{ "schema_version": "0.1", "name": "[[288,6,28]] metacyclic 2BGA", "code_type": "CSS", "n": 288, "k": 6, "checks": { "X": [ [ 58, 60, 116, 143, 153, 208, 248, 275 ], [ 59, 61, 117, 140, 154, 209, 249, 272 ], [ 56, 62, 118, 141, 155, 210, 250, 273 ], [ 57, 63, 119, 142, 152, 211, 251, 274 ], [ 62, 64, 75, 120, 157, 212, 252, 279 ], [ 63, 65, 72, 121, 158, 213, 253, 276 ], [ 60, 66, 73, 122, 159, 214, 254, 277 ], [ 61, 67, 74, 123, 156, 215, 255, 278 ], [ 7, 66, 68, 124, 161, 216, 256, 283 ], [ 4, 67, 69, 125, 162, 217, 257, 280 ], [ 5, 64, 70, 126, 163, 218, 258, 281 ], [ 6, 65, 71, 127, 160, 219, 259, 282 ], [ 70, 72, 83, 128, 165, 220, 260, 287 ], [ 71, 73, 80, 129, 166, 221, 261, 284 ], [ 68, 74, 81, 130, 167, 222, 262, 285 ], [ 69, 75, 82, 131, 164, 223, 263, 286 ], [ 15, 74, 76, 132, 147, 169, 224, 264 ], [ 12, 75, 77, 133, 144, 170, 225, 265 ], [ 13, 72, 78, 134, 145, 171, 226, 266 ], [ 14, 73, 79, 135, 146, 168, 227, 267 ], [ 78, 80, 91, 136, 151, 173, 228, 268 ], [ 79, 81, 88, 137, 148, 174, 229, 269 ], [ 76, 82, 89, 138, 149, 175, 230, 270 ], [ 77, 83, 90, 139, 150, 172, 231, 271 ], [ 23, 82, 84, 140, 155, 177, 232, 272 ], [ 20, 83, 85, 141, 152, 178, 233, 273 ], [ 21, 80, 86, 142, 153, 179, 234, 274 ], [ 22, 81, 87, 143, 154, 176, 235, 275 ], [ 0, 86, 88, 99, 159, 181, 236, 276 ], [ 1, 87, 89, 96, 156, 182, 237, 277 ], [ 2, 84, 90, 97, 157, 183, 238, 278 ], [ 3, 85, 91, 98, 158, 180, 239, 279 ], [ 4, 31, 90, 92, 163, 185, 240, 280 ], [ 5, 28, 91, 93, 160, 186, 241, 281 ], [ 6, 29, 88, 94, 161, 187, 242, 282 ], [ 7, 30, 89, 95, 162, 184, 243, 283 ], [ 8, 94, 96, 107, 167, 189, 244, 284 ], [ 9, 95, 97, 104, 164, 190, 245, 285 ], [ 10, 92, 98, 105, 165, 191, 246, 286 ], [ 11, 93, 99, 106, 166, 188, 247, 287 ], [ 12, 39, 98, 100, 144, 171, 193, 248 ], [ 13, 36, 99, 101, 145, 168, 194, 249 ], [ 14, 37, 96, 102, 146, 169, 195, 250 ], [ 15, 38, 97, 103, 147, 170, 192, 251 ], [ 16, 102, 104, 115, 148, 175, 197, 252 ], [ 17, 103, 105, 112, 149, 172, 198, 253 ], [ 18, 100, 106, 113, 150, 173, 199, 254 ], [ 19, 101, 107, 114, 151, 174, 196, 255 ], [ 20, 47, 106, 108, 152, 179, 201, 256 ], [ 21, 44, 107, 109, 153, 176, 202, 257 ], [ 22, 45, 104, 110, 154, 177, 203, 258 ], [ 23, 46, 105, 111, 155, 178, 200, 259 ], [ 24, 110, 112, 123, 156, 183, 205, 260 ], [ 25, 111, 113, 120, 157, 180, 206, 261 ], [ 26, 108, 114, 121, 158, 181, 207, 262 ], [ 27, 109, 115, 122, 159, 182, 204, 263 ], [ 28, 55, 114, 116, 160, 187, 209, 264 ], [ 29, 52, 115, 117, 161, 184, 210, 265 ], [ 30, 53, 112, 118, 162, 185, 211, 266 ], [ 31, 54, 113, 119, 163, 186, 208, 267 ], [ 32, 118, 120, 131, 164, 191, 213, 268 ], [ 33, 119, 121, 128, 165, 188, 214, 269 ], [ 34, 116, 122, 129, 166, 189, 215, 270 ], [ 35, 117, 123, 130, 167, 190, 212, 271 ], [ 36, 63, 122, 124, 168, 195, 217, 272 ], [ 37, 60, 123, 125, 169, 192, 218, 273 ], [ 38, 61, 120, 126, 170, 193, 219, 274 ], [ 39, 62, 121, 127, 171, 194, 216, 275 ], [ 40, 126, 128, 139, 172, 199, 221, 276 ], [ 41, 127, 129, 136, 173, 196, 222, 277 ], [ 42, 124, 130, 137, 174, 197, 223, 278 ], [ 43, 125, 131, 138, 175, 198, 220, 279 ], [ 44, 71, 130, 132, 176, 203, 225, 280 ], [ 45, 68, 131, 133, 177, 200, 226, 281 ], [ 46, 69, 128, 134, 178, 201, 227, 282 ], [ 47, 70, 129, 135, 179, 202, 224, 283 ], [ 3, 48, 134, 136, 180, 207, 229, 284 ], [ 0, 49, 135, 137, 181, 204, 230, 285 ], [ 1, 50, 132, 138, 182, 205, 231, 286 ], [ 2, 51, 133, 139, 183, 206, 228, 287 ], [ 52, 79, 138, 140, 144, 184, 211, 233 ], [ 53, 76, 139, 141, 145, 185, 208, 234 ], [ 54, 77, 136, 142, 146, 186, 209, 235 ], [ 55, 78, 137, 143, 147, 187, 210, 232 ], [ 0, 11, 56, 142, 148, 188, 215, 237 ], [ 1, 8, 57, 143, 149, 189, 212, 238 ], [ 2, 9, 58, 140, 150, 190, 213, 239 ], [ 3, 10, 59, 141, 151, 191, 214, 236 ], [ 2, 4, 60, 87, 152, 192, 219, 241 ], [ 3, 5, 61, 84, 153, 193, 216, 242 ], [ 0, 6, 62, 85, 154, 194, 217, 243 ], [ 1, 7, 63, 86, 155, 195, 218, 240 ], [ 6, 8, 19, 64, 156, 196, 223, 245 ], [ 7, 9, 16, 65, 157, 197, 220, 246 ], [ 4, 10, 17, 66, 158, 198, 221, 247 ], [ 5, 11, 18, 67, 159, 199, 222, 244 ], [ 10, 12, 68, 95, 160, 200, 227, 249 ], [ 11, 13, 69, 92, 161, 201, 224, 250 ], [ 8, 14, 70, 93, 162, 202, 225, 251 ], [ 9, 15, 71, 94, 163, 203, 226, 248 ], [ 14, 16, 27, 72, 164, 204, 231, 253 ], [ 15, 17, 24, 73, 165, 205, 228, 254 ], [ 12, 18, 25, 74, 166, 206, 229, 255 ], [ 13, 19, 26, 75, 167, 207, 230, 252 ], [ 18, 20, 76, 103, 168, 208, 235, 257 ], [ 19, 21, 77, 100, 169, 209, 232, 258 ], [ 16, 22, 78, 101, 170, 210, 233, 259 ], [ 17, 23, 79, 102, 171, 211, 234, 256 ], [ 22, 24, 35, 80, 172, 212, 239, 261 ], [ 23, 25, 32, 81, 173, 213, 236, 262 ], [ 20, 26, 33, 82, 174, 214, 237, 263 ], [ 21, 27, 34, 83, 175, 215, 238, 260 ], [ 26, 28, 84, 111, 176, 216, 243, 265 ], [ 27, 29, 85, 108, 177, 217, 240, 266 ], [ 24, 30, 86, 109, 178, 218, 241, 267 ], [ 25, 31, 87, 110, 179, 219, 242, 264 ], [ 30, 32, 43, 88, 180, 220, 247, 269 ], [ 31, 33, 40, 89, 181, 221, 244, 270 ], [ 28, 34, 41, 90, 182, 222, 245, 271 ], [ 29, 35, 42, 91, 183, 223, 246, 268 ], [ 34, 36, 92, 119, 184, 224, 251, 273 ], [ 35, 37, 93, 116, 185, 225, 248, 274 ], [ 32, 38, 94, 117, 186, 226, 249, 275 ], [ 33, 39, 95, 118, 187, 227, 250, 272 ], [ 38, 40, 51, 96, 188, 228, 255, 277 ], [ 39, 41, 48, 97, 189, 229, 252, 278 ], [ 36, 42, 49, 98, 190, 230, 253, 279 ], [ 37, 43, 50, 99, 191, 231, 254, 276 ], [ 42, 44, 100, 127, 192, 232, 259, 281 ], [ 43, 45, 101, 124, 193, 233, 256, 282 ], [ 40, 46, 102, 125, 194, 234, 257, 283 ], [ 41, 47, 103, 126, 195, 235, 258, 280 ], [ 46, 48, 59, 104, 196, 236, 263, 285 ], [ 47, 49, 56, 105, 197, 237, 260, 286 ], [ 44, 50, 57, 106, 198, 238, 261, 287 ], [ 45, 51, 58, 107, 199, 239, 262, 284 ], [ 50, 52, 108, 135, 145, 200, 240, 267 ], [ 51, 53, 109, 132, 146, 201, 241, 264 ], [ 48, 54, 110, 133, 147, 202, 242, 265 ], [ 49, 55, 111, 134, 144, 203, 243, 266 ], [ 54, 56, 67, 112, 149, 204, 244, 271 ], [ 55, 57, 64, 113, 150, 205, 245, 268 ], [ 52, 58, 65, 114, 151, 206, 246, 269 ], [ 53, 59, 66, 115, 148, 207, 247, 270 ] ], "Z": [ [ 17, 40, 80, 139, 172, 221, 228, 234 ], [ 18, 41, 81, 136, 173, 222, 229, 235 ], [ 19, 42, 82, 137, 174, 223, 230, 232 ], [ 16, 43, 83, 138, 175, 220, 231, 233 ], [ 21, 44, 84, 143, 153, 176, 232, 238 ], [ 22, 45, 85, 140, 154, 177, 233, 239 ], [ 23, 46, 86, 141, 155, 178, 234, 236 ], [ 20, 47, 87, 142, 152, 179, 235, 237 ], [ 3, 25, 48, 88, 180, 229, 236, 242 ], [ 0, 26, 49, 89, 181, 230, 237, 243 ], [ 1, 27, 50, 90, 182, 231, 238, 240 ], [ 2, 24, 51, 91, 183, 228, 239, 241 ], [ 7, 29, 52, 92, 161, 184, 240, 246 ], [ 4, 30, 53, 93, 162, 185, 241, 247 ], [ 5, 31, 54, 94, 163, 186, 242, 244 ], [ 6, 28, 55, 95, 160, 187, 243, 245 ], [ 11, 33, 56, 96, 188, 237, 244, 250 ], [ 8, 34, 57, 97, 189, 238, 245, 251 ], [ 9, 35, 58, 98, 190, 239, 246, 248 ], [ 10, 32, 59, 99, 191, 236, 247, 249 ], [ 15, 37, 60, 100, 169, 192, 248, 254 ], [ 12, 38, 61, 101, 170, 193, 249, 255 ], [ 13, 39, 62, 102, 171, 194, 250, 252 ], [ 14, 36, 63, 103, 168, 195, 251, 253 ], [ 19, 41, 64, 104, 196, 245, 252, 258 ], [ 16, 42, 65, 105, 197, 246, 253, 259 ], [ 17, 43, 66, 106, 198, 247, 254, 256 ], [ 18, 40, 67, 107, 199, 244, 255, 257 ], [ 23, 45, 68, 108, 177, 200, 256, 262 ], [ 20, 46, 69, 109, 178, 201, 257, 263 ], [ 21, 47, 70, 110, 179, 202, 258, 260 ], [ 22, 44, 71, 111, 176, 203, 259, 261 ], [ 27, 49, 72, 112, 204, 253, 260, 266 ], [ 24, 50, 73, 113, 205, 254, 261, 267 ], [ 25, 51, 74, 114, 206, 255, 262, 264 ], [ 26, 48, 75, 115, 207, 252, 263, 265 ], [ 31, 53, 76, 116, 185, 208, 264, 270 ], [ 28, 54, 77, 117, 186, 209, 265, 271 ], [ 29, 55, 78, 118, 187, 210, 266, 268 ], [ 30, 52, 79, 119, 184, 211, 267, 269 ], [ 35, 57, 80, 120, 212, 261, 268, 274 ], [ 32, 58, 81, 121, 213, 262, 269, 275 ], [ 33, 59, 82, 122, 214, 263, 270, 272 ], [ 34, 56, 83, 123, 215, 260, 271, 273 ], [ 39, 61, 84, 124, 193, 216, 272, 278 ], [ 36, 62, 85, 125, 194, 217, 273, 279 ], [ 37, 63, 86, 126, 195, 218, 274, 276 ], [ 38, 60, 87, 127, 192, 219, 275, 277 ], [ 43, 65, 88, 128, 220, 269, 276, 282 ], [ 40, 66, 89, 129, 221, 270, 277, 283 ], [ 41, 67, 90, 130, 222, 271, 278, 280 ], [ 42, 64, 91, 131, 223, 268, 279, 281 ], [ 47, 69, 92, 132, 201, 224, 280, 286 ], [ 44, 70, 93, 133, 202, 225, 281, 287 ], [ 45, 71, 94, 134, 203, 226, 282, 284 ], [ 46, 68, 95, 135, 200, 227, 283, 285 ], [ 51, 73, 96, 136, 146, 228, 277, 284 ], [ 48, 74, 97, 137, 147, 229, 278, 285 ], [ 49, 75, 98, 138, 144, 230, 279, 286 ], [ 50, 72, 99, 139, 145, 231, 276, 287 ], [ 55, 77, 100, 140, 144, 150, 209, 232 ], [ 52, 78, 101, 141, 145, 151, 210, 233 ], [ 53, 79, 102, 142, 146, 148, 211, 234 ], [ 54, 76, 103, 143, 147, 149, 208, 235 ], [ 0, 59, 81, 104, 148, 154, 236, 285 ], [ 1, 56, 82, 105, 149, 155, 237, 286 ], [ 2, 57, 83, 106, 150, 152, 238, 287 ], [ 3, 58, 80, 107, 151, 153, 239, 284 ], [ 4, 63, 85, 108, 152, 158, 217, 240 ], [ 5, 60, 86, 109, 153, 159, 218, 241 ], [ 6, 61, 87, 110, 154, 156, 219, 242 ], [ 7, 62, 84, 111, 155, 157, 216, 243 ], [ 8, 67, 89, 112, 149, 156, 162, 244 ], [ 9, 64, 90, 113, 150, 157, 163, 245 ], [ 10, 65, 91, 114, 151, 158, 160, 246 ], [ 11, 66, 88, 115, 148, 159, 161, 247 ], [ 12, 71, 93, 116, 160, 166, 225, 248 ], [ 13, 68, 94, 117, 161, 167, 226, 249 ], [ 14, 69, 95, 118, 162, 164, 227, 250 ], [ 15, 70, 92, 119, 163, 165, 224, 251 ], [ 16, 75, 97, 120, 157, 164, 170, 252 ], [ 17, 72, 98, 121, 158, 165, 171, 253 ], [ 18, 73, 99, 122, 159, 166, 168, 254 ], [ 19, 74, 96, 123, 156, 167, 169, 255 ], [ 20, 79, 101, 124, 168, 174, 233, 256 ], [ 21, 76, 102, 125, 169, 175, 234, 257 ], [ 22, 77, 103, 126, 170, 172, 235, 258 ], [ 23, 78, 100, 127, 171, 173, 232, 259 ], [ 24, 83, 105, 128, 165, 172, 178, 260 ], [ 25, 80, 106, 129, 166, 173, 179, 261 ], [ 26, 81, 107, 130, 167, 174, 176, 262 ], [ 27, 82, 104, 131, 164, 175, 177, 263 ], [ 28, 87, 109, 132, 176, 182, 241, 264 ], [ 29, 84, 110, 133, 177, 183, 242, 265 ], [ 30, 85, 111, 134, 178, 180, 243, 266 ], [ 31, 86, 108, 135, 179, 181, 240, 267 ], [ 32, 91, 113, 136, 173, 180, 186, 268 ], [ 33, 88, 114, 137, 174, 181, 187, 269 ], [ 34, 89, 115, 138, 175, 182, 184, 270 ], [ 35, 90, 112, 139, 172, 183, 185, 271 ], [ 36, 95, 117, 140, 184, 190, 249, 272 ], [ 37, 92, 118, 141, 185, 191, 250, 273 ], [ 38, 93, 119, 142, 186, 188, 251, 274 ], [ 39, 94, 116, 143, 187, 189, 248, 275 ], [ 0, 40, 99, 121, 181, 188, 194, 276 ], [ 1, 41, 96, 122, 182, 189, 195, 277 ], [ 2, 42, 97, 123, 183, 190, 192, 278 ], [ 3, 43, 98, 120, 180, 191, 193, 279 ], [ 4, 44, 103, 125, 192, 198, 257, 280 ], [ 5, 45, 100, 126, 193, 199, 258, 281 ], [ 6, 46, 101, 127, 194, 196, 259, 282 ], [ 7, 47, 102, 124, 195, 197, 256, 283 ], [ 8, 48, 107, 129, 189, 196, 202, 284 ], [ 9, 49, 104, 130, 190, 197, 203, 285 ], [ 10, 50, 105, 131, 191, 198, 200, 286 ], [ 11, 51, 106, 128, 188, 199, 201, 287 ], [ 12, 52, 111, 133, 144, 200, 206, 265 ], [ 13, 53, 108, 134, 145, 201, 207, 266 ], [ 14, 54, 109, 135, 146, 202, 204, 267 ], [ 15, 55, 110, 132, 147, 203, 205, 264 ], [ 16, 56, 115, 137, 148, 197, 204, 210 ], [ 17, 57, 112, 138, 149, 198, 205, 211 ], [ 18, 58, 113, 139, 150, 199, 206, 208 ], [ 19, 59, 114, 136, 151, 196, 207, 209 ], [ 20, 60, 119, 141, 152, 208, 214, 273 ], [ 21, 61, 116, 142, 153, 209, 215, 274 ], [ 22, 62, 117, 143, 154, 210, 212, 275 ], [ 23, 63, 118, 140, 155, 211, 213, 272 ], [ 1, 24, 64, 123, 156, 205, 212, 218 ], [ 2, 25, 65, 120, 157, 206, 213, 219 ], [ 3, 26, 66, 121, 158, 207, 214, 216 ], [ 0, 27, 67, 122, 159, 204, 215, 217 ], [ 5, 28, 68, 127, 160, 216, 222, 281 ], [ 6, 29, 69, 124, 161, 217, 223, 282 ], [ 7, 30, 70, 125, 162, 218, 220, 283 ], [ 4, 31, 71, 126, 163, 219, 221, 280 ], [ 9, 32, 72, 131, 164, 213, 220, 226 ], [ 10, 33, 73, 128, 165, 214, 221, 227 ], [ 11, 34, 74, 129, 166, 215, 222, 224 ], [ 8, 35, 75, 130, 167, 212, 223, 225 ], [ 13, 36, 76, 135, 145, 168, 224, 230 ], [ 14, 37, 77, 132, 146, 169, 225, 231 ], [ 15, 38, 78, 133, 147, 170, 226, 228 ], [ 12, 39, 79, 134, 144, 171, 227, 229 ] ] }, "distance": { "d": 28, "X": { "value": 28, "confidence": "upper_bound", "witness": [ 6, 7, 23, 24, 52, 64, 75, 89, 97, 111, 118, 135, 154, 162, 177, 178, 183, 185, 197, 210, 223, 230, 245, 259, 263, 267, 270, 285 ] }, "Z": { "value": 28, "confidence": "upper_bound", "witness": [ 4, 8, 14, 27, 37, 45, 60, 64, 66, 69, 73, 110, 112, 113, 115, 120, 131, 134, 149, 161, 163, 175, 193, 242, 248, 254, 266, 284 ] } }, "provenance": { "authors": [ "@trevor-vincent" ], "construction": "2BGA on metacyclic Z_36 rtimes Z_4 (r=19), a=[28, 77, 84, 90], b=[17, 40, 80, 139]. Mutation orbit around [[288,6,26]]/[[288,4,28]].", "references": [ "arXiv:2306.16400" ], "date": "2026-10-01", "notes": "Literature check 2026-10-01: no published [[288,6,28]] found; the systematic 2BGA enumeration (arXiv:2306.16400) covers non-abelian groups only to n<=200; nearest published n=288 codes ([[288,16,18]] of arXiv:2608.08996, ZSZ-LP of arXiv:2607.27644) have d<=18. Novelty vs literature: no match found. Distance evidence: RIS ladder flat at 28 (5k..16M CPU trials, 8 seeds) and 5e8 GPU trials per side (verify/ris_gpu.py) found nothing lighter; both sides carry weight-28 witnesses.", "model": "Claude Fable 5" }, "family": "generalized-bicycle" }