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"witness": [ 3, 19, 32, 45, 48, 70, 86, 99, 153, 164, 178, 207, 220, 236, 248, 261, 286, 293, 302, 306, 332, 338, 342, 394, 398, 413, 423, 440, 454, 460, 479, 516, 560, 578, 610, 616 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 50000000, "seeds": [ 777 ], "tool": "GPU deep kernel (full basis, pair depth 8)", "survived_samples": 60000000 } }, "Z": { "value": 36, "confidence": "upper_bound", "witness": [ 2, 21, 50, 58, 115, 125, 133, 152, 158, 177, 199, 214, 233, 241, 253, 261, 288, 290, 299, 307, 309, 359, 369, 404, 413, 420, 436, 467, 474, 506, 527, 544, 560, 564, 614, 620 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 2000000, "seeds": [ 72000163601 ], "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_35 x Z_9 (research/kit/bb.py build_bb): A = x^0 y^2 + x^29 y^0 + x^21 y^6, B = x^30 y^6 + x^32 y^4 + x^24 y^6 (monomial exponent pairs (i, j) as in the kit); H_X = [A | B], H_Z = [B^T | A^T]; n = 2 l m = 630, 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 36, Z 36; finalist deep-kernel GPU pass: X 36 at 50,000,000 trials (seed 777); Z 36 at 50,000,000 trials (seed 778); board fast pass 36 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\": 35, \"m\": 9, \"A\": [[0, 2], [29, 0], [21, 6]], \"B\": [[30, 6], [32, 4], [24, 6]]}" } }