{ "schema_version": "0.2", "name": "[[579,13,15]] reduction of [[599,13,15]]", "code_type": "CSS", "n": 579, "k": 13, "checks": { "X": [ [ 5, 31, 278, 292 ], [ 9, 10, 36, 297 ], [ 38, 279, 280, 299 ], [ 3, 16, 42, 281, 304 ], [ 4, 16, 43, 282, 305 ], [ 5, 18, 44, 282, 306 ], [ 6, 18, 45, 283, 307 ], [ 7, 46, 283, 284, 308 ], [ 9, 48, 285, 286, 310 ], [ 1, 11, 22, 50, 287, 313 ], [ 4, 14, 25, 53, 288, 316 ], [ 8, 18, 57, 289, 290, 320 ], [ 9, 19, 58, 290, 291, 321 ], [ 11, 20, 60, 292, 293, 324 ], [ 12, 21, 61, 293, 294, 325 ], [ 13, 22, 62, 294, 295, 326 ], [ 14, 23, 63, 295, 296, 327 ], [ 15, 24, 64, 296, 297, 328 ], [ 16, 25, 65, 297, 298, 329 ], [ 17, 26, 66, 298, 299, 330 ], [ 18, 27, 67, 299, 300, 331 ], [ 19, 28, 68, 300, 301, 332 ], [ 20, 29, 70, 303, 304, 335 ], [ 21, 30, 71, 304, 305, 336 ], [ 22, 31, 72, 305, 306, 337 ], [ 23, 32, 73, 306, 307, 338 ], [ 24, 33, 74, 307, 308, 339 ], [ 25, 34, 75, 308, 309, 340 ], [ 26, 35, 76, 309, 310, 341 ], [ 27, 36, 77, 310, 311, 342 ], [ 28, 37, 78, 311, 312, 343 ], [ 29, 39, 80, 314, 315, 346 ], [ 30, 40, 81, 315, 316, 347 ], [ 31, 41, 82, 316, 317, 348 ], [ 32, 42, 83, 317, 318, 349 ], [ 33, 43, 84, 318, 319, 350 ], [ 34, 44, 85, 319, 320, 351 ], [ 35, 45, 86, 320, 321, 352 ], [ 36, 46, 87, 321, 322, 353 ], [ 37, 47, 88, 322, 323, 354 ], [ 39, 49, 90, 325, 326, 357 ], [ 40, 50, 91, 326, 327, 358 ], [ 41, 51, 92, 327, 328, 359 ], [ 42, 52, 93, 328, 329, 360 ], [ 43, 53, 94, 329, 330, 361 ], [ 44, 54, 95, 330, 331, 362 ], [ 45, 55, 96, 331, 332, 363 ], [ 46, 56, 97, 332, 333, 364 ], [ 47, 57, 98, 333, 334, 365 ], [ 49, 59, 100, 336, 337, 368 ], [ 50, 60, 101, 337, 338, 369 ], [ 51, 61, 102, 338, 339, 370 ], [ 52, 62, 103, 339, 340, 371 ], [ 53, 63, 104, 340, 341, 372 ], [ 54, 64, 105, 341, 342, 373 ], [ 55, 65, 106, 342, 343, 374 ], [ 56, 66, 107, 343, 344, 375 ], [ 57, 67, 108, 344, 345, 376 ], [ 59, 69, 110, 347, 348, 379 ], [ 60, 70, 111, 348, 349, 380 ], [ 61, 71, 112, 349, 350, 381 ], [ 62, 72, 113, 350, 351, 382 ], [ 63, 73, 114, 351, 352, 383 ], [ 64, 74, 115, 352, 353, 384 ], [ 65, 75, 116, 353, 354, 385 ], [ 66, 76, 117, 354, 355, 386 ], [ 67, 77, 118, 355, 356, 387 ], [ 69, 79, 120, 358, 359, 390 ], [ 70, 80, 121, 359, 360, 391 ], [ 71, 81, 122, 360, 361, 392 ], [ 72, 82, 123, 361, 362, 393 ], [ 73, 83, 124, 362, 363, 394 ], [ 74, 84, 125, 363, 364, 395 ], [ 75, 85, 126, 364, 365, 396 ], [ 76, 86, 127, 365, 366, 397 ], [ 77, 87, 128, 366, 367, 398 ], [ 79, 89, 130, 369, 370, 401 ], [ 80, 90, 131, 370, 371, 402 ], [ 81, 91, 132, 371, 372, 403 ], [ 82, 92, 133, 372, 373, 404 ], [ 83, 93, 134, 373, 374, 405 ], [ 84, 94, 135, 374, 375, 406 ], [ 85, 95, 136, 375, 376, 407 ], [ 86, 96, 137, 376, 377, 408 ], [ 87, 97, 138, 377, 378, 409 ], [ 89, 99, 140, 380, 381, 412 ], [ 90, 100, 141, 381, 382, 413 ], [ 91, 101, 142, 382, 383, 414 ], [ 92, 102, 143, 383, 384, 415 ], [ 93, 103, 144, 384, 385, 416 ], [ 94, 104, 145, 385, 386, 417 ], [ 95, 105, 146, 386, 387, 418 ], [ 96, 106, 147, 387, 388, 419 ], [ 97, 107, 148, 388, 389, 420 ], [ 99, 109, 150, 391, 392, 423 ], [ 100, 110, 151, 392, 393, 424 ], [ 101, 111, 152, 393, 394, 425 ], [ 102, 112, 153, 394, 395, 426 ], [ 103, 113, 154, 395, 396, 427 ], [ 104, 114, 155, 396, 397, 428 ], [ 105, 115, 156, 397, 398, 429 ], [ 106, 116, 157, 398, 399, 430 ], [ 107, 117, 158, 399, 400, 431 ], [ 109, 119, 160, 402, 403, 434 ], [ 110, 120, 161, 403, 404, 435 ], [ 111, 121, 162, 404, 405, 436 ], [ 112, 122, 163, 405, 406, 437 ], [ 113, 123, 164, 406, 407, 438 ], [ 114, 124, 165, 407, 408, 439 ], [ 115, 125, 166, 408, 409, 440 ], [ 116, 126, 167, 409, 410, 441 ], [ 117, 127, 168, 410, 411, 442 ], [ 119, 129, 170, 413, 414, 445 ], [ 120, 130, 171, 414, 415, 446 ], [ 121, 131, 172, 415, 416, 447 ], [ 122, 132, 173, 416, 417, 448 ], [ 123, 133, 174, 417, 418, 449 ], [ 124, 134, 175, 418, 419, 450 ], [ 125, 135, 176, 419, 420, 451 ], [ 126, 136, 177, 420, 421, 452 ], [ 127, 137, 178, 421, 422, 453 ], [ 129, 139, 180, 424, 425, 456 ], [ 130, 140, 181, 425, 426, 457 ], [ 131, 141, 182, 426, 427, 458 ], [ 132, 142, 183, 427, 428, 459 ], [ 133, 143, 184, 428, 429, 460 ], [ 134, 144, 185, 429, 430, 461 ], [ 135, 145, 186, 430, 431, 462 ], [ 136, 146, 187, 431, 432, 463 ], [ 137, 147, 188, 432, 433, 464 ], [ 139, 149, 190, 435, 436, 467 ], [ 140, 150, 191, 436, 437, 468 ], [ 141, 151, 192, 437, 438, 469 ], [ 142, 152, 193, 438, 439, 470 ], [ 143, 153, 194, 439, 440, 471 ], [ 144, 154, 195, 440, 441, 472 ], [ 145, 155, 196, 441, 442, 473 ], [ 146, 156, 197, 442, 443, 474 ], [ 147, 157, 198, 443, 444, 475 ], [ 149, 159, 200, 446, 447, 477 ], [ 150, 160, 201, 447, 448, 478 ], [ 151, 161, 202, 448, 449, 479 ], [ 152, 162, 203, 449, 450, 480 ], [ 153, 163, 204, 450, 451, 481 ], [ 154, 164, 205, 451, 452, 482 ], [ 155, 165, 206, 452, 453, 483 ], [ 156, 166, 207, 453, 454, 484 ], [ 157, 167, 208, 454, 455, 485 ], [ 159, 169, 210, 457, 458, 488 ], [ 160, 170, 211, 458, 459, 489 ], [ 161, 171, 212, 459, 460, 490 ], [ 162, 172, 213, 460, 461, 491 ], [ 163, 173, 214, 461, 462, 492 ], [ 164, 174, 215, 462, 463, 493 ], [ 165, 175, 216, 463, 464, 494 ], [ 166, 176, 217, 464, 465, 495 ], [ 167, 177, 218, 465, 466, 496 ], [ 169, 179, 220, 468, 469, 498 ], [ 170, 180, 221, 469, 470, 499 ], [ 171, 181, 222, 470, 471, 500 ], [ 172, 182, 223, 471, 472, 501 ], [ 173, 183, 224, 472, 473, 502 ], [ 174, 184, 225, 473, 474, 503 ], [ 175, 185, 226, 474, 475, 504 ], [ 176, 186, 227, 475, 476, 505 ], [ 179, 189, 229, 478, 479, 509 ], [ 180, 190, 230, 479, 480, 510 ], [ 181, 191, 231, 480, 481, 511 ], [ 182, 192, 232, 481, 482, 512 ], [ 183, 193, 233, 482, 483, 513 ], [ 184, 194, 234, 483, 484, 514 ], [ 185, 195, 235, 484, 485, 515 ], [ 186, 196, 236, 485, 486, 516 ], [ 187, 197, 237, 486, 487, 517 ], [ 189, 199, 239, 489, 490, 520 ], [ 190, 200, 240, 490, 491, 521 ], [ 191, 201, 241, 491, 492, 522 ], [ 192, 202, 242, 492, 493, 523 ], [ 193, 203, 243, 493, 494, 524 ], [ 194, 204, 244, 494, 495, 525 ], [ 195, 205, 245, 495, 496, 526 ], [ 196, 206, 246, 496, 497, 527 ], [ 199, 209, 248, 499, 500, 531 ], [ 200, 210, 249, 500, 501, 532 ], [ 201, 211, 250, 501, 502, 533 ], [ 202, 212, 251, 502, 503, 534 ], [ 203, 213, 252, 503, 504, 535 ], [ 204, 214, 253, 504, 505, 536 ], [ 205, 215, 254, 505, 506, 537 ], [ 206, 216, 255, 506, 507, 538 ], [ 207, 217, 256, 507, 508, 539 ], [ 209, 219, 258, 510, 511, 541 ], [ 210, 220, 259, 511, 512, 542 ], [ 211, 221, 260, 512, 513, 543 ], [ 212, 222, 261, 513, 514, 544 ], [ 213, 223, 262, 514, 515, 545 ], [ 214, 224, 263, 515, 516, 546 ], [ 215, 225, 264, 516, 517, 547 ], [ 216, 226, 265, 517, 518, 548 ], [ 217, 227, 266, 518, 519, 549 ], [ 219, 228, 267, 521, 522, 551 ], [ 220, 229, 268, 522, 523, 552 ], [ 221, 230, 269, 523, 524, 553 ], [ 222, 231, 270, 524, 525, 554 ], [ 223, 232, 271, 525, 526, 555 ], [ 224, 233, 272, 526, 527, 556 ], [ 225, 234, 273, 527, 528, 557 ], [ 226, 235, 274, 528, 529, 558 ], [ 227, 236, 275, 529, 530, 559 ], [ 2, 276 ], [ 2, 12, 24, 51, 287, 314 ], [ 0, 1, 13, 14, 40, 302 ], [ 23, 287 ], [ 3, 13, 24, 25, 52, 315 ], [ 26, 288 ], [ 5, 27, 54, 281, 288, 317 ], [ 6, 16, 27, 28, 55, 318 ], [ 7, 17, 28, 56, 289, 319 ], [ 4, 278 ], [ 5, 7, 32, 33, 293, 294 ], [ 5, 6, 32, 293 ], [ 7, 8, 34, 295 ], [ 8, 9, 35, 296 ], [ 10, 37, 279, 298 ], [ 2, 14, 41, 281, 303 ], [ 15, 281 ], [ 17, 282 ], [ 19, 283 ], [ 8, 47, 284, 285, 309 ], [ 258, 267, 563, 564 ], [ 259, 268, 564, 565 ], [ 260, 269, 565, 566 ], [ 261, 270, 566, 567 ], [ 262, 271, 567, 568 ], [ 263, 272, 568, 569 ], [ 264, 265, 273, 274, 569, 570 ], [ 238, 247, 542, 543, 571 ], [ 239, 248, 543, 544, 572 ], [ 240, 249, 267, 544, 545, 573 ], [ 241, 250, 545, 546, 573 ], [ 242, 251, 546, 547, 574 ], [ 243, 252, 547, 548, 575 ], [ 244, 253, 548, 549, 576 ], [ 245, 254, 549, 550, 577 ], [ 228, 238, 532, 533, 561 ], [ 229, 239, 533, 534, 562 ], [ 230, 240, 534, 535, 563 ], [ 231, 241, 535, 536, 564 ], [ 232, 242, 536, 537, 565 ], [ 233, 243, 537, 538, 566 ], [ 234, 244, 538, 539, 567 ], [ 235, 245, 539, 540, 568 ], [ 257, 267, 562, 563, 572, 573 ], [ 268, 573, 574 ], [ 269, 574, 575 ], [ 270, 575, 576 ], [ 272, 577, 578 ], [ 271, 272, 576, 578 ], [ 247, 257, 552, 553 ], [ 248, 258, 553, 554 ], [ 249, 259, 554, 555 ], [ 250, 260, 555, 556 ], [ 251, 261, 556, 557 ], [ 252, 262, 557, 558 ], [ 253, 263, 558, 559 ], [ 254, 264, 559, 560 ], [ 3, 4, 277, 278 ] ], "Z": [ [ 3, 29, 30, 277, 304, 315 ], [ 4, 30, 31, 278, 305, 316 ], [ 5, 31, 32, 306, 317 ], [ 6, 32, 33, 307, 318 ], [ 7, 33, 34, 308, 319 ], [ 8, 34, 35, 309, 320 ], [ 9, 35, 36, 310, 321 ], [ 10, 36, 37, 311, 322 ], [ 38, 280 ], [ 13, 39, 40, 315, 326 ], [ 14, 40, 41, 316, 327 ], [ 15, 41, 42, 281, 317, 328 ], [ 16, 42, 43, 318, 329 ], [ 17, 43, 44, 282, 319, 330 ], [ 18, 44, 45, 320, 331 ], [ 19, 45, 46, 283, 321, 332 ], [ 46, 47, 284, 322, 333 ], [ 48, 286 ], [ 22, 49, 50, 326, 337 ], [ 23, 50, 51, 287, 327, 338 ], [ 24, 51, 52, 328, 339 ], [ 25, 52, 53, 329, 340 ], [ 26, 53, 54, 288, 330, 341 ], [ 27, 54, 55, 331, 342 ], [ 28, 55, 56, 332, 343 ], [ 56, 57, 289, 333, 344 ], [ 58, 291 ], [ 31, 59, 60, 292, 337, 348 ], [ 32, 60, 61, 293, 338, 349 ], [ 33, 61, 62, 294, 339, 350 ], [ 34, 62, 63, 295, 340, 351 ], [ 35, 63, 64, 296, 341, 352 ], [ 36, 64, 65, 297, 342, 353 ], [ 37, 65, 66, 298, 343, 354 ], [ 38, 66, 67, 299, 344, 355 ], [ 67, 68, 300, 345, 356 ], [ 41, 69, 70, 303, 348, 359 ], [ 42, 70, 71, 304, 349, 360 ], [ 43, 71, 72, 305, 350, 361 ], [ 44, 72, 73, 306, 351, 362 ], [ 45, 73, 74, 307, 352, 363 ], [ 46, 74, 75, 308, 353, 364 ], [ 47, 75, 76, 309, 354, 365 ], [ 48, 76, 77, 310, 355, 366 ], [ 77, 78, 311, 356, 367 ], [ 51, 79, 80, 314, 359, 370 ], [ 52, 80, 81, 315, 360, 371 ], [ 53, 81, 82, 316, 361, 372 ], [ 54, 82, 83, 317, 362, 373 ], [ 55, 83, 84, 318, 363, 374 ], [ 56, 84, 85, 319, 364, 375 ], [ 57, 85, 86, 320, 365, 376 ], [ 58, 86, 87, 321, 366, 377 ], [ 87, 88, 322, 367, 378 ], [ 61, 89, 90, 325, 370, 381 ], [ 62, 90, 91, 326, 371, 382 ], [ 63, 91, 92, 327, 372, 383 ], [ 64, 92, 93, 328, 373, 384 ], [ 65, 93, 94, 329, 374, 385 ], [ 66, 94, 95, 330, 375, 386 ], [ 67, 95, 96, 331, 376, 387 ], [ 68, 96, 97, 332, 377, 388 ], [ 97, 98, 333, 378, 389 ], [ 71, 99, 100, 336, 381, 392 ], [ 72, 100, 101, 337, 382, 393 ], [ 73, 101, 102, 338, 383, 394 ], [ 74, 102, 103, 339, 384, 395 ], [ 75, 103, 104, 340, 385, 396 ], [ 76, 104, 105, 341, 386, 397 ], [ 77, 105, 106, 342, 387, 398 ], [ 78, 106, 107, 343, 388, 399 ], [ 107, 108, 344, 389, 400 ], [ 81, 109, 110, 347, 392, 403 ], [ 82, 110, 111, 348, 393, 404 ], [ 83, 111, 112, 349, 394, 405 ], [ 84, 112, 113, 350, 395, 406 ], [ 85, 113, 114, 351, 396, 407 ], [ 86, 114, 115, 352, 397, 408 ], [ 87, 115, 116, 353, 398, 409 ], [ 88, 116, 117, 354, 399, 410 ], [ 117, 118, 355, 400, 411 ], [ 91, 119, 120, 358, 403, 414 ], [ 92, 120, 121, 359, 404, 415 ], [ 93, 121, 122, 360, 405, 416 ], [ 94, 122, 123, 361, 406, 417 ], [ 95, 123, 124, 362, 407, 418 ], [ 96, 124, 125, 363, 408, 419 ], [ 97, 125, 126, 364, 409, 420 ], [ 98, 126, 127, 365, 410, 421 ], [ 127, 128, 366, 411, 422 ], [ 101, 129, 130, 369, 414, 425 ], [ 102, 130, 131, 370, 415, 426 ], [ 103, 131, 132, 371, 416, 427 ], [ 104, 132, 133, 372, 417, 428 ], [ 105, 133, 134, 373, 418, 429 ], [ 106, 134, 135, 374, 419, 430 ], [ 107, 135, 136, 375, 420, 431 ], [ 108, 136, 137, 376, 421, 432 ], [ 137, 138, 377, 422, 433 ], [ 111, 139, 140, 380, 425, 436 ], [ 112, 140, 141, 381, 426, 437 ], [ 113, 141, 142, 382, 427, 438 ], [ 114, 142, 143, 383, 428, 439 ], [ 115, 143, 144, 384, 429, 440 ], [ 116, 144, 145, 385, 430, 441 ], [ 117, 145, 146, 386, 431, 442 ], [ 118, 146, 147, 387, 432, 443 ], [ 147, 148, 388, 433, 444 ], [ 121, 149, 150, 391, 436, 447 ], [ 122, 150, 151, 392, 437, 448 ], [ 123, 151, 152, 393, 438, 449 ], [ 124, 152, 153, 394, 439, 450 ], [ 125, 153, 154, 395, 440, 451 ], [ 126, 154, 155, 396, 441, 452 ], [ 127, 155, 156, 397, 442, 453 ], [ 128, 156, 157, 398, 443, 454 ], [ 157, 158, 399, 444, 455 ], [ 131, 159, 160, 402, 447, 458 ], [ 132, 160, 161, 403, 448, 459 ], [ 133, 161, 162, 404, 449, 460 ], [ 134, 162, 163, 405, 450, 461 ], [ 135, 163, 164, 406, 451, 462 ], [ 136, 164, 165, 407, 452, 463 ], [ 137, 165, 166, 408, 453, 464 ], [ 138, 166, 167, 409, 454, 465 ], [ 167, 168, 410, 455, 466 ], [ 141, 169, 170, 413, 458, 469 ], [ 142, 170, 171, 414, 459, 470 ], [ 143, 171, 172, 415, 460, 471 ], [ 144, 172, 173, 416, 461, 472 ], [ 145, 173, 174, 417, 462, 473 ], [ 146, 174, 175, 418, 463, 474 ], [ 147, 175, 176, 419, 464, 475 ], [ 148, 176, 177, 420, 465, 476 ], [ 177, 178, 421, 466 ], [ 151, 179, 180, 424, 469, 479 ], [ 152, 180, 181, 425, 470, 480 ], [ 153, 181, 182, 426, 471, 481 ], [ 154, 182, 183, 427, 472, 482 ], [ 155, 183, 184, 428, 473, 483 ], [ 156, 184, 185, 429, 474, 484 ], [ 157, 185, 186, 430, 475, 485 ], [ 158, 186, 187, 431, 476, 486 ], [ 187, 188, 432, 487 ], [ 161, 189, 190, 435, 479, 490 ], [ 162, 190, 191, 436, 480, 491 ], [ 163, 191, 192, 437, 481, 492 ], [ 164, 192, 193, 438, 482, 493 ], [ 165, 193, 194, 439, 483, 494 ], [ 166, 194, 195, 440, 484, 495 ], [ 167, 195, 196, 441, 485, 496 ], [ 168, 196, 197, 442, 486, 497 ], [ 197, 198, 443, 487 ], [ 171, 199, 200, 446, 490, 500 ], [ 172, 200, 201, 447, 491, 501 ], [ 173, 201, 202, 448, 492, 502 ], [ 174, 202, 203, 449, 493, 503 ], [ 175, 203, 204, 450, 494, 504 ], [ 176, 204, 205, 451, 495, 505 ], [ 177, 205, 206, 452, 496, 506 ], [ 178, 206, 207, 453, 497, 507 ], [ 207, 208, 454, 508 ], [ 181, 209, 210, 457, 500, 511 ], [ 182, 210, 211, 458, 501, 512 ], [ 183, 211, 212, 459, 502, 513 ], [ 184, 212, 213, 460, 503, 514 ], [ 185, 213, 214, 461, 504, 515 ], [ 186, 214, 215, 462, 505, 516 ], [ 187, 215, 216, 463, 506, 517 ], [ 188, 216, 217, 464, 507, 518 ], [ 217, 218, 465, 508, 519 ], [ 191, 219, 220, 468, 511, 522 ], [ 192, 220, 221, 469, 512, 523 ], [ 193, 221, 222, 470, 513, 524 ], [ 194, 222, 223, 471, 514, 525 ], [ 195, 223, 224, 472, 515, 526 ], [ 196, 224, 225, 473, 516, 527 ], [ 197, 225, 226, 474, 517, 528 ], [ 198, 226, 227, 475, 518, 529 ], [ 227, 476, 519, 530 ], [ 201, 228, 229, 478, 522, 533 ], [ 202, 229, 230, 479, 523, 534 ], [ 203, 230, 231, 480, 524, 535 ], [ 204, 231, 232, 481, 525, 536 ], [ 205, 232, 233, 482, 526, 537 ], [ 206, 233, 234, 483, 527, 538 ], [ 207, 234, 235, 484, 528, 539 ], [ 208, 235, 236, 485, 529, 540 ], [ 236, 237, 486, 530 ], [ 211, 238, 239, 489, 533, 543 ], [ 212, 239, 240, 490, 534, 544 ], [ 213, 240, 241, 491, 535, 545 ], [ 214, 241, 242, 492, 536, 546 ], [ 215, 242, 243, 493, 537, 547 ], [ 216, 243, 244, 494, 538, 548 ], [ 217, 244, 245, 495, 539, 549 ], [ 218, 245, 246, 496, 540, 550 ], [ 246, 497 ], [ 221, 247, 248, 499, 543, 553 ], [ 222, 248, 249, 500, 544, 554 ], [ 223, 249, 250, 501, 545, 555 ], [ 224, 250, 251, 502, 546, 556 ], [ 225, 251, 252, 503, 547, 557 ], [ 226, 252, 253, 504, 548, 558 ], [ 227, 253, 254, 505, 549, 559 ], [ 254, 255, 506, 550, 560 ], [ 255, 256, 507 ], [ 230, 257, 258, 510, 553, 563 ], [ 231, 258, 259, 511, 554, 564 ], [ 232, 259, 260, 512, 555, 565 ], [ 233, 260, 261, 513, 556, 566 ], [ 234, 261, 262, 514, 557, 567 ], [ 235, 262, 263, 515, 558, 568 ], [ 236, 263, 264, 516, 559, 569 ], [ 237, 264, 265, 517, 560 ], [ 265, 266, 518, 570 ], [ 240, 267, 521, 563 ], [ 241, 267, 268, 522, 564, 573 ], [ 242, 268, 269, 523, 565, 574 ], [ 243, 269, 270, 524, 566, 575 ], [ 244, 270, 271, 525, 567, 576 ], [ 245, 271, 272, 526, 568, 577 ], [ 246, 272, 273, 527, 569, 578 ], [ 273, 274, 528 ], [ 274, 275, 529, 570 ], [ 2, 29, 276, 303, 314 ], [ 12, 39, 314, 325 ], [ 21, 49, 325, 336 ], [ 30, 59, 336, 347 ], [ 40, 69, 302, 347, 358 ], [ 50, 79, 313, 358, 369 ], [ 60, 89, 324, 369, 380 ], [ 70, 99, 335, 380, 391 ], [ 80, 109, 346, 391, 402 ], [ 90, 119, 357, 402, 413 ], [ 100, 129, 368, 413, 424 ], [ 110, 139, 379, 424, 435 ], [ 120, 149, 390, 435, 446 ], [ 130, 159, 401, 446, 457 ], [ 140, 169, 412, 457, 468 ], [ 150, 179, 423, 468, 478 ], [ 160, 189, 434, 478, 489 ], [ 170, 199, 445, 489, 499 ], [ 180, 209, 456, 499, 510 ], [ 190, 219, 467, 510, 521 ], [ 200, 228, 477, 521, 532 ], [ 210, 238, 488, 532, 542 ], [ 220, 247, 498, 542, 552 ], [ 229, 257, 509, 552, 562 ], [ 239, 520, 562, 572 ], [ 1, 302, 313 ], [ 11, 313, 324 ], [ 20, 324, 335 ], [ 29, 335, 346 ], [ 39, 346, 357 ], [ 49, 357, 368 ], [ 59, 368, 379 ], [ 69, 379, 390 ], [ 79, 390, 401 ], [ 89, 401, 412 ], [ 99, 412, 423 ], [ 109, 423, 434 ], [ 119, 434, 445 ], [ 129, 445, 456 ], [ 139, 456, 467 ], [ 149, 467, 477 ], [ 159, 477, 488 ], [ 169, 488, 498 ], [ 179, 498, 509 ], [ 189, 509, 520 ], [ 199, 520, 531 ], [ 209, 531, 541 ], [ 219, 541, 551 ], [ 228, 551, 561 ], [ 238, 561, 571 ], [ 68, 301 ], [ 78, 312 ], [ 88, 323 ], [ 98, 334 ], [ 108, 345 ], [ 118, 356 ], [ 128, 367 ], [ 138, 378 ], [ 148, 389 ], [ 158, 400 ], [ 168, 411 ], [ 178, 422 ], [ 188, 433 ], [ 198, 444 ], [ 208, 455 ], [ 218, 466 ], [ 237, 487 ], [ 256, 508 ], [ 266, 519 ], [ 275, 530 ], [ 37, 279, 280, 312, 323 ], [ 47, 285, 286, 323, 334 ], [ 57, 290, 291, 334, 345 ], [ 0, 302 ] ] }, "distance": { "d": 15, "X": { "value": 15, "confidence": "upper_bound", "witness": [ 287, 293, 294, 338, 350, 361, 372, 383, 406, 428, 462, 473, 516, 569, 578 ], "witness_provenance": { "found_by": [ "@dorakingx" ], "date": "2026-10-05", "found_at_samples": 20000, "survived_samples": 20000000, "tool": "gf2_fast RIS ladder (verify/gf2_fast.cpp), both sides searched jointly", "seeds": [ 777001, 777138, 777275, 777412, 777549 ] } }, "Z": { "value": 15, "confidence": "upper_bound", "witness": [ 148, 205, 245, 254, 388, 419, 450, 451, 480, 510, 511, 540, 542, 560, 571 ], "witness_provenance": { "found_by": [ "@dorakingx" ], "date": "2026-10-05", "found_at_samples": 4000, "survived_samples": 20000000, "tool": "gf2_fast RIS in the packaging search; the ladder searched both sides jointly", "seeds": [ 7, 777001, 777138, 777275, 777412, 777549 ] } } }, "provenance": { "authors": [ "@dorakingx" ], "construction": "Reduction of the board's codes/599-13-15.json ([[599,13,15]]) by 20 qubits at unchanged k, unchanged check-weight class and unchanged locality class, by one move applied to a fixpoint: graft a qubit away using a low-weight element of the stabilizer ROW SPACE. Let S be an element of the row space of H_X with support T and let a be in T. Replace one generator of the subset summing to S by S itself -- the span is unchanged, that generator being S plus the rest of the subset -- and add S into every other X row meeting a, so that a survives only in S. Then apply the CNOT fan-out from a to T\\{a}, which acts on the check matrices as H_X[:, b] ^= H_X[:, a] and H_Z[:, a] ^= H_Z[:, b] for each b in T\\{a}. Only S still meets a, so the first substitution turns S into the weight-1 stabilizer X_a and leaves every other X row alone; the second zeroes column a of H_Z, because commutation forces every Z row to meet T an even number of times. Qubit a is then disentangled and is deleted: n -> n-1, k unchanged, and the Z rows only LOSE an index, so their weights and support diameters cannot rise. The weight of S separates three regimes, and the difference is entirely in the clearing step R ^= S. |S| = 1: nothing is added anywhere, so the weights, the radius AND THE DISTANCE are all preserved exactly, and no distance search is needed -- this is the row-space form of the weight-1 stabilizer cleanup of Liang, Eberhardt and Chen (arXiv:2504.08887 Sec. III D step 4), which the implementation in research/local2d/boundary_engine.py applies only to literal weight-1 generator ROWS. |S| = 2: R loses a and toggles one other index, so its weight changes by 0 or -2 and can never rise. |S| >= 3: R can grow, so every touched row is checked against the code's weight class and its locality radius, measured in the source's own layout. This generalises the capped merge-graft I introduced with [[454,8,17]], which only ever built S from the generators a single qubit happens to lie in. Here the accepted grafts were |S| = 2: 6, |S| = 3: 1, |S| = 4: 6, |S| = 5: 2, |S| = 6: 5. Low-weight row-space elements are enumerated as sums of at most three checks with a connected overlap pattern. Every graft with |S| >= 2 was accepted only if k was unchanged and a bit-packed RIS search found nothing lighter than 15, screened once and confirmed twice with independent seeds; those in-loop rungs are a filter, not the evidence. QUBIT POSITIONS ARE THE SOURCE'S: every surviving qubit keeps the coordinate it has in codes/599-13-15.json, so the layout is inherited rather than re-derived, and the reduction only deletes. The surviving qubits' indices into the source numbering are [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]... (full list implied by the coordinates in this file).", "references": [ "arXiv:2504.08887" ], "date": "2026-10-05", "notes": "Derived from codes/599-13-15.json, not an independent construction; that entry is my own earlier reduction, and this one goes further with a larger move set. The gate reports no exact duplicate and no WL-equivalent entry. It dominates [[599,13,15]], [[612,13,15]] on (n, k, d, w), which therefore leave the frontier of every cell they share with it. The measured interaction radius is unchanged at 6.32456, so the reduced code is no less local than the source. Distance is a witness-backed upper bound: the deepest null result is 20000000 fresh-seed RIS trials. Literature novelty is unverified.", "model": "Claude Opus 5 (Claude Code)", "origin": "submission", "novelty": "unknown" }, "family": "bivariate-bicycle", "locality": { "coordinates": [ [ 1.0, 0.0 ], [ 2.0, 0.0 ], [ 2.0, 1.0 ], [ 2.0, 2.0 ], [ 2.0, 3.0 ], [ 2.0, 4.0 ], [ 2.0, 5.0 ], [ 2.0, 6.0 ], [ 2.0, 7.0 ], [ 2.0, 8.0 ], [ 2.0, 9.0 ], [ 3.0, 0.0 ], [ 3.0, 1.0 ], [ 3.0, 2.0 ], [ 3.0, 3.0 ], [ 3.0, 4.0 ], [ 3.0, 5.0 ], [ 3.0, 6.0 ], [ 3.0, 7.0 ], [ 3.0, 8.0 ], [ 4.0, 0.0 ], [ 4.0, 1.0 ], [ 4.0, 2.0 ], [ 4.0, 3.0 ], [ 4.0, 4.0 ], [ 4.0, 5.0 ], [ 4.0, 6.0 ], [ 4.0, 7.0 ], [ 4.0, 8.0 ], [ 5.0, 0.0 ], [ 5.0, 1.0 ], [ 5.0, 2.0 ], [ 5.0, 3.0 ], [ 5.0, 4.0 ], [ 5.0, 5.0 ], [ 5.0, 6.0 ], [ 5.0, 7.0 ], [ 5.0, 8.0 ], [ 5.0, 9.0 ], [ 6.0, 0.0 ], [ 6.0, 1.0 ], [ 6.0, 2.0 ], [ 6.0, 3.0 ], [ 6.0, 4.0 ], [ 6.0, 5.0 ], [ 6.0, 6.0 ], [ 6.0, 7.0 ], [ 6.0, 8.0 ], [ 6.0, 9.0 ], [ 7.0, 0.0 ], [ 7.0, 1.0 ], [ 7.0, 2.0 ], [ 7.0, 3.0 ], [ 7.0, 4.0 ], [ 7.0, 5.0 ], [ 7.0, 6.0 ], [ 7.0, 7.0 ], [ 7.0, 8.0 ], [ 7.0, 9.0 ], [ 8.0, 0.0 ], [ 8.0, 1.0 ], [ 8.0, 2.0 ], [ 8.0, 3.0 ], [ 8.0, 4.0 ], [ 8.0, 5.0 ], [ 8.0, 6.0 ], [ 8.0, 7.0 ], [ 8.0, 8.0 ], [ 8.0, 9.0 ], [ 9.0, 0.0 ], [ 9.0, 1.0 ], [ 9.0, 2.0 ], [ 9.0, 3.0 ], [ 9.0, 4.0 ], [ 9.0, 5.0 ], [ 9.0, 6.0 ], [ 9.0, 7.0 ], [ 9.0, 8.0 ], [ 9.0, 9.0 ], [ 10.0, 0.0 ], [ 10.0, 1.0 ], [ 10.0, 2.0 ], [ 10.0, 3.0 ], [ 10.0, 4.0 ], [ 10.0, 5.0 ], [ 10.0, 6.0 ], [ 10.0, 7.0 ], [ 10.0, 8.0 ], [ 10.0, 9.0 ], [ 11.0, 0.0 ], [ 11.0, 1.0 ], [ 11.0, 2.0 ], [ 11.0, 3.0 ], [ 11.0, 4.0 ], [ 11.0, 5.0 ], [ 11.0, 6.0 ], [ 11.0, 7.0 ], [ 11.0, 8.0 ], [ 11.0, 9.0 ], [ 12.0, 0.0 ], [ 12.0, 1.0 ], [ 12.0, 2.0 ], [ 12.0, 3.0 ], [ 12.0, 4.0 ], [ 12.0, 5.0 ], [ 12.0, 6.0 ], [ 12.0, 7.0 ], [ 12.0, 8.0 ], [ 12.0, 9.0 ], [ 13.0, 0.0 ], [ 13.0, 1.0 ], [ 13.0, 2.0 ], [ 13.0, 3.0 ], [ 13.0, 4.0 ], [ 13.0, 5.0 ], [ 13.0, 6.0 ], [ 13.0, 7.0 ], [ 13.0, 8.0 ], [ 13.0, 9.0 ], [ 14.0, 0.0 ], [ 14.0, 1.0 ], [ 14.0, 2.0 ], [ 14.0, 3.0 ], [ 14.0, 4.0 ], [ 14.0, 5.0 ], [ 14.0, 6.0 ], [ 14.0, 7.0 ], [ 14.0, 8.0 ], [ 14.0, 9.0 ], [ 15.0, 0.0 ], [ 15.0, 1.0 ], [ 15.0, 2.0 ], [ 15.0, 3.0 ], [ 15.0, 4.0 ], [ 15.0, 5.0 ], [ 15.0, 6.0 ], [ 15.0, 7.0 ], [ 15.0, 8.0 ], [ 15.0, 9.0 ], [ 16.0, 0.0 ], [ 16.0, 1.0 ], [ 16.0, 2.0 ], [ 16.0, 3.0 ], [ 16.0, 4.0 ], [ 16.0, 5.0 ], [ 16.0, 6.0 ], [ 16.0, 7.0 ], [ 16.0, 8.0 ], [ 16.0, 9.0 ], [ 17.0, 0.0 ], [ 17.0, 1.0 ], [ 17.0, 2.0 ], [ 17.0, 3.0 ], [ 17.0, 4.0 ], [ 17.0, 5.0 ], [ 17.0, 6.0 ], [ 17.0, 7.0 ], [ 17.0, 8.0 ], [ 17.0, 9.0 ], [ 18.0, 0.0 ], [ 18.0, 1.0 ], [ 18.0, 2.0 ], [ 18.0, 3.0 ], [ 18.0, 4.0 ], [ 18.0, 5.0 ], [ 18.0, 6.0 ], [ 18.0, 7.0 ], [ 18.0, 8.0 ], [ 18.0, 9.0 ], [ 19.0, 0.0 ], [ 19.0, 1.0 ], [ 19.0, 2.0 ], [ 19.0, 3.0 ], [ 19.0, 4.0 ], [ 19.0, 5.0 ], [ 19.0, 6.0 ], [ 19.0, 7.0 ], [ 19.0, 8.0 ], [ 19.0, 9.0 ], [ 20.0, 0.0 ], [ 20.0, 1.0 ], [ 20.0, 2.0 ], [ 20.0, 3.0 ], [ 20.0, 4.0 ], [ 20.0, 5.0 ], [ 20.0, 6.0 ], [ 20.0, 7.0 ], [ 20.0, 8.0 ], [ 20.0, 9.0 ], [ 21.0, 0.0 ], [ 21.0, 1.0 ], [ 21.0, 2.0 ], [ 21.0, 3.0 ], [ 21.0, 4.0 ], [ 21.0, 5.0 ], [ 21.0, 6.0 ], [ 21.0, 7.0 ], [ 21.0, 8.0 ], [ 21.0, 9.0 ], [ 22.0, 0.0 ], [ 22.0, 1.0 ], [ 22.0, 2.0 ], [ 22.0, 3.0 ], [ 22.0, 4.0 ], [ 22.0, 5.0 ], [ 22.0, 6.0 ], [ 22.0, 7.0 ], [ 22.0, 8.0 ], [ 22.0, 9.0 ], [ 23.0, 0.0 ], [ 23.0, 1.0 ], [ 23.0, 2.0 ], [ 23.0, 3.0 ], [ 23.0, 4.0 ], [ 23.0, 5.0 ], [ 23.0, 6.0 ], [ 23.0, 7.0 ], [ 23.0, 8.0 ], [ 23.0, 9.0 ], [ 24.0, 0.0 ], [ 24.0, 1.0 ], [ 24.0, 2.0 ], [ 24.0, 3.0 ], [ 24.0, 4.0 ], [ 24.0, 5.0 ], [ 24.0, 6.0 ], [ 24.0, 7.0 ], [ 24.0, 8.0 ], [ 25.0, 0.0 ], [ 25.0, 1.0 ], [ 25.0, 2.0 ], [ 25.0, 3.0 ], [ 25.0, 4.0 ], [ 25.0, 5.0 ], [ 25.0, 6.0 ], [ 25.0, 7.0 ], [ 25.0, 8.0 ], [ 25.0, 9.0 ], [ 26.0, 0.0 ], [ 26.0, 1.0 ], [ 26.0, 2.0 ], [ 26.0, 3.0 ], [ 26.0, 4.0 ], [ 26.0, 5.0 ], [ 26.0, 6.0 ], [ 26.0, 7.0 ], [ 26.0, 8.0 ], [ 27.0, 0.0 ], [ 27.0, 1.0 ], [ 27.0, 2.0 ], [ 27.0, 3.0 ], [ 27.0, 4.0 ], [ 27.0, 5.0 ], [ 27.0, 6.0 ], [ 27.0, 7.0 ], [ 27.0, 8.0 ], [ 27.0, 9.0 ], [ 28.0, 0.0 ], [ 28.0, 1.0 ], [ 28.0, 2.0 ], [ 28.0, 3.0 ], [ 28.0, 4.0 ], [ 28.0, 5.0 ], [ 28.0, 6.0 ], [ 28.0, 7.0 ], [ 28.0, 8.0 ], [ 28.0, 9.0 ], [ 29.0, 1.0 ], [ 29.0, 2.0 ], [ 29.0, 3.0 ], [ 29.0, 4.0 ], [ 29.0, 5.0 ], [ 29.0, 6.0 ], [ 29.0, 7.0 ], [ 29.0, 8.0 ], [ 29.0, 9.0 ], [ 0.0, 0.0 ], [ 0.0, 1.0 ], [ 0.0, 2.0 ], [ 0.0, 9.0 ], [ 0.0, 10.0 ], [ 1.0, 3.0 ], [ 1.0, 5.0 ], [ 1.0, 7.0 ], [ 1.0, 8.0 ], [ 1.0, 9.0 ], [ 1.0, 10.0 ], [ 2.0, 2.0 ], [ 2.0, 5.0 ], [ 2.0, 8.0 ], [ 2.0, 9.0 ], [ 2.0, 10.0 ], [ 3.0, 1.0 ], [ 3.0, 2.0 ], [ 3.0, 3.0 ], [ 3.0, 4.0 ], [ 3.0, 5.0 ], [ 3.0, 6.0 ], [ 3.0, 7.0 ], [ 3.0, 8.0 ], [ 3.0, 9.0 ], [ 3.0, 10.0 ], [ 4.0, 0.0 ], [ 4.0, 1.0 ], [ 4.0, 2.0 ], [ 4.0, 3.0 ], [ 4.0, 4.0 ], [ 4.0, 5.0 ], [ 4.0, 6.0 ], [ 4.0, 7.0 ], [ 4.0, 8.0 ], [ 4.0, 9.0 ], [ 4.0, 10.0 ], [ 5.0, 0.0 ], [ 5.0, 1.0 ], [ 5.0, 2.0 ], [ 5.0, 3.0 ], [ 5.0, 4.0 ], [ 5.0, 5.0 ], [ 5.0, 6.0 ], [ 5.0, 7.0 ], [ 5.0, 8.0 ], [ 5.0, 9.0 ], [ 5.0, 10.0 ], [ 6.0, 0.0 ], [ 6.0, 1.0 ], [ 6.0, 2.0 ], [ 6.0, 3.0 ], [ 6.0, 4.0 ], [ 6.0, 5.0 ], [ 6.0, 6.0 ], [ 6.0, 7.0 ], [ 6.0, 8.0 ], [ 6.0, 9.0 ], [ 6.0, 10.0 ], [ 7.0, 0.0 ], [ 7.0, 1.0 ], [ 7.0, 2.0 ], [ 7.0, 3.0 ], [ 7.0, 4.0 ], [ 7.0, 5.0 ], [ 7.0, 6.0 ], [ 7.0, 7.0 ], [ 7.0, 8.0 ], [ 7.0, 9.0 ], [ 7.0, 10.0 ], [ 8.0, 0.0 ], [ 8.0, 1.0 ], [ 8.0, 2.0 ], [ 8.0, 3.0 ], [ 8.0, 4.0 ], [ 8.0, 5.0 ], [ 8.0, 6.0 ], [ 8.0, 7.0 ], [ 8.0, 8.0 ], [ 8.0, 9.0 ], [ 8.0, 10.0 ], [ 9.0, 0.0 ], [ 9.0, 1.0 ], [ 9.0, 2.0 ], [ 9.0, 3.0 ], [ 9.0, 4.0 ], [ 9.0, 5.0 ], [ 9.0, 6.0 ], [ 9.0, 7.0 ], [ 9.0, 8.0 ], [ 9.0, 9.0 ], [ 9.0, 10.0 ], [ 10.0, 0.0 ], [ 10.0, 1.0 ], [ 10.0, 2.0 ], [ 10.0, 3.0 ], [ 10.0, 4.0 ], [ 10.0, 5.0 ], [ 10.0, 6.0 ], [ 10.0, 7.0 ], [ 10.0, 8.0 ], [ 10.0, 9.0 ], [ 10.0, 10.0 ], [ 11.0, 0.0 ], [ 11.0, 1.0 ], [ 11.0, 2.0 ], [ 11.0, 3.0 ], [ 11.0, 4.0 ], [ 11.0, 5.0 ], [ 11.0, 6.0 ], [ 11.0, 7.0 ], [ 11.0, 8.0 ], [ 11.0, 9.0 ], [ 11.0, 10.0 ], [ 12.0, 0.0 ], [ 12.0, 1.0 ], [ 12.0, 2.0 ], [ 12.0, 3.0 ], [ 12.0, 4.0 ], [ 12.0, 5.0 ], [ 12.0, 6.0 ], [ 12.0, 7.0 ], [ 12.0, 8.0 ], [ 12.0, 9.0 ], [ 12.0, 10.0 ], [ 13.0, 0.0 ], [ 13.0, 1.0 ], [ 13.0, 2.0 ], [ 13.0, 3.0 ], [ 13.0, 4.0 ], [ 13.0, 5.0 ], [ 13.0, 6.0 ], [ 13.0, 7.0 ], [ 13.0, 8.0 ], [ 13.0, 9.0 ], [ 13.0, 10.0 ], [ 14.0, 0.0 ], [ 14.0, 1.0 ], [ 14.0, 2.0 ], [ 14.0, 3.0 ], [ 14.0, 4.0 ], [ 14.0, 5.0 ], [ 14.0, 6.0 ], [ 14.0, 7.0 ], [ 14.0, 8.0 ], [ 14.0, 9.0 ], [ 14.0, 10.0 ], [ 15.0, 0.0 ], [ 15.0, 1.0 ], [ 15.0, 2.0 ], [ 15.0, 3.0 ], [ 15.0, 4.0 ], [ 15.0, 5.0 ], [ 15.0, 6.0 ], [ 15.0, 7.0 ], [ 15.0, 8.0 ], [ 15.0, 9.0 ], [ 15.0, 10.0 ], [ 16.0, 0.0 ], [ 16.0, 1.0 ], [ 16.0, 2.0 ], [ 16.0, 3.0 ], [ 16.0, 4.0 ], [ 16.0, 5.0 ], [ 16.0, 6.0 ], [ 16.0, 7.0 ], [ 16.0, 8.0 ], [ 16.0, 9.0 ], [ 16.0, 10.0 ], [ 17.0, 0.0 ], [ 17.0, 1.0 ], [ 17.0, 2.0 ], [ 17.0, 3.0 ], [ 17.0, 4.0 ], [ 17.0, 5.0 ], [ 17.0, 6.0 ], [ 17.0, 7.0 ], [ 17.0, 8.0 ], [ 17.0, 9.0 ], [ 17.0, 10.0 ], [ 18.0, 0.0 ], [ 18.0, 1.0 ], [ 18.0, 2.0 ], [ 18.0, 3.0 ], [ 18.0, 4.0 ], [ 18.0, 5.0 ], [ 18.0, 6.0 ], [ 18.0, 7.0 ], [ 18.0, 8.0 ], [ 18.0, 9.0 ], [ 18.0, 10.0 ], [ 19.0, 0.0 ], [ 19.0, 1.0 ], [ 19.0, 2.0 ], [ 19.0, 3.0 ], [ 19.0, 4.0 ], [ 19.0, 5.0 ], [ 19.0, 6.0 ], [ 19.0, 7.0 ], [ 19.0, 8.0 ], [ 19.0, 9.0 ], [ 20.0, 0.0 ], [ 20.0, 1.0 ], [ 20.0, 2.0 ], [ 20.0, 3.0 ], [ 20.0, 4.0 ], [ 20.0, 5.0 ], [ 20.0, 6.0 ], [ 20.0, 7.0 ], [ 20.0, 8.0 ], [ 20.0, 9.0 ], [ 20.0, 10.0 ], [ 21.0, 0.0 ], [ 21.0, 1.0 ], [ 21.0, 2.0 ], [ 21.0, 3.0 ], [ 21.0, 4.0 ], [ 21.0, 5.0 ], [ 21.0, 6.0 ], [ 21.0, 7.0 ], [ 21.0, 8.0 ], [ 21.0, 9.0 ], [ 22.0, 0.0 ], [ 22.0, 1.0 ], [ 22.0, 2.0 ], [ 22.0, 3.0 ], [ 22.0, 4.0 ], [ 22.0, 5.0 ], [ 22.0, 6.0 ], [ 22.0, 7.0 ], [ 22.0, 8.0 ], [ 22.0, 9.0 ], [ 22.0, 10.0 ], [ 23.0, 0.0 ], [ 23.0, 1.0 ], [ 23.0, 2.0 ], [ 23.0, 3.0 ], [ 23.0, 4.0 ], [ 23.0, 5.0 ], [ 23.0, 6.0 ], [ 23.0, 7.0 ], [ 23.0, 8.0 ], [ 23.0, 9.0 ], [ 23.0, 10.0 ], [ 24.0, 0.0 ], [ 24.0, 1.0 ], [ 24.0, 2.0 ], [ 24.0, 3.0 ], [ 24.0, 4.0 ], [ 24.0, 5.0 ], [ 24.0, 6.0 ], [ 24.0, 7.0 ], [ 24.0, 8.0 ], [ 24.0, 9.0 ], [ 24.0, 10.0 ], [ 25.0, 0.0 ], [ 25.0, 1.0 ], [ 25.0, 2.0 ], [ 25.0, 3.0 ], [ 25.0, 4.0 ], [ 25.0, 5.0 ], [ 25.0, 6.0 ], [ 25.0, 7.0 ], [ 25.0, 8.0 ], [ 25.0, 9.0 ], [ 26.0, 0.0 ], [ 26.0, 1.0 ], [ 26.0, 2.0 ], [ 26.0, 3.0 ], [ 26.0, 4.0 ], [ 26.0, 5.0 ], [ 26.0, 6.0 ], [ 26.0, 7.0 ], [ 26.0, 8.0 ], [ 26.0, 9.0 ], [ 27.0, 0.0 ], [ 27.0, 1.0 ], [ 27.0, 2.0 ], [ 27.0, 3.0 ], [ 27.0, 4.0 ], [ 27.0, 5.0 ], [ 27.0, 6.0 ], [ 27.0, 7.0 ], [ 27.0, 8.0 ], [ 27.0, 9.0 ], [ 28.0, 0.0 ], [ 28.0, 1.0 ], [ 28.0, 2.0 ], [ 28.0, 3.0 ], [ 28.0, 4.0 ], [ 28.0, 5.0 ], [ 28.0, 6.0 ], [ 28.0, 7.0 ], [ 28.0, 8.0 ], [ 28.0, 10.0 ], [ 29.0, 0.0 ], [ 29.0, 1.0 ], [ 29.0, 3.0 ], [ 29.0, 4.0 ], [ 29.0, 5.0 ], [ 29.0, 6.0 ], [ 29.0, 7.0 ], [ 29.0, 8.0 ] ], "interaction_radius": 6.324555320336759, "layers": 2 } }