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"d": 12, "X": { "value": 12, "confidence": "upper_bound", "witness": [ 12, 14, 18, 39, 79, 146, 176, 216, 223, 238, 245, 255 ] }, "Z": { "value": 12, "confidence": "upper_bound", "witness": [ 13, 42, 66, 71, 116, 154, 172, 174, 194, 221, 223, 235 ] } }, "provenance": { "authors": [ "@MathysRennela" ], "construction": "Pair-partition CPM-PP CSS (Okada-Kasai family, arXiv:2607.14091) at (J,L,P)=(3,8,32): H[i*P+r, j*P+(r-E[i][j]) mod P] = 1 on both sides from the 3x8 circulant exponent arrays E_X, E_Z printed in Maskara et al. arXiv:2610.06749 Appendix F.1 eq. (61). E_X=[[9,0,15,11,16,14,29,6],[10,18,23,14,6,18,26,23],[23,11,3,12,16,22,3,10]], E_Z=[[23,30,3,6,30,9,17,4],[11,25,17,3,7,7,20,30],[31,29,12,19,24,29,12,28]] mod 32. CSS commutation H_X H_Z^T = 0 reproduced from the printed arrays; k recomputed from the binary ranks (rank H_X = rank H_Z = 94, n = 256) and matched the paper's 68; row weight 8 and column weight 3 on both sides. P = 32 is even, a lift size the family's odd-P construction theory does not cover and that no board entry uses.", "origin": "submission", "date": "2026-10-06", "model": "Mimo-V2.6-Flash", "novelty": "known_parameters", "references": [ "arXiv:2610.06749", "arXiv:2607.14091" ], "notes": "Known parameters: the [[256,68,12]] triple and the explicit 3x8 circulant exponent arrays are printed in Maskara et al., arXiv:2610.06749, Appendix F.1 eq. (61), as the base code PP256 of a parallel-surgery gadget; that paper reports no new parameters of its own and contributes logical gates rather than codes. This entry is an independent reconstruction and re-measurement from those printed arrays, not a new construction, and origin stays 'submission' because the matrices were rebuilt here rather than copied from a data file. The pair-partition construction the arrays instantiate is Okada-Kasai, arXiv:2607.14091. The claimed distance is a witness-backed upper bound from this repository's own search; no lower-bound certificate for this instance is held here, and the paper's exact-distance argument is not reproduced. Two things are genuinely new to the board: the lift P=32 is even, and no board entry uses an even lift of the (3,8) branch (all of P = 29,31,37,59,61,71,73,79,83,89,97,101,103,113 are odd primes); and at n=256 no entry in the weight-8 x unrestricted cell carries k>=68 at d>=12, so this is a frontier point rather than a re-find of [[248,66,12]] at P=31. Equivalence checklist: the exact-fingerprint match reported when this entry was built is against this very file, not against a board entry -- the submit was run twice against the same tree and the second run matched the first run's uncommitted output. Against the committed board the gate reports exact_duplicate_of: null and wl_equivalent_of: null." }, "family": "pair-partition-cpm" }