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420, 439, 446 ] }, "Z": { "value": 30, "confidence": "upper_bound", "witness": [ 9, 20, 21, 29, 76, 104, 117, 121, 128, 132, 139, 141, 161, 216, 221, 229, 232, 243, 254, 268, 294, 305, 316, 323, 330, 377, 379, 421, 450, 461 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-26", "found_at_samples": 300000000, "survived_samples": 300000000, "tool": "verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified)", "seeds": [ 4102 ] } } }, "provenance": { "authors": [ "@vprusso" ], "construction": "Two-block group algebra (2BGA) code over the non-abelian metacyclic group C_3 semidirect_2 C_80 of order 240: H_X=[Lm(a)|Rm(b)], H_Z=[Rm(b)^T|Lm(a)^T] from the left and right regular representations, which commute for any group so the CSS condition holds without G abelian. Element (i,j) = x^i y^j indexed as i*80+j, with (i1,j1)(i2,j2) = (i1 + i2*2^j1 mod 3, j1+j2 mod 80). a = {0,108,220}, b = {0,142,233}. Construction of arXiv:2306.16400 applied past that paper's Table 1 range; the builder reproduces the board's [[540,12,28]] on C_9 semidirect C_30 exactly (n, k and w, and d reaching 28 at 2M trials).", "origin": "submission", "date": "2026-09-06", "model": "Claude Opus 5" }, "family": "2bga-coset" }