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    "tool": "accelerated RIS (research/kit distance_rand_witness), fast backend",
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  "model": "Claude Fable 5.1 (Claude Code)",
  "construction": "Code [[64,20,8]]cons:qrm6 of arXiv:2610.06730 (Dua, Holmes, Gullans, Albert, 'Qubit CSS codes with Universal Transversal Gates'), Table I: a depth-one universal code grown from the [[24,8,4]] seed by the paper's seed-and-kernel coupling construction. The check matrices are the paper's optimized stabilizer generating set (ldpc_generators of the record with uuid ff1cfd18-78d8-430c-0328-58eca26b471d in the ancillary file depth_one_universal_codes.json), 22 X and 22 Z checks, every one of weight 16, with the two generating sets spanning the same GF(2) row space (self-dual CSS), qubit degree at most 12; k = 20 recomputed by GF(2) rank. The paper's point about this code, a generating set of depth-one layers of two-qubit gates that is universal and tolerates one faulty gate per layer, is a property the board does not yet express in circuit.gates and is recorded in the note only.",
  "references": [
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  "date": "2026-10-08",
  "notes": "Literature reconstruction. The paper's database states d = 8. Readings here, accelerated RIS: X side 200000 trials 8; X side 2000000 trials 8; Z side 200000 trials 8; Z side 2000000 trials 8. Witnessed upper bound. Of the 47 codes in the paper's Table I screened against the board at their stated check weights, this is the only one the four-axis rule leaves undominated; [[72,20,6]] (weight 16) is dominated by the board's [[66,20,7]], the [[37,1,7]] and [[63,2,7]] triples are already on the board, and the rest are dominated by lighter or larger entries."
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