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455 ], [ 65, 70, 250, 253, 443, 444, 456, 463 ], [ 73, 78, 258, 261, 451, 452, 464, 471 ] ] }, "distance": { "d": 16, "X": { "value": 16, "confidence": "exact", "witness": [ 0, 4, 5, 30, 120, 127, 162, 210, 215, 269, 276, 285, 340, 368, 374, 438 ] }, "Z": { "value": 16, "confidence": "exact", "witness": [ 0, 1, 28, 31, 161, 165, 187, 189, 209, 211, 388, 390, 444, 447, 456, 461 ] } }, "provenance": { "authors": [ "Okada, Koki", "Kasai, Kenta" ], "origin": "baseline", "construction": "Cyclic all-one pair-partition CPM CSS construction (arXiv:2607.14091), girth-8 seed instance qc_472_122_16_g8: lift size p=59, (J,L)=(3,8), n=8p=472, 3p=177 checks per side, column weight 3, row weight 8. CPM exponent arrays (rows = the three CPM block-rows per side, columns = the 8 block-columns): E_X = [[0,0,0,0,0,0,0,0],[0,30,22,33,2,7,45,31],[0,57,39,23,15,26,11,8]], E_Z = [[0,31,15,46,15,0,46,31],[0,7,20,8,0,7,20,8],[0,49,26,2,2,26,49,0]]; qubit p*j+s in block-column j carries cyclic shift s, and check row i of CPM block-row b on side S is {p*j + ((E_S[b][j]+i) mod p) : j=0..7}. Every mixed X/Z row overlap is 0 or 2 (CSS-orthogonal) and both Tanner graphs have girth exactly 8. Obtained by the authors from their girth-6 p=59 seed [[472,122,14]] via displacement search in the CPM-label space without changing the matching array or lift size. Check rows taken verbatim from Hx_rows.json/Hz_rows.json in the authors' bundle https://kasai.ict.eng.isct.ac.jp/pair_partition_cpm_css_codes_data/bundles/qc_472_122_16_g8.zip (zip sha256 8653e2f67720de812fe20d79eb73c52447e2405c08c73950677409873fe63c28; candidate.json sha256 5c9aeaa6252fa8bb75743b082886a608793264bfd5e5268646f8f93860028e83).", "date": "2026", "references": [ "arXiv:2607.14091" ], "novelty": "known_parameters", "notes": "Literature baseline, seeded 2026-08-14. Published as the girth-8 seed instance in the Okada\u2013Kasai pair-partition CPM catalogue (arXiv:2607.14091; catalogue page updated 2026-08-13). The authors provide a public, SHA-256-pinned, machine-checkable certificate: a complete connected-support exhaustion for all weights <16 (bundle detail/distance_lt16.json), plus explicit weight-16 non-boundary logicals on both sides (detail/weight16_logical_witnesses.json), so d=16 is claimed exact. The verifier/site still treat an exact claim as an upper bound until this repo produces a cert under certs/ (never silently upgrade). Reproduction was validated end to end: the bundle's check rows give a CSS-orthogonal (3,8)-regular pair with GF(2) ranks 175/175 (k=122), and both published witnesses were re-verified to lie in the opposing kernel and outside the same-side row space. This entry strictly dominates the existing [[472,122,14]] weight-8 baseline (same n and k, distance 16 vs 14)." }, "family": "pair-partition-cpm" }