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259, 345 ], "Z": [ 50, 118, 329, 372 ] }, { "X": [ 20, 131, 260, 346 ], "Z": [ 49, 117, 328, 371 ] }, { "X": [ 21, 132, 261, 347 ], "Z": [ 48, 116, 327, 370 ] }, { "X": [ 22, 133, 262, 348 ], "Z": [ 47, 115, 326, 369 ] }, { "X": [ 23, 134, 263, 349 ], "Z": [ 46, 114, 325, 368 ] }, { "X": [ 24, 135, 264, 350 ], "Z": [ 45, 113, 324, 367 ] }, { "X": [ 25, 136, 265, 351 ], "Z": [ 44, 225, 323, 366 ] }, { "X": [ 26, 137, 266, 352 ], "Z": [ 43, 224, 322, 365 ] }, { "X": [ 27, 138, 267, 353 ], "Z": [ 42, 223, 321, 364 ] } ] }, "distance": { "d": 18, "P": { "value": 18, "confidence": "upper_bound", "witness": { "X": [ 14, 22, 166, 170, 246, 254, 275, 334, 344, 365, 420, 445 ], "Z": [ 102, 106, 137, 166, 170, 191, 246, 254, 399, 420, 432, 445 ] } } }, "provenance": { "authors": [ "@MicheldeMessieres" ], "construction": "Symplectic halving (mirror fold) of the board's CSS entry codes/904-230-22.json ([[904,230,22]], by @vprusso), a pair-partition CPM CSS code of Okada and Kasai (arXiv:2607.14091), (J,L)=(3,8), prime lift P=113. The fold uses a fixed-point-free involution tau of the parent's qubits that maps the X-check rowspace onto the Z-check rowspace: tau(l,t) = (sigma(l), c_l - t mod 113) on parent qubit l*113+t, with sigma = (0 7)(1 2)(3 4)(5 6) on the 8 block columns and c = (c_0..c_7) = (0,109,109,78,78,56,56,0). Fold qubit i is the pair {q_i, tau(q_i)}, q_i the i-th smallest qubit with q_i < tau(q_i). Each parent X-check row gives one generator: X on the pairs whose q_i is in the row, Z on the pairs whose tau(q_i) is in the row. S = (A|B) is isotropic, k = 230/2 = 115, check weight 8, not CSS under any local Clifford.", "origin": "submission", "date": "2026-10-09", "model": "Claude Opus 5.5 (Claude Code)", "notes": "Derived from codes/904-230-22.json by @vprusso (pair-partition CPM CSS code of Okada and Kasai (arXiv:2607.14091), (J,L)=(3,8), prime lift P=113). The halving/doubling correspondence is the board's fieldnote fieldnotes/2026-09-28-symplectic-doubling-and-halving.md (@MathysRennela; Prop. 4 of arXiv:2609.30069), and the abelian mirror-code construction of Khesin and Lu (arXiv:2603.05496); mirror folds of bicycle codes are already on the board from @mrvee-qC-bee (codes/155-6-21.json, codes/155-6-23.json, codes/144-10-16-b.json) and CPM halvings from @MathysRennela (codes/145-32-6.json, codes/188-49-6.json). Our part, stated narrowly: we enumerated all X<->Z mirror symmetries of the parent (fixed-point-free involutions swapping the X and Z checks, up to conjugacy) via its automorphism group (nauty + GAP), folded along each, and kept the mirror whose lightest logical found stayed heaviest; then ran a deep distance search on the fold (3.1 CPU-h on this fold: orbit trick: 1.3 CPU-h, 403689 trials; exact SAT floor ladder: 0.3 CPU-h; frame-randomised Pauli RIS: 1.4 CPU-h, 369598 trials; symmetry-restricted SAT: 0.1 CPU-h; light logicals shared between mirrors of the same parent). Distance d = 18 is the Pauli weight of the lightest logical any method found: a witness-backed upper bound, not an exact certificate. Proved floor: an exact SAT search (in the parent's coordinates, weight counted per pair) shows no nontrivial logical of weight <= 6, so 7 <= d <= 18. Choosing the strongest of several mirrors by their upper bounds can favour a mirror that was simply searched less well; see the note. Construction and literature novelty are not claimed.", "references": [ "arXiv:2607.14091", "arXiv:2609.30069", "arXiv:2603.05496", "arXiv:2111.03654" ], "novelty": "unknown", "search_budget": { "cpu_hours": 3.1 } }, "family": "pair-partition-cpm" }