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137, 156, 163, 179, 232, 257, 259, 322, 326, 349, 391, 426, 431, 451, 462, 466, 489, 491, 506, 531 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 2000000, "seeds": [ 72000073600 ], "tool": "GPU deep kernel (full basis, pair depth 8), screen stage 3", "survived_samples": 60000000 } }, "Z": { "value": 32, "confidence": "upper_bound", "witness": [ 16, 57, 60, 79, 121, 159, 161, 162, 184, 187, 201, 224, 226, 267, 287, 296, 302, 318, 328, 338, 339, 362, 383, 403, 409, 429, 435, 450, 461, 482, 487, 531 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 2000000, "seeds": [ 72000073601 ], "tool": "GPU deep kernel (full basis, pair depth 8), screen stage 3", "survived_samples": 60000000 } } }, "family": "bivariate-bicycle", "provenance": { "authors": [ "@vprusso" ], "origin": "submission", "novelty": "new_parameters", "construction": "Bivariate bicycle code on Z_18 x Z_15 (research/kit/bb.py build_bb): A = x^8 y^2 + x^17 y^7 + x^1 y^2, B = x^10 y^4 + x^17 y^0 + x^9 y^13 (monomial exponent pairs (i, j) as in the kit); H_X = [A | B], H_Z = [B^T | A^T]; n = 2 l m = 540, k = 8, every check has weight 6.", "references": [ "arXiv:2308.07915", "arXiv:2111.03654" ], "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 bivariate bicycle codes with weight-3 polynomials at n <= 700; see the research note for the ladder. Lightest logicals: X 32, Z 32; finalist deep-kernel GPU pass: X 32 at 50,000,000 trials (seed 777); Z 32 at 50,000,000 trials (seed 778); board fast pass 32 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\": \"bb\", \"l\": 18, \"m\": 15, \"A\": [[8, 2], [17, 7], [1, 2]], \"B\": [[10, 4], [17, 0], [9, 13]]}" } }