{ "schema_version": "0.1", "name": "[[336,88,12]]", "code_type": "CSS", "n": 336, "k": 88, "checks": { "X": [ [ 29, 73, 101, 154, 203, 212, 268, 317 ], [ 28, 74, 100, 153, 202, 210, 267, 316 ], [ 27, 72, 99, 155, 201, 211, 269, 315 ], [ 26, 76, 98, 151, 200, 215, 265, 314 ], [ 25, 77, 97, 150, 199, 213, 264, 313 ], [ 24, 75, 96, 152, 198, 214, 266, 312 ], [ 35, 79, 107, 160, 209, 218, 274, 323 ], [ 34, 80, 106, 159, 208, 216, 273, 322 ], [ 33, 78, 105, 161, 207, 217, 275, 321 ], [ 32, 82, 104, 157, 206, 221, 271, 320 ], [ 31, 83, 103, 156, 205, 219, 270, 319 ], [ 30, 81, 102, 158, 204, 220, 272, 318 ], [ 41, 43, 113, 166, 173, 224, 280, 329 ], [ 40, 44, 112, 165, 172, 222, 279, 328 ], [ 39, 42, 111, 167, 171, 223, 281, 327 ], [ 38, 46, 110, 163, 170, 227, 277, 326 ], [ 37, 47, 109, 162, 169, 225, 276, 325 ], [ 36, 45, 108, 164, 168, 226, 278, 324 ], [ 5, 49, 119, 130, 179, 230, 286, 335 ], [ 4, 50, 118, 129, 178, 228, 285, 334 ], [ 3, 48, 117, 131, 177, 229, 287, 333 ], [ 2, 52, 116, 127, 176, 233, 283, 332 ], [ 1, 53, 115, 126, 175, 231, 282, 331 ], [ 0, 51, 114, 128, 174, 232, 284, 330 ], [ 11, 55, 125, 136, 185, 236, 292, 299 ], [ 10, 56, 124, 135, 184, 234, 291, 298 ], [ 9, 54, 123, 137, 183, 235, 293, 297 ], [ 8, 58, 122, 133, 182, 239, 289, 296 ], [ 7, 59, 121, 132, 181, 237, 288, 295 ], [ 6, 57, 120, 134, 180, 238, 290, 294 ], [ 17, 61, 89, 142, 191, 242, 256, 305 ], [ 16, 62, 88, 141, 190, 240, 255, 304 ], [ 15, 60, 87, 143, 189, 241, 257, 303 ], [ 14, 64, 86, 139, 188, 245, 253, 302 ], [ 13, 65, 85, 138, 187, 243, 252, 301 ], [ 12, 63, 84, 140, 186, 244, 254, 300 ], [ 23, 67, 95, 148, 197, 248, 262, 311 ], [ 22, 68, 94, 147, 196, 246, 261, 310 ], [ 21, 66, 93, 149, 195, 247, 263, 309 ], [ 20, 70, 92, 145, 194, 251, 259, 308 ], [ 19, 71, 91, 144, 193, 249, 258, 307 ], [ 18, 69, 90, 146, 192, 250, 260, 306 ], [ 17, 46, 121, 144, 182, 216, 279, 323 ], [ 16, 45, 122, 145, 180, 217, 281, 322 ], [ 15, 47, 120, 146, 181, 218, 280, 321 ], [ 14, 43, 124, 147, 185, 219, 276, 320 ], [ 13, 42, 125, 148, 183, 220, 278, 319 ], [ 12, 44, 123, 149, 184, 221, 277, 318 ], [ 23, 52, 85, 150, 188, 222, 285, 329 ], [ 22, 51, 86, 151, 186, 223, 287, 328 ], [ 21, 53, 84, 152, 187, 224, 286, 327 ], [ 20, 49, 88, 153, 191, 225, 282, 326 ], [ 19, 48, 89, 154, 189, 226, 284, 325 ], [ 18, 50, 87, 155, 190, 227, 283, 324 ], [ 29, 58, 91, 156, 194, 228, 291, 335 ], [ 28, 57, 92, 157, 192, 229, 293, 334 ], [ 27, 59, 90, 158, 193, 230, 292, 333 ], [ 26, 55, 94, 159, 197, 231, 288, 332 ], [ 25, 54, 95, 160, 195, 232, 290, 331 ], [ 24, 56, 93, 161, 196, 233, 289, 330 ], [ 35, 64, 97, 162, 200, 234, 255, 299 ], [ 34, 63, 98, 163, 198, 235, 257, 298 ], [ 33, 65, 96, 164, 199, 236, 256, 297 ], [ 32, 61, 100, 165, 203, 237, 252, 296 ], [ 31, 60, 101, 166, 201, 238, 254, 295 ], [ 30, 62, 99, 167, 202, 239, 253, 294 ], [ 41, 70, 103, 126, 206, 240, 261, 305 ], [ 40, 69, 104, 127, 204, 241, 263, 304 ], [ 39, 71, 102, 128, 205, 242, 262, 303 ], [ 38, 67, 106, 129, 209, 243, 258, 302 ], [ 37, 66, 107, 130, 207, 244, 260, 301 ], [ 36, 68, 105, 131, 208, 245, 259, 300 ], [ 5, 76, 109, 132, 170, 246, 267, 311 ], [ 4, 75, 110, 133, 168, 247, 269, 310 ], [ 3, 77, 108, 134, 169, 248, 268, 309 ], [ 2, 73, 112, 135, 173, 249, 264, 308 ], [ 1, 72, 113, 136, 171, 250, 266, 307 ], [ 0, 74, 111, 137, 172, 251, 265, 306 ], [ 11, 82, 115, 138, 176, 210, 273, 317 ], [ 10, 81, 116, 139, 174, 211, 275, 316 ], [ 9, 83, 114, 140, 175, 212, 274, 315 ], [ 8, 79, 118, 141, 179, 213, 270, 314 ], [ 7, 78, 119, 142, 177, 214, 272, 313 ], [ 6, 80, 117, 143, 178, 215, 271, 312 ], [ 8, 69, 99, 136, 187, 222, 273, 320 ], [ 6, 71, 101, 135, 188, 223, 275, 318 ], [ 7, 70, 100, 137, 186, 224, 274, 319 ], [ 11, 66, 96, 133, 190, 225, 270, 323 ], [ 9, 68, 98, 132, 191, 226, 272, 321 ], [ 10, 67, 97, 134, 189, 227, 271, 322 ], [ 14, 75, 105, 142, 193, 228, 279, 326 ], [ 12, 77, 107, 141, 194, 229, 281, 324 ], [ 13, 76, 106, 143, 192, 230, 280, 325 ], [ 17, 72, 102, 139, 196, 231, 276, 329 ], [ 15, 74, 104, 138, 197, 232, 278, 327 ], [ 16, 73, 103, 140, 195, 233, 277, 328 ], [ 20, 81, 111, 148, 199, 234, 285, 332 ], [ 18, 83, 113, 147, 200, 235, 287, 330 ], [ 19, 82, 112, 149, 198, 236, 286, 331 ], [ 23, 78, 108, 145, 202, 237, 282, 335 ], [ 21, 80, 110, 144, 203, 238, 284, 333 ], [ 22, 79, 109, 146, 201, 239, 283, 334 ], [ 26, 45, 117, 154, 205, 240, 291, 296 ], [ 24, 47, 119, 153, 206, 241, 293, 294 ], [ 25, 46, 118, 155, 204, 242, 292, 295 ], [ 29, 42, 114, 151, 208, 243, 288, 299 ], [ 27, 44, 116, 150, 209, 244, 290, 297 ], [ 28, 43, 115, 152, 207, 245, 289, 298 ], [ 32, 51, 123, 160, 169, 246, 255, 302 ], [ 30, 53, 125, 159, 170, 247, 257, 300 ], [ 31, 52, 124, 161, 168, 248, 256, 301 ], [ 35, 48, 120, 157, 172, 249, 252, 305 ], [ 33, 50, 122, 156, 173, 250, 254, 303 ], [ 34, 49, 121, 158, 171, 251, 253, 304 ], [ 38, 57, 87, 166, 175, 210, 261, 308 ], [ 36, 59, 89, 165, 176, 211, 263, 306 ], [ 37, 58, 88, 167, 174, 212, 262, 307 ], [ 41, 54, 84, 163, 178, 213, 258, 311 ], [ 39, 56, 86, 162, 179, 214, 260, 309 ], [ 40, 55, 85, 164, 177, 215, 259, 310 ], [ 2, 63, 93, 130, 181, 216, 267, 314 ], [ 0, 65, 95, 129, 182, 217, 269, 312 ], [ 1, 64, 94, 131, 180, 218, 268, 313 ], [ 5, 60, 90, 127, 184, 219, 264, 317 ], [ 3, 62, 92, 126, 185, 220, 266, 315 ], [ 4, 61, 91, 128, 183, 221, 265, 316 ] ], "Z": [ [ 11, 66, 125, 138, 168, 247, 278, 301 ], [ 10, 67, 124, 139, 169, 248, 276, 302 ], [ 9, 68, 123, 140, 170, 246, 277, 300 ], [ 8, 69, 122, 141, 171, 250, 281, 304 ], [ 7, 70, 121, 142, 172, 251, 279, 305 ], [ 6, 71, 120, 143, 173, 249, 280, 303 ], [ 17, 72, 89, 144, 174, 211, 284, 307 ], [ 16, 73, 88, 145, 175, 212, 282, 308 ], [ 15, 74, 87, 146, 176, 210, 283, 306 ], [ 14, 75, 86, 147, 177, 214, 287, 310 ], [ 13, 76, 85, 148, 178, 215, 285, 311 ], [ 12, 77, 84, 149, 179, 213, 286, 309 ], [ 23, 78, 95, 150, 180, 217, 290, 313 ], [ 22, 79, 94, 151, 181, 218, 288, 314 ], [ 21, 80, 93, 152, 182, 216, 289, 312 ], [ 20, 81, 92, 153, 183, 220, 293, 316 ], [ 19, 82, 91, 154, 184, 221, 291, 317 ], [ 18, 83, 90, 155, 185, 219, 292, 315 ], [ 29, 42, 101, 156, 186, 223, 254, 319 ], [ 28, 43, 100, 157, 187, 224, 252, 320 ], [ 27, 44, 99, 158, 188, 222, 253, 318 ], [ 26, 45, 98, 159, 189, 226, 257, 322 ], [ 25, 46, 97, 160, 190, 227, 255, 323 ], [ 24, 47, 96, 161, 191, 225, 256, 321 ], [ 35, 48, 107, 162, 192, 229, 260, 325 ], [ 34, 49, 106, 163, 193, 230, 258, 326 ], [ 33, 50, 105, 164, 194, 228, 259, 324 ], [ 32, 51, 104, 165, 195, 232, 263, 328 ], [ 31, 52, 103, 166, 196, 233, 261, 329 ], [ 30, 53, 102, 167, 197, 231, 262, 327 ], [ 41, 54, 113, 126, 198, 235, 266, 331 ], [ 40, 55, 112, 127, 199, 236, 264, 332 ], [ 39, 56, 111, 128, 200, 234, 265, 330 ], [ 38, 57, 110, 129, 201, 238, 269, 334 ], [ 37, 58, 109, 130, 202, 239, 267, 335 ], [ 36, 59, 108, 131, 203, 237, 268, 333 ], [ 5, 60, 119, 132, 204, 241, 272, 295 ], [ 4, 61, 118, 133, 205, 242, 270, 296 ], [ 3, 62, 117, 134, 206, 240, 271, 294 ], [ 2, 63, 116, 135, 207, 244, 275, 298 ], [ 1, 64, 115, 136, 208, 245, 273, 299 ], [ 0, 65, 114, 137, 209, 243, 274, 297 ], [ 18, 69, 87, 147, 206, 241, 261, 320 ], [ 19, 71, 89, 149, 204, 242, 263, 318 ], [ 20, 70, 88, 148, 205, 240, 262, 319 ], [ 21, 66, 84, 144, 209, 244, 258, 323 ], [ 22, 68, 86, 146, 207, 245, 260, 321 ], [ 23, 67, 85, 145, 208, 243, 259, 322 ], [ 24, 75, 93, 153, 170, 247, 267, 326 ], [ 25, 77, 95, 155, 168, 248, 269, 324 ], [ 26, 76, 94, 154, 169, 246, 268, 325 ], [ 27, 72, 90, 150, 173, 250, 264, 329 ], [ 28, 74, 92, 152, 171, 251, 266, 327 ], [ 29, 73, 91, 151, 172, 249, 265, 328 ], [ 30, 81, 99, 159, 176, 211, 273, 332 ], [ 31, 83, 101, 161, 174, 212, 275, 330 ], [ 32, 82, 100, 160, 175, 210, 274, 331 ], [ 33, 78, 96, 156, 179, 214, 270, 335 ], [ 34, 80, 98, 158, 177, 215, 272, 333 ], [ 35, 79, 97, 157, 178, 213, 271, 334 ], [ 36, 45, 105, 165, 182, 217, 279, 296 ], [ 37, 47, 107, 167, 180, 218, 281, 294 ], [ 38, 46, 106, 166, 181, 216, 280, 295 ], [ 39, 42, 102, 162, 185, 220, 276, 299 ], [ 40, 44, 104, 164, 183, 221, 278, 297 ], [ 41, 43, 103, 163, 184, 219, 277, 298 ], [ 0, 51, 111, 129, 188, 223, 285, 302 ], [ 1, 53, 113, 131, 186, 224, 287, 300 ], [ 2, 52, 112, 130, 187, 222, 286, 301 ], [ 3, 48, 108, 126, 191, 226, 282, 305 ], [ 4, 50, 110, 128, 189, 227, 284, 303 ], [ 5, 49, 109, 127, 190, 225, 283, 304 ], [ 6, 57, 117, 135, 194, 229, 291, 308 ], [ 7, 59, 119, 137, 192, 230, 293, 306 ], [ 8, 58, 118, 136, 193, 228, 292, 307 ], [ 9, 54, 114, 132, 197, 232, 288, 311 ], [ 10, 56, 116, 134, 195, 233, 290, 309 ], [ 11, 55, 115, 133, 196, 231, 289, 310 ], [ 12, 63, 123, 141, 200, 235, 255, 314 ], [ 13, 65, 125, 143, 198, 236, 257, 312 ], [ 14, 64, 124, 142, 199, 234, 256, 313 ], [ 15, 60, 120, 138, 203, 238, 252, 317 ], [ 16, 62, 122, 140, 201, 239, 254, 315 ], [ 17, 61, 121, 139, 202, 237, 253, 316 ], [ 34, 63, 121, 159, 208, 216, 288, 300 ], [ 33, 65, 122, 161, 207, 217, 289, 301 ], [ 35, 64, 120, 160, 209, 218, 290, 302 ], [ 31, 60, 124, 156, 205, 219, 291, 303 ], [ 30, 62, 125, 158, 204, 220, 292, 304 ], [ 32, 61, 123, 157, 206, 221, 293, 305 ], [ 40, 69, 85, 165, 172, 222, 252, 306 ], [ 39, 71, 86, 167, 171, 223, 253, 307 ], [ 41, 70, 84, 166, 173, 224, 254, 308 ], [ 37, 66, 88, 162, 169, 225, 255, 309 ], [ 36, 68, 89, 164, 168, 226, 256, 310 ], [ 38, 67, 87, 163, 170, 227, 257, 311 ], [ 4, 75, 91, 129, 178, 228, 258, 312 ], [ 3, 77, 92, 131, 177, 229, 259, 313 ], [ 5, 76, 90, 130, 179, 230, 260, 314 ], [ 1, 72, 94, 126, 175, 231, 261, 315 ], [ 0, 74, 95, 128, 174, 232, 262, 316 ], [ 2, 73, 93, 127, 176, 233, 263, 317 ], [ 10, 81, 97, 135, 184, 234, 264, 318 ], [ 9, 83, 98, 137, 183, 235, 265, 319 ], [ 11, 82, 96, 136, 185, 236, 266, 320 ], [ 7, 78, 100, 132, 181, 237, 267, 321 ], [ 6, 80, 101, 134, 180, 238, 268, 322 ], [ 8, 79, 99, 133, 182, 239, 269, 323 ], [ 16, 45, 103, 141, 190, 240, 270, 324 ], [ 15, 47, 104, 143, 189, 241, 271, 325 ], [ 17, 46, 102, 142, 191, 242, 272, 326 ], [ 13, 42, 106, 138, 187, 243, 273, 327 ], [ 12, 44, 107, 140, 186, 244, 274, 328 ], [ 14, 43, 105, 139, 188, 245, 275, 329 ], [ 22, 51, 109, 147, 196, 246, 276, 330 ], [ 21, 53, 110, 149, 195, 247, 277, 331 ], [ 23, 52, 108, 148, 197, 248, 278, 332 ], [ 19, 48, 112, 144, 193, 249, 279, 333 ], [ 18, 50, 113, 146, 192, 250, 280, 334 ], [ 20, 49, 111, 145, 194, 251, 281, 335 ], [ 28, 57, 115, 153, 202, 210, 282, 294 ], [ 27, 59, 116, 155, 201, 211, 283, 295 ], [ 29, 58, 114, 154, 203, 212, 284, 296 ], [ 25, 54, 118, 150, 199, 213, 285, 297 ], [ 24, 56, 119, 152, 198, 214, 286, 298 ], [ 26, 55, 117, 151, 200, 215, 287, 299 ] ] }, "distance": { "d": 12, "X": { "value": 12, "confidence": "upper_bound", "witness": [ 7, 46, 59, 100, 120, 160, 172, 249, 252, 272, 295, 333 ] }, "Z": { "value": 12, "confidence": "upper_bound", "witness": [ 22, 41, 51, 72, 139, 166, 174, 201, 258, 261, 302, 307 ] } }, "provenance": { "authors": [ "@MathysRennela", "Okada, Koki", "Kasai, Kenta", "Maskara, Nishad" ], "construction": "Pair-partition CPM/GPM CSS code (Okada-Kasai arXiv:2607.14091 catalogue), (J,L,P)=(3,8,42), check weight 8; H_X and H_Z taken verbatim from the published instance at https://kasai.ict.eng.isct.ac.jp/pair_partition_cpm_css_codes_data/distance_records/gpm_pp_frontier_20260811/s3c7_d12/gpm_pp_s3c7_frontier.npz (sha256 4eb37b67d1c19638c9de37b16ed5647534673f7ea73ff2a42354d3f4f5e65484), structure and distance re-verified here", "origin": "baseline", "date": "2026-09-29", "model": "Mimo-V2.6-Flash", "notes": "Literature reproduction of a published instance from the Okada-Kasai pair-partition catalogue (https://kasai.ict.eng.isct.ac.jp/pair_partition_cpm_css_codes_20260714.html), not a new construction search. Equivalence checked at submission time: the dedup gate finds no exact or graph-equivalent existing entry, and verify/validate_candidate.py reports nothing dominating this code in its cell.", "novelty": "known_parameters", "references": [ "arXiv:2607.14091" ] }, "family": "pair-partition-cpm" }