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15000000, "survived_samples": 30000000, "tool": "verify/ris_gpu --pair-depth 24", "seeds": [ 1, 2 ] } }, "Z": { "value": 22, "confidence": "upper_bound", "witness": [ 3, 62, 78, 97, 104, 130, 156, 198, 215, 250, 283, 309, 318, 339, 419, 460, 462, 501, 584, 625, 638, 640 ], "witness_provenance": { "found_by": [ "@FarLab" ], "date": "2026-08-19", "found_at_samples": 15000000, "survived_samples": 30000000, "tool": "verify/ris_gpu --pair-depth 24", "seeds": [ 1, 2 ] } } }, "provenance": { "authors": [ "@FarLab" ], "origin": "submission", "novelty": "new_parameters", "construction": "Generalized bicycle (two-block) code on Z_341: H_X=[A|B], H_Z=[B^T|A^T], a(x)=x^41+x^67+x^288, b(x)=x^27+x^149+x^327; g=gcd(a,b,x^341-1) irreducible of degree 10, k=2*deg(g)=20, row weight 6. Full 341-row circulant check sets kept (redundant rows carry the translation symmetry).", "model": "Claude Fable 5", "references": [ "arXiv:2203.17216", "arXiv:2306.16400" ], "date": "2026-08-19", "notes": "Found in a two-orbit-structure GB search (orbit-prescribed gcd factorization). Logical space = 2 Singer packets over F_2[x]/(g); ord_341(x)=341 splits each packet into 3 translation orbits; the full Tanner automorphism group (incl. multiplier maps) acts with 6 orbits on the 20 canonical logical classes. Distance evidence: GPU deep-RIS 15M full-kernel pair trials x 2 seeds per side (all four runs find 22, CPU-verified witnesses) + sqetch 20Mx2 trials/side; no operator below 22 found by any engine. Novelty basis: 2026-08-19 lit pass (Wang-Pryadko 2203.17216 exhaustive tables are k=2-family/ell<=217; Lin-Pryadko 2306.16400 is n<=100; no zoo/board/recent-paper hits)." }, "family": "generalized-bicycle" }