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265, 279, 329, 390, 394, 416, 430, 436, 454, 470, 480, 508 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 2000000, "seeds": [ 71000044606 ], "tool": "GPU deep kernel (full basis, pair depth 8), screen stage 3", "survived_samples": 60000000 } }, "Z": { "value": 26, "confidence": "upper_bound", "witness": [ 6, 32, 137, 151, 173, 181, 185, 197, 201, 213, 223, 227, 235, 239, 257, 287, 382, 396, 426, 430, 442, 448, 466, 476, 478, 494 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 2000000, "seeds": [ 71000044607 ], "tool": "GPU deep kernel (full basis, pair depth 8), screen stage 3", "survived_samples": 60000000 } } }, "family": "generalized-bicycle", "provenance": { "authors": [ "@vprusso" ], "origin": "submission", "novelty": "new_parameters", "construction": "Cyclic (single-circulant-pair) generalized-bicycle code over Z_255 (research/cyclic_gb.py build_cyclic_gb): a(x) = 1 + x^26 + x^76, b(x) = 1 + x^30 + x^66; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 255] = v[j]. n = 2m = 510, k = 2 deg gcd(a, b, x^255 - 1) = 16, every check has weight 6. a and b were drawn as weight-3 multiples of a degree-8 divisor g of x^255 - 1 (g as a little-endian bit integer: 419).", "references": [ "arXiv:1904.02703", "arXiv:2203.17216" ], "date": "2026-09-23", "model": "Claude Fable 5.1 (Claude Code)", "notes": "Found by a GPU random-information-set screen (verify/ris_gpu.cu deep kernel: full-basis RREF plus pair sums, pair depth 8) over weight-6 cyclic generalized-bicycle codes with weight-3 polynomials at n <= 700; see the research note for the ladder. Lightest logicals: X 26, Z 26; finalist deep-kernel GPU pass: X 26 at 50,000,000 trials (seed 777); Z 26 at 50,000,000 trials (seed 778); board fast pass 26 at 8,000,000 trials. Every operator re-verified with verify/gf2.py. Distance is a witness-backed upper bound. Novelty: new_parameters by a nauty canonical-form check of the typed Tanner graph against the board and the 2BGA, GB, BB, QECDB, and codetables data (a submitter claim). Generator spec: {\"family\": \"cyclic-gb\", \"m\": 255, \"g_int\": 419, \"deg_g\": 8, \"a\": [0, 26, 76], \"b\": [0, 30, 66]}" } }