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"witness": [ 16, 19, 47, 176, 207, 210, 238, 244, 253, 269, 272, 275, 278, 281, 284, 287, 300, 320, 390, 437, 465, 537, 565, 607 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 2000000, "seeds": [ 71000011604 ], "tool": "GPU deep kernel (full basis, pair depth 8), screen stage 3", "survived_samples": 60000000 } }, "Z": { "value": 24, "confidence": "upper_bound", "witness": [ 62, 77, 82, 107, 152, 162, 177, 222, 252, 277, 307, 327, 330, 361, 540, 543, 546, 549, 552, 574, 583, 608, 611, 614 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 2000000, "seeds": [ 71000011605 ], "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_315 (research/cyclic_gb.py build_cyclic_gb): a(x) = 1 + x^70 + x^215, b(x) = 1 + x^3 + x^284; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T] with circ(v)[i, (i + j) mod 315] = v[j]. n = 2m = 630, k = 2 deg gcd(a, b, x^315 - 1) = 20, every check has weight 6. a and b were drawn as weight-3 multiples of a degree-10 divisor g of x^315 - 1 (g as a little-endian bit integer: 1269).", "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 24, Z 24; finalist deep-kernel GPU pass: X 24 at 50,000,000 trials (seed 777); Z 24 at 50,000,000 trials (seed 778); board fast pass 24 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\": 315, \"g_int\": 1269, \"deg_g\": 10, \"a\": [0, 70, 215], \"b\": [0, 3, 284]}" } }