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159, 201, 277, 300, 347 ], [ 10, 80, 113, 160, 202, 278, 294, 348 ], [ 11, 81, 114, 154, 196, 279, 295, 349 ], [ 12, 82, 115, 155, 197, 273, 296, 343 ], [ 20, 90, 123, 163, 205, 281, 304, 351 ], [ 14, 84, 124, 164, 206, 282, 305, 352 ], [ 15, 85, 125, 165, 207, 283, 306, 353 ], [ 16, 86, 119, 166, 208, 284, 307, 354 ], [ 17, 87, 120, 167, 209, 285, 301, 355 ], [ 18, 88, 121, 161, 203, 286, 302, 356 ], [ 19, 89, 122, 162, 204, 280, 303, 350 ] ] }, "distance": { "d": 14, "X": { "value": 14, "confidence": "exact", "witness": [ 0, 31, 70, 96, 98, 99, 129, 197, 236, 264, 272, 273, 337, 369 ] }, "Z": { "value": 14, "confidence": "exact", "witness": [ 0, 47, 53, 66, 75, 93, 110, 132, 176, 185, 220, 229, 315, 340 ] } }, "provenance": { "authors": [ "Okada, Koki", "Kasai, Kenta" ], "origin": "baseline", "construction": "Pair-partition GPM (generalized permutation matrix) CSS construction over C7 x C7 with regular action (arXiv:2607.14091), instance gpm_pp_c7c7_frontier: group order 49, (J,L)=(3,8), n=8*49=392, 147 checks per side, column weight 3, row weight 8, no Tanner 4-cycles. H_X and H_Z are taken verbatim from the authors' NumPy archive https://kasai.ict.eng.isct.ac.jp/pair_partition_cpm_css_codes_data/distance_records/gpm_pp_frontier_20260811/c7c7_d14/gpm_pp_c7c7_frontier.npz (sha256 ee438d409916e85abc0a386d0bdf9f5fb4abf092703996df851005444995d23b), which also carries the pair-partition array M and GPM exponent arrays E, D used to build them.", "date": "2026", "references": [ "arXiv:2607.14091" ], "novelty": "known_parameters", "notes": "Literature baseline, seeded 2026-08-14. Listed as the GPM-PP instance [[392,102,14]] (C7 x C7) in the primary table of the Okada-Kasai pair-partition CPM catalogue (arXiv:2607.14091; catalogue page updated 2026-08-13). The authors publish an exact-distance certificate (https://kasai.ict.eng.isct.ac.jp/pair_partition_cpm_css_codes_data/distance_records/gpm_pp_frontier_20260811/c7c7_d14/final_certificate.json, sha256 7f4fb595507f6383704aa6cf90b0996bbf70765fc7e3d9640ab8cac2e11bf109): a complete connected-support search through weight 12 on both sides plus explicit weight-14 logicals, which are the witnesses here, re-verified in this repo (kernel membership, row-space non-membership). Marked exact on the strength of that public certificate; per board policy the entry still displays as an upper bound until this repo's own certification. Reproduction was validated end to end: the archive's H_X/H_Z are CSS-orthogonal, (3,8)-regular, GF(2) ranks 145/145 (k=102), matching the certificate's matrix audit." }, "family": "pair-partition-cpm" }