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], [ 3, 5, 162, 218, 275, 298, 343, 372, 373, 388, 453, 464 ], [ 15, 17, 174, 230, 287, 310, 355, 384, 385, 400, 465, 476 ], [ 27, 29, 186, 242, 299, 322, 367, 396, 397, 412, 477, 488 ], [ 8, 39, 41, 198, 254, 311, 334, 379, 408, 409, 424, 489 ], [ 9, 20, 51, 53, 210, 266, 323, 346, 391, 420, 421, 436 ] ] }, "distance": { "d": 20, "X": { "value": 20, "confidence": "exact", "witness": [ 1, 16, 54, 126, 131, 134, 244, 265, 282, 288, 300, 301, 322, 337, 354, 367, 395, 441, 467, 485 ] }, "Z": { "value": 20, "confidence": "exact", "witness": [ 5, 12, 34, 49, 52, 70, 77, 106, 107, 119, 138, 146, 175, 269, 276, 341, 370, 403, 432, 453 ] } }, "provenance": { "authors": [ "Okada, Koki", "Kasai, Kenta" ], "construction": "Pair-partition CPM CSS (Okada-Kasai arXiv:2607.14091): J=4, L=12, P=41, girth 6. Exact d=20 certified by 1362 hybrid second/third-branch certificates and verified X/Z involution.", "origin": "baseline", "references": [ "arXiv:2607.14091" ], "date": "2026", "notes": "Literature baseline (arXiv:2607.14091). Exact d=20: 1330 second-branch + 32 third-branch certificates exclude through weight 18; verified X/Z involution. Published X (X_w20_witness_search.json) and Z (Z_w20_mapped_witness.json) witnesses." }, "family": "pair-partition-cpm" }