{ "schema_version": "0.2", "name": "[[306,106,3]] two-block code over C51 x C3", "code_type": "CSS", "n": 306, "k": 106, "checks": { "X": [ [ 0, 4, 124, 130, 153, 157, 304, 305 ], [ 0, 1, 130, 136, 153, 154, 301, 305 ], [ 2, 10, 132, 138, 155, 163, 293, 298 ], [ 3, 11, 133, 139, 156, 164, 165, 171 ], [ 1, 4, 124, 136, 154, 157, 301, 304 ], [ 2, 5, 138, 143, 155, 158, 287, 298 ], [ 3, 6, 139, 144, 156, 159, 160, 171 ], [ 7, 18, 116, 122, 160, 171, 300, 303 ], [ 8, 19, 141, 146, 154, 157, 161, 172 ], [ 9, 20, 142, 147, 162, 173, 174, 180 ], [ 5, 10, 132, 143, 158, 163, 287, 293 ], [ 6, 11, 133, 144, 159, 160, 164, 165 ], [ 7, 12, 122, 128, 160, 165, 295, 303 ], [ 8, 13, 146, 149, 153, 157, 161, 166 ], [ 9, 14, 147, 150, 162, 167, 168, 180 ], [ 15, 27, 125, 131, 158, 163, 168, 180 ], [ 16, 28, 148, 151, 159, 164, 169, 181 ], [ 2, 5, 17, 29, 170, 182, 183, 189 ], [ 12, 18, 116, 128, 165, 171, 295, 300 ], [ 13, 19, 141, 149, 153, 154, 166, 172 ], [ 14, 20, 142, 150, 167, 168, 173, 174 ], [ 15, 21, 131, 137, 155, 163, 168, 174 ], [ 16, 22, 151, 152, 156, 164, 169, 175 ], [ 5, 10, 17, 23, 170, 176, 177, 189 ], [ 24, 36, 134, 140, 166, 172, 177, 189 ], [ 7, 12, 25, 37, 167, 173, 178, 190 ], [ 8, 13, 26, 38, 179, 191, 192, 198 ], [ 21, 27, 125, 137, 155, 158, 174, 180 ], [ 22, 28, 148, 152, 156, 159, 175, 181 ], [ 2, 10, 23, 29, 176, 177, 182, 183 ], [ 24, 30, 140, 145, 161, 172, 177, 183 ], [ 12, 18, 25, 31, 162, 173, 178, 184 ], [ 13, 19, 26, 32, 179, 185, 186, 198 ], [ 0, 1, 33, 45, 175, 181, 186, 198 ], [ 15, 21, 34, 46, 176, 182, 187, 199 ], [ 16, 22, 35, 47, 188, 200, 201, 207 ], [ 30, 36, 134, 145, 161, 166, 183, 189 ], [ 7, 18, 31, 37, 162, 167, 184, 190 ], [ 8, 19, 32, 38, 185, 186, 191, 192 ], [ 1, 4, 33, 39, 169, 181, 186, 192 ], [ 21, 27, 34, 40, 170, 182, 187, 193 ], [ 22, 28, 35, 41, 188, 194, 195, 207 ], [ 3, 6, 42, 54, 184, 190, 195, 207 ], [ 24, 30, 43, 55, 185, 191, 196, 208 ], [ 25, 31, 44, 56, 197, 209, 210, 216 ], [ 0, 4, 39, 45, 169, 175, 192, 198 ], [ 15, 27, 40, 46, 170, 176, 193, 199 ], [ 16, 28, 41, 47, 194, 195, 200, 201 ], [ 6, 11, 42, 48, 178, 190, 195, 201 ], [ 30, 36, 43, 49, 179, 191, 196, 202 ], [ 31, 37, 44, 50, 197, 203, 204, 216 ], [ 9, 14, 51, 63, 193, 199, 204, 216 ], [ 33, 39, 52, 64, 194, 200, 205, 217 ], [ 34, 40, 53, 65, 206, 218, 219, 225 ], [ 3, 11, 48, 54, 178, 184, 201, 207 ], [ 24, 36, 49, 55, 179, 185, 202, 208 ], [ 25, 37, 50, 56, 203, 204, 209, 210 ], [ 14, 20, 51, 57, 187, 199, 204, 210 ], [ 39, 45, 52, 58, 188, 200, 205, 211 ], [ 40, 46, 53, 59, 206, 212, 213, 225 ], [ 17, 23, 60, 72, 202, 208, 213, 225 ], [ 42, 48, 61, 73, 203, 209, 214, 226 ], [ 43, 49, 62, 74, 215, 227, 228, 234 ], [ 9, 20, 57, 63, 187, 193, 210, 216 ], [ 33, 45, 58, 64, 188, 194, 211, 217 ], [ 34, 46, 59, 65, 212, 213, 218, 219 ], [ 23, 29, 60, 66, 196, 208, 213, 219 ], [ 48, 54, 61, 67, 197, 209, 214, 220 ], [ 49, 55, 62, 68, 215, 221, 222, 234 ], [ 26, 32, 69, 81, 211, 217, 222, 234 ], [ 51, 57, 70, 82, 212, 218, 223, 235 ], [ 52, 58, 71, 83, 224, 236, 237, 243 ], [ 17, 29, 66, 72, 196, 202, 219, 225 ], [ 42, 54, 67, 73, 197, 203, 220, 226 ], [ 43, 55, 68, 74, 221, 222, 227, 228 ], [ 32, 38, 69, 75, 205, 217, 222, 228 ], [ 57, 63, 70, 76, 206, 218, 223, 229 ], [ 58, 64, 71, 77, 224, 230, 231, 243 ], [ 35, 41, 78, 90, 220, 226, 231, 243 ], [ 60, 66, 79, 91, 221, 227, 232, 244 ], [ 61, 67, 80, 92, 233, 245, 246, 252 ], [ 26, 38, 75, 81, 205, 211, 228, 234 ], [ 51, 63, 76, 82, 206, 212, 229, 235 ], [ 52, 64, 77, 83, 230, 231, 236, 237 ], [ 41, 47, 78, 84, 214, 226, 231, 237 ], [ 66, 72, 79, 85, 215, 227, 232, 238 ], [ 67, 73, 80, 86, 233, 239, 240, 252 ], [ 44, 50, 87, 99, 229, 235, 240, 252 ], [ 69, 75, 88, 100, 230, 236, 241, 253 ], [ 70, 76, 89, 101, 242, 254, 255, 261 ], [ 35, 47, 84, 90, 214, 220, 237, 243 ], [ 60, 72, 85, 91, 215, 221, 238, 244 ], [ 61, 73, 86, 92, 239, 240, 245, 246 ], [ 50, 56, 87, 93, 223, 235, 240, 246 ], [ 75, 81, 88, 94, 224, 236, 241, 247 ], [ 76, 82, 89, 95, 242, 248, 249, 261 ], [ 53, 59, 96, 108, 238, 244, 249, 261 ], [ 78, 84, 97, 109, 239, 245, 250, 262 ], [ 79, 85, 98, 110, 251, 263, 264, 270 ], [ 44, 56, 93, 99, 223, 229, 246, 252 ], [ 69, 81, 94, 100, 224, 230, 247, 253 ], [ 70, 82, 95, 101, 248, 249, 254, 255 ], [ 59, 65, 96, 102, 232, 244, 249, 255 ], [ 84, 90, 97, 103, 233, 245, 250, 256 ], [ 85, 91, 98, 104, 251, 257, 258, 270 ], [ 62, 68, 105, 117, 247, 253, 258, 270 ], [ 87, 93, 106, 118, 248, 254, 259, 271 ], [ 88, 94, 107, 119, 260, 272, 273, 279 ], [ 53, 65, 102, 108, 232, 238, 255, 261 ], [ 78, 90, 103, 109, 233, 239, 256, 262 ], [ 79, 91, 104, 110, 257, 258, 263, 264 ], [ 68, 74, 105, 111, 241, 253, 258, 264 ], [ 93, 99, 106, 112, 242, 254, 259, 265 ], [ 94, 100, 107, 113, 260, 266, 267, 279 ], [ 71, 77, 114, 126, 256, 262, 267, 279 ], [ 96, 102, 115, 127, 257, 263, 268, 280 ], [ 97, 103, 116, 128, 269, 281, 282, 288 ], [ 62, 74, 111, 117, 241, 247, 264, 270 ], [ 87, 99, 112, 118, 242, 248, 265, 271 ], [ 88, 100, 113, 119, 266, 267, 272, 273 ], [ 77, 83, 114, 120, 250, 262, 267, 273 ], [ 102, 108, 115, 121, 251, 263, 268, 274 ], [ 103, 109, 116, 122, 269, 275, 276, 288 ], [ 80, 86, 123, 135, 265, 271, 276, 288 ], [ 105, 111, 124, 136, 266, 272, 277, 289 ], [ 106, 112, 125, 137, 278, 290, 291, 296 ], [ 71, 83, 120, 126, 250, 256, 273, 279 ], [ 96, 108, 121, 127, 251, 257, 274, 280 ], [ 97, 109, 122, 128, 275, 276, 281, 282 ], [ 86, 92, 123, 129, 259, 271, 276, 282 ], [ 111, 117, 124, 130, 260, 272, 277, 283 ], [ 112, 118, 125, 131, 278, 284, 285, 296 ], [ 89, 95, 132, 143, 274, 280, 285, 296 ], [ 114, 120, 133, 144, 275, 281, 286, 297 ], [ 115, 121, 134, 145, 287, 298, 299, 302 ], [ 80, 92, 129, 135, 259, 265, 282, 288 ], [ 105, 117, 130, 136, 260, 266, 283, 289 ], [ 106, 118, 131, 137, 284, 285, 290, 291 ], [ 95, 101, 132, 138, 268, 280, 285, 291 ], [ 120, 126, 133, 139, 269, 281, 286, 292 ], [ 121, 127, 134, 140, 287, 293, 294, 302 ], [ 98, 104, 141, 149, 283, 289, 294, 302 ], [ 123, 129, 142, 150, 284, 290, 295, 303 ], [ 89, 101, 138, 143, 268, 274, 291, 296 ], [ 114, 126, 139, 144, 269, 275, 292, 297 ], [ 115, 127, 140, 145, 293, 294, 298, 299 ], [ 104, 110, 141, 146, 277, 289, 294, 299 ], [ 129, 135, 142, 147, 278, 290, 295, 300 ], [ 107, 113, 148, 152, 292, 297, 301, 305 ], [ 98, 110, 146, 149, 277, 283, 299, 302 ], [ 123, 135, 147, 150, 278, 284, 300, 303 ], [ 113, 119, 148, 151, 286, 297, 301, 304 ], [ 107, 119, 151, 152, 286, 292, 304, 305 ] ], "Z": [ [ 0, 1, 13, 19, 153, 154, 186, 198 ], [ 1, 4, 8, 19, 154, 157, 186, 192 ], [ 2, 5, 21, 27, 155, 158, 170, 182 ], [ 3, 6, 22, 28, 156, 159, 195, 207 ], [ 0, 4, 8, 13, 153, 157, 192, 198 ], [ 5, 10, 15, 27, 158, 163, 170, 176 ], [ 6, 11, 16, 28, 159, 164, 195, 201 ], [ 6, 7, 11, 12, 160, 165, 178, 190 ], [ 8, 13, 30, 36, 161, 166, 179, 191 ], [ 9, 14, 31, 37, 162, 167, 204, 216 ], [ 2, 10, 15, 21, 155, 163, 176, 182 ], [ 3, 11, 16, 22, 156, 164, 201, 207 ], [ 3, 11, 12, 18, 165, 171, 178, 184 ], [ 13, 19, 24, 36, 166, 172, 179, 185 ], [ 14, 20, 25, 37, 167, 173, 204, 210 ], [ 14, 15, 20, 21, 168, 174, 187, 199 ], [ 16, 22, 39, 45, 169, 175, 188, 200 ], [ 17, 23, 40, 46, 170, 176, 213, 225 ], [ 3, 6, 7, 18, 160, 171, 184, 190 ], [ 8, 19, 24, 30, 161, 172, 185, 191 ], [ 9, 20, 25, 31, 162, 173, 210, 216 ], [ 9, 20, 21, 27, 174, 180, 187, 193 ], [ 22, 28, 33, 45, 175, 181, 188, 194 ], [ 23, 29, 34, 46, 176, 182, 213, 219 ], [ 23, 24, 29, 30, 177, 183, 196, 208 ], [ 25, 31, 48, 54, 178, 184, 197, 209 ], [ 26, 32, 49, 55, 179, 185, 222, 234 ], [ 9, 14, 15, 27, 168, 180, 193, 199 ], [ 16, 28, 33, 39, 169, 181, 194, 200 ], [ 17, 29, 34, 40, 170, 182, 219, 225 ], [ 17, 29, 30, 36, 183, 189, 196, 202 ], [ 31, 37, 42, 54, 184, 190, 197, 203 ], [ 32, 38, 43, 55, 185, 191, 222, 228 ], [ 32, 33, 38, 39, 186, 192, 205, 217 ], [ 34, 40, 57, 63, 187, 193, 206, 218 ], [ 35, 41, 58, 64, 188, 194, 231, 243 ], [ 17, 23, 24, 36, 177, 189, 202, 208 ], [ 25, 37, 42, 48, 178, 190, 203, 209 ], [ 26, 38, 43, 49, 179, 191, 228, 234 ], [ 26, 38, 39, 45, 192, 198, 205, 211 ], [ 40, 46, 51, 63, 193, 199, 206, 212 ], [ 41, 47, 52, 64, 194, 200, 231, 237 ], [ 41, 42, 47, 48, 195, 201, 214, 226 ], [ 43, 49, 66, 72, 196, 202, 215, 227 ], [ 44, 50, 67, 73, 197, 203, 240, 252 ], [ 26, 32, 33, 45, 186, 198, 211, 217 ], [ 34, 46, 51, 57, 187, 199, 212, 218 ], [ 35, 47, 52, 58, 188, 200, 237, 243 ], [ 35, 47, 48, 54, 201, 207, 214, 220 ], [ 49, 55, 60, 72, 202, 208, 215, 221 ], [ 50, 56, 61, 73, 203, 209, 240, 246 ], [ 50, 51, 56, 57, 204, 210, 223, 235 ], [ 52, 58, 75, 81, 205, 211, 224, 236 ], [ 53, 59, 76, 82, 206, 212, 249, 261 ], [ 35, 41, 42, 54, 195, 207, 220, 226 ], [ 43, 55, 60, 66, 196, 208, 221, 227 ], [ 44, 56, 61, 67, 197, 209, 246, 252 ], [ 44, 56, 57, 63, 210, 216, 223, 229 ], [ 58, 64, 69, 81, 211, 217, 224, 230 ], [ 59, 65, 70, 82, 212, 218, 249, 255 ], [ 59, 60, 65, 66, 213, 219, 232, 244 ], [ 61, 67, 84, 90, 214, 220, 233, 245 ], [ 62, 68, 85, 91, 215, 221, 258, 270 ], [ 44, 50, 51, 63, 204, 216, 229, 235 ], [ 52, 64, 69, 75, 205, 217, 230, 236 ], [ 53, 65, 70, 76, 206, 218, 255, 261 ], [ 53, 65, 66, 72, 219, 225, 232, 238 ], [ 67, 73, 78, 90, 220, 226, 233, 239 ], [ 68, 74, 79, 91, 221, 227, 258, 264 ], [ 68, 69, 74, 75, 222, 228, 241, 253 ], [ 70, 76, 93, 99, 223, 229, 242, 254 ], [ 71, 77, 94, 100, 224, 230, 267, 279 ], [ 53, 59, 60, 72, 213, 225, 238, 244 ], [ 61, 73, 78, 84, 214, 226, 239, 245 ], [ 62, 74, 79, 85, 215, 227, 264, 270 ], [ 62, 74, 75, 81, 228, 234, 241, 247 ], [ 76, 82, 87, 99, 229, 235, 242, 248 ], [ 77, 83, 88, 100, 230, 236, 267, 273 ], [ 77, 78, 83, 84, 231, 237, 250, 262 ], [ 79, 85, 102, 108, 232, 238, 251, 263 ], [ 80, 86, 103, 109, 233, 239, 276, 288 ], [ 62, 68, 69, 81, 222, 234, 247, 253 ], [ 70, 82, 87, 93, 223, 235, 248, 254 ], [ 71, 83, 88, 94, 224, 236, 273, 279 ], [ 71, 83, 84, 90, 237, 243, 250, 256 ], [ 85, 91, 96, 108, 238, 244, 251, 257 ], [ 86, 92, 97, 109, 239, 245, 276, 282 ], [ 86, 87, 92, 93, 240, 246, 259, 271 ], [ 88, 94, 111, 117, 241, 247, 260, 272 ], [ 89, 95, 112, 118, 242, 248, 285, 296 ], [ 71, 77, 78, 90, 231, 243, 256, 262 ], [ 79, 91, 96, 102, 232, 244, 257, 263 ], [ 80, 92, 97, 103, 233, 245, 282, 288 ], [ 80, 92, 93, 99, 246, 252, 259, 265 ], [ 94, 100, 105, 117, 247, 253, 260, 266 ], [ 95, 101, 106, 118, 248, 254, 285, 291 ], [ 95, 96, 101, 102, 249, 255, 268, 280 ], [ 97, 103, 120, 126, 250, 256, 269, 281 ], [ 98, 104, 121, 127, 251, 257, 294, 302 ], [ 80, 86, 87, 99, 240, 252, 265, 271 ], [ 88, 100, 105, 111, 241, 253, 266, 272 ], [ 89, 101, 106, 112, 242, 254, 291, 296 ], [ 89, 101, 102, 108, 255, 261, 268, 274 ], [ 103, 109, 114, 126, 256, 262, 269, 275 ], [ 104, 110, 115, 127, 257, 263, 294, 299 ], [ 104, 105, 110, 111, 258, 264, 277, 289 ], [ 106, 112, 129, 135, 259, 265, 278, 290 ], [ 107, 113, 130, 136, 260, 266, 301, 305 ], [ 89, 95, 96, 108, 249, 261, 274, 280 ], [ 97, 109, 114, 120, 250, 262, 275, 281 ], [ 98, 110, 115, 121, 251, 263, 299, 302 ], [ 98, 110, 111, 117, 264, 270, 277, 283 ], [ 112, 118, 123, 135, 265, 271, 278, 284 ], [ 113, 119, 124, 136, 266, 272, 301, 304 ], [ 113, 114, 119, 120, 267, 273, 286, 297 ], [ 115, 121, 138, 143, 268, 274, 287, 298 ], [ 116, 122, 139, 144, 160, 171, 269, 275 ], [ 98, 104, 105, 117, 258, 270, 283, 289 ], [ 106, 118, 123, 129, 259, 271, 284, 290 ], [ 107, 119, 124, 130, 260, 272, 304, 305 ], [ 107, 119, 120, 126, 273, 279, 286, 292 ], [ 121, 127, 132, 143, 274, 280, 287, 293 ], [ 122, 128, 133, 144, 160, 165, 275, 281 ], [ 122, 123, 128, 129, 276, 282, 295, 303 ], [ 124, 130, 146, 149, 153, 157, 277, 283 ], [ 125, 131, 147, 150, 168, 180, 278, 284 ], [ 107, 113, 114, 126, 267, 279, 292, 297 ], [ 115, 127, 132, 138, 268, 280, 293, 298 ], [ 116, 128, 133, 139, 165, 171, 269, 281 ], [ 116, 128, 129, 135, 282, 288, 295, 300 ], [ 130, 136, 141, 149, 153, 154, 283, 289 ], [ 131, 137, 142, 150, 168, 174, 284, 290 ], [ 131, 132, 137, 138, 155, 163, 285, 291 ], [ 133, 139, 151, 152, 156, 164, 286, 292 ], [ 5, 10, 134, 140, 177, 189, 287, 293 ], [ 116, 122, 123, 135, 276, 288, 300, 303 ], [ 124, 136, 141, 146, 154, 157, 277, 289 ], [ 125, 137, 142, 147, 174, 180, 278, 290 ], [ 125, 137, 138, 143, 155, 158, 291, 296 ], [ 139, 144, 148, 152, 156, 159, 292, 297 ], [ 2, 10, 140, 145, 177, 183, 293, 298 ], [ 140, 141, 145, 146, 161, 172, 294, 299 ], [ 12, 18, 142, 147, 162, 173, 295, 300 ], [ 125, 131, 132, 143, 158, 163, 285, 296 ], [ 133, 144, 148, 151, 159, 164, 286, 297 ], [ 2, 5, 134, 145, 183, 189, 287, 298 ], [ 134, 145, 146, 149, 161, 166, 299, 302 ], [ 7, 18, 147, 150, 162, 167, 300, 303 ], [ 1, 4, 148, 151, 169, 181, 301, 304 ], [ 134, 140, 141, 149, 166, 172, 294, 302 ], [ 7, 12, 142, 150, 167, 173, 295, 303 ], [ 0, 4, 151, 152, 169, 175, 304, 305 ], [ 0, 1, 148, 152, 175, 181, 301, 305 ] ] }, "distance": { "d": 3, "X": { "value": 3, "confidence": "upper_bound", "witness": [ 206, 212, 218 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-12", "found_at_samples": 2000, "survived_samples": 2000, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 1042 ] } }, "Z": { "value": 3, "confidence": "upper_bound", "witness": [ 62, 68, 74 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-12", "found_at_samples": 2000, "survived_samples": 2000, "tool": "research/kit/surrogate.lightest_logical", "seeds": [ 1043 ] } } }, "provenance": { "authors": [ "Lee, Gideon" ], "construction": "Two-block group-algebra code C(a,b) over C51 x C3 = SmallGroup(153, 2) (order 153), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 306; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 1, 33, 45}, b = {0, 1, 13, 19} as element indices. Check weight 8. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race.", "references": [ "arXiv:2610.13880" ], "date": "2026-10-12", "notes": "Parameters and construction taken from the public database of arXiv:2610.13880v1. Distance is an upper bound certified by the witnesses attached here. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race @ aed705a, CC BY 4.0; rebuilt here with the repo's own group data. Distance is an upper bound certified by the attached witnesses, not the paper's exact distance.", "origin": "baseline", "novelty": "known_parameters", "model": "Mimo-V2.6-Flash" }, "family": "generalized-bicycle", "locality": { "coordinates": [ [ 5.0, 5.0 ], [ 1.0, 4.0 ], [ 7.0, 9.0 ], [ 10.0, 2.0 ], [ 1.0, 2.0 ], [ 8.0, 9.0 ], [ 11.0, 0.0 ], [ 11.0, 1.0 ], [ 1.0, 6.0 ], [ 12.0, 7.0 ], [ 9.0, 10.0 ], [ 10.0, 0.0 ], [ 12.0, 3.0 ], [ 5.0, 6.0 ], [ 12.0, 8.0 ], [ 10.0, 11.0 ], [ 6.0, 0.0 ], [ 4.0, 11.0 ], [ 10.0, 3.0 ], [ 3.0, 6.0 ], [ 12.0, 7.0 ], [ 11.0, 11.0 ], [ 8.0, 3.0 ], [ 4.0, 12.0 ], [ 1.0, 9.0 ], [ 10.0, 5.0 ], [ 3.0, 6.0 ], [ 11.0, 9.0 ], [ 8.0, 2.0 ], [ 5.0, 12.0 ], [ 1.0, 8.0 ], [ 12.0, 4.0 ], [ 1.0, 5.0 ], [ 6.0, 5.0 ], [ 6.0, 10.0 ], [ 6.0, 2.0 ], [ 3.0, 10.0 ], [ 11.0, 4.0 ], [ 0.0, 6.0 ], [ 4.0, 4.0 ], [ 7.0, 10.0 ], [ 5.0, 1.0 ], [ 8.0, 0.0 ], [ 4.0, 9.0 ], [ 8.0, 6.0 ], [ 4.0, 3.0 ], [ 7.0, 8.0 ], [ 7.0, 0.0 ], [ 9.0, 0.0 ], [ 0.0, 8.0 ], [ 9.0, 6.0 ], [ 7.0, 7.0 ], [ 2.0, 2.0 ], [ 6.0, 9.0 ], [ 11.0, 2.0 ], [ 1.0, 10.0 ], [ 8.0, 4.0 ], [ 9.0, 9.0 ], [ 3.0, 4.0 ], [ 7.0, 12.0 ], [ 2.0, 12.0 ], [ 6.0, 5.0 ], [ 0.0, 10.0 ], [ 7.0, 6.0 ], [ 3.0, 2.0 ], [ 7.0, 12.0 ], [ 3.0, 12.0 ], [ 9.0, 3.0 ], [ 3.0, 8.0 ], [ 0.0, 5.0 ], [ 9.0, 8.0 ], [ 5.0, 1.0 ], [ 2.0, 12.0 ], [ 10.0, 2.0 ], [ 1.0, 11.0 ], [ 2.0, 6.0 ], [ 9.0, 10.0 ], [ 3.0, 3.0 ], [ 5.0, 3.0 ], [ 4.0, 9.0 ], [ 7.0, 6.0 ], [ 1.0, 7.0 ], [ 8.0, 8.0 ], [ 4.0, 1.0 ], [ 6.0, 4.0 ], [ 1.0, 9.0 ], [ 9.0, 4.0 ], [ 10.0, 5.0 ], [ 0.0, 4.0 ], [ 9.0, 12.0 ], [ 5.0, 2.0 ], [ 2.0, 10.0 ], [ 8.0, 5.0 ], [ 9.0, 6.0 ], [ 0.0, 4.0 ], [ 10.0, 12.0 ], [ 4.0, 10.0 ], [ 6.0, 4.0 ], [ 2.0, 9.0 ], [ 11.0, 7.0 ], [ 2.0, 4.0 ], [ 10.0, 12.0 ], [ 5.0, 9.0 ], [ 7.0, 4.0 ], [ 2.0, 10.0 ], [ 1.0, 8.0 ], [ 12.0, 10.0 ], [ 2.0, 0.0 ], [ 5.0, 12.0 ], [ 6.0, 3.0 ], [ 3.0, 9.0 ], [ 3.0, 7.0 ], [ 10.0, 10.0 ], [ 2.0, 1.0 ], [ 3.0, 2.0 ], [ 5.0, 8.0 ], [ 9.0, 4.0 ], [ 2.0, 7.0 ], [ 11.0, 8.0 ], [ 0.0, 1.0 ], [ 3.0, 1.0 ], [ 4.0, 11.0 ], [ 9.0, 2.0 ], [ 9.0, 7.0 ], [ 3.0, 5.0 ], [ 12.0, 9.0 ], [ 4.0, 0.0 ], [ 4.0, 12.0 ], [ 11.0, 4.0 ], [ 11.0, 6.0 ], [ 4.0, 5.0 ], [ 12.0, 9.0 ], [ 8.0, 11.0 ], [ 9.0, 3.0 ], [ 6.0, 7.0 ], [ 8.0, 6.0 ], [ 2.0, 3.0 ], [ 11.0, 9.0 ], [ 8.0, 11.0 ], [ 7.0, 3.0 ], [ 6.0, 6.0 ], [ 5.0, 7.0 ], [ 12.0, 5.0 ], [ 7.0, 11.0 ], [ 9.0, 1.0 ], [ 6.0, 7.0 ], [ 3.0, 5.0 ], [ 11.0, 5.0 ], [ 5.0, 3.0 ], [ 0.0, 7.0 ], [ 11.0, 5.0 ], [ 4.0, 3.0 ], [ 4.0, 2.0 ], [ 2.0, 5.0 ], [ 2.0, 4.0 ], [ 10.0, 11.0 ], [ 6.0, 1.0 ], [ 0.0, 5.0 ], [ 8.0, 10.0 ], [ 6.0, 1.0 ], [ 11.0, 1.0 ], [ 4.0, 6.0 ], [ 11.0, 3.0 ], [ 9.0, 11.0 ], [ 7.0, 0.0 ], [ 11.0, 2.0 ], [ 4.0, 6.0 ], [ 12.0, 3.0 ], [ 10.0, 8.0 ], [ 5.0, 4.0 ], [ 7.0, 11.0 ], [ 11.0, 0.0 ], [ 5.0, 6.0 ], [ 12.0, 5.0 ], [ 11.0, 8.0 ], [ 4.0, 4.0 ], [ 9.0, 12.0 ], [ 5.0, 10.0 ], [ 12.0, 1.0 ], [ 2.0, 9.0 ], [ 12.0, 8.0 ], [ 5.0, 4.0 ], [ 8.0, 12.0 ], [ 5.0, 8.0 ], [ 12.0, 0.0 ], [ 4.0, 8.0 ], [ 1.0, 4.0 ], [ 11.0, 10.0 ], [ 7.0, 1.0 ], [ 5.0, 9.0 ], [ 9.0, 2.0 ], [ 2.0, 6.0 ], [ 3.0, 4.0 ], [ 7.0, 8.0 ], [ 7.0, 3.0 ], [ 9.0, 0.0 ], [ 3.0, 10.0 ], [ 9.0, 5.0 ], [ 1.0, 5.0 ], [ 10.0, 10.0 ], [ 6.0, 3.0 ], [ 8.0, 1.0 ], [ 2.0, 8.0 ], [ 10.0, 3.0 ], [ 10.0, 6.0 ], [ 4.0, 5.0 ], [ 7.0, 9.0 ], [ 8.0, 2.0 ], [ 1.0, 11.0 ], [ 8.0, 3.0 ], [ 12.0, 6.0 ], [ 1.0, 3.0 ], [ 10.0, 9.0 ], [ 6.0, 11.0 ], [ 6.0, 0.0 ], [ 0.0, 11.0 ], [ 12.0, 6.0 ], [ 2.0, 2.0 ], [ 9.0, 11.0 ], [ 6.0, 12.0 ], [ 7.0, 2.0 ], [ 1.0, 12.0 ], [ 4.0, 7.0 ], [ 8.0, 7.0 ], [ 0.0, 2.0 ], [ 6.0, 8.0 ], [ 7.0, 2.0 ], [ 5.0, 11.0 ], [ 3.0, 7.0 ], [ 8.0, 7.0 ], [ 3.0, 3.0 ], [ 3.0, 1.0 ], [ 3.0, 9.0 ], [ 7.0, 4.0 ], [ 2.0, 7.0 ], [ 11.0, 7.0 ], [ 0.0, 3.0 ], [ 5.0, 5.0 ], [ 5.0, 11.0 ], [ 7.0, 1.0 ], [ 8.0, 5.0 ], [ 1.0, 6.0 ], [ 11.0, 10.0 ], [ 2.0, 1.0 ], [ 2.0, 11.0 ], [ 6.0, 2.0 ], [ 6.0, 6.0 ], [ 1.0, 7.0 ], [ 9.0, 9.0 ], [ 7.0, 10.0 ], [ 3.0, 0.0 ], [ 3.0, 12.0 ], [ 8.0, 4.0 ], [ 0.0, 6.0 ], [ 12.0, 10.0 ], [ 6.0, 9.0 ], [ 4.0, 2.0 ], [ 2.0, 11.0 ], [ 0.0, 10.0 ], [ 11.0, 6.0 ], [ 2.0, 3.0 ], [ 8.0, 9.0 ], [ 4.0, 0.0 ], [ 3.0, 11.0 ], [ 3.0, 11.0 ], [ 10.0, 7.0 ], [ 1.0, 2.0 ], [ 0.0, 0.0 ], [ 5.0, 10.0 ], [ 8.0, 0.0 ], [ 0.0, 9.0 ], [ 10.0, 6.0 ], [ 0.0, 3.0 ], [ 2.0, 0.0 ], [ 6.0, 12.0 ], [ 8.0, 1.0 ], [ 10.0, 4.0 ], [ 0.0, 7.0 ], [ 10.0, 8.0 ], [ 0.0, 0.0 ], [ 6.0, 11.0 ], [ 9.0, 1.0 ], [ 7.0, 5.0 ], [ 0.0, 8.0 ], [ 9.0, 7.0 ], [ 8.0, 12.0 ], [ 5.0, 2.0 ], [ 6.0, 10.0 ], [ 7.0, 5.0 ], [ 3.0, 8.0 ], [ 10.0, 7.0 ], [ 9.0, 8.0 ], [ 4.0, 1.0 ], [ 6.0, 8.0 ], [ 4.0, 7.0 ], [ 10.0, 4.0 ], [ 10.0, 9.0 ], [ 5.0, 0.0 ], [ 7.0, 7.0 ], [ 2.0, 8.0 ], [ 11.0, 3.0 ], [ 0.0, 2.0 ], [ 4.0, 10.0 ], [ 9.0, 5.0 ], [ 1.0, 3.0 ], [ 2.0, 5.0 ] ], "layers": 2, "interaction_radius": 6.3246, "contributed_by": { "by": [ "@MathysRennela" ], "date": "2026-10-13", "method": "Simulated annealing over integer-grid site assignments with the repo's own research/local2d/fold_layout.search_layout, single layer at radius 4 then two layers at 7, plus a divisor scan of the two-block index convention Z_l x Z_m which gives the tighter embedding here; radius and per-site occupancy re-measured with the verifier's own rule." } } }