 119, 141, 167, 239, 261, 287, 359, 360, 368, 385, 391, 404, 461, 467, 469, 475, 480, 488, 505, 511, 524, 581, 587, 589, 595, 600, 608, 625, 631, 644, 701, 707, 709, 715 ], "witness_provenance": { "found_by": [ "@MicheldeMessieres" ], "date": "2026-10-08", "found_at_samples": 100000, "survived_samples": 300000, "tool": "bit-packed RIS (sym-restricted, then plain)" } } }, "provenance": { "construction": "Two-block group-algebra (2BGA) code, check weight 6, over G = C18 x Dic5 (order 360; Dic5 = C5 : C4 = , z of order 18 central). Element z^c x^i y^j is indexed 20c+4i+j; product (c1,i1,j1)(c2,i2,j2) = (c1+c2 mod 18, i1+(-1)^j1 i2 mod 5, j1+j2 mod 4). H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] with L(a)[g,h]=1 iff g=alpha h, R(b)[g,h]=1 iff g=h beta; qubits 0..359 = block 1, 360..719 = block 2. a={1, z^3 x^2, z^14 x y^2}, b={1, z y^3, z^6 x y^2}. Found by an exhaustive symmetry-reduced census of weight-6 2BGA codes over C_m x Dic5 (two-sided translations and Aut(G) removed).", "authors": [ "@MicheldeMessieres" ], "origin": "submission", "date": "2026-10-09", "model": "Claude Opus 5.5 (Claude Code)", "novelty": "unknown", "references": [ "arXiv:2306.16400" ], "notes": "Our contribution: the choice of group C18 x Dic5 and the supports a, b, found by an exhaustive symmetry-reduced enumeration of weight-6 2BGA codes (the 2BGA construction itself is Lin and Pryadko's, arXiv:2306.16400). The gate reports no exact duplicate and no WL-equivalent entry. Distance is a witness-backed upper bound: the deepest null result is 300000 random-information-set trials per side plus a 500 x 20000 incremental search. Literature novelty is unverified. Search direction inspired by codes/672-20-32.json by @vprusso (the cell leader; cyclic x small non-abelian group).", "search_budget": { "cpu_hours": 1.0, "ris_trials_per_side": 300000 } }, "family": "2bga-coset" }