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340, 350, 367, 377, 396, 422, 423, 432, 449, 459, 468, 495, 504 ], "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 ] } }, "Z": { "value": 24, "confidence": "upper_bound", "witness": [ 4, 30, 42, 50, 78, 114, 160, 167, 187, 203, 213, 223, 239, 272, 301, 336, 342, 356, 362, 368, 391, 397, 493, 501 ], "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": "known_parameters", "construction": "Generalized bicycle (two-block) code on Z_255: H_X=[A|B], H_Z=[B^T|A^T], a(x)=x^151+x^197+x^233, b(x)=x^37+x^196+x^202; g=gcd(a,b,x^255-1) irreducible of degree 8, k=16, row weight 6. Full circulant check sets kept (symmetry-visible).", "model": "Claude Fable 5", "references": [ "arXiv:2203.17216", "arXiv:2306.16400", "arXiv:2502.19406" ], "date": "2026-08-19", "notes": "Member of the known [[2^(m+1)-2, 2m]] GB family (m=8); marked known_parameters accordingly \u2014 the contribution is the distance datum d<=24 for this instance (no published distance found in the 2026-08-19 lit pass) plus the documented symmetry: TWO orbits of the 16 canonical logical classes under the full Tanner automorphism group (Singer packets, x primitive mod g). Evidence: GPU deep-RIS 15Mx2/side (CPU-verified witnesses) + sqetch 20Mx2/side; original 26-claim refuted down to 24 by the GPU engine itself." }, "family": "generalized-bicycle" }