{ "schema_version": "0.1", "name": "[[648,434,3]]", "code_type": "CSS", "n": 648, "k": 434, "checks": { "X": [ [ 4, 6, 8, 10, 17, 19, 21, 23, 37, 39, 156, 158 ], [ 16, 18, 20, 22, 29, 31, 33, 35, 47, 49, 164, 166 ], [ 5, 7, 9, 11, 28, 30, 32, 34, 57, 59, 172, 174 ], [ 0, 2, 8, 9, 41, 43, 45, 60, 62, 64, 67, 69 ], [ 12, 14, 20, 21, 40, 42, 44, 51, 53, 55, 77, 79 ], [ 24, 26, 32, 33, 50, 52, 54, 61, 63, 65, 87, 89 ], [ 36, 38, 44, 45, 70, 72, 74, 81, 83, 85, 97, 99 ], [ 46, 48, 54, 55, 80, 82, 84, 91, 93, 95, 107, 109 ], [ 56, 58, 64, 65, 71, 73, 75, 90, 92, 94, 117, 119 ], [ 66, 68, 74, 75, 101, 103, 105, 120, 122, 124, 127, 129 ], [ 76, 78, 84, 85, 100, 102, 104, 111, 113, 115, 137, 139 ], [ 86, 88, 94, 95, 110, 112, 114, 121, 123, 125, 147, 149 ], [ 96, 98, 104, 105, 130, 132, 134, 141, 143, 145, 157, 159 ], [ 106, 108, 114, 115, 140, 142, 144, 151, 153, 155, 165, 167 ], [ 116, 118, 124, 125, 131, 133, 135, 150, 152, 154, 173, 175 ], [ 1, 3, 10, 11, 126, 128, 134, 135, 161, 163, 176, 178 ], [ 13, 15, 22, 23, 136, 138, 144, 145, 160, 162, 169, 171 ], [ 25, 27, 34, 35, 146, 148, 154, 155, 168, 170, 177, 179 ], [ 0, 1, 4, 5, 183, 185, 187, 198, 200, 202, 205, 276 ], [ 12, 13, 16, 17, 182, 184, 186, 191, 193, 195, 211, 280 ], [ 24, 25, 28, 29, 190, 192, 194, 199, 201, 203, 217, 284 ], [ 36, 37, 40, 41, 180, 184, 185, 206, 208, 213, 215, 223 ], [ 46, 47, 50, 51, 188, 192, 193, 212, 214, 219, 221, 229 ], [ 56, 57, 60, 61, 196, 200, 201, 207, 209, 218, 220, 235 ], [ 66, 67, 70, 71, 204, 208, 209, 225, 227, 236, 238, 241 ], [ 76, 77, 80, 81, 210, 214, 215, 224, 226, 231, 233, 247 ], [ 86, 87, 90, 91, 216, 220, 221, 230, 232, 237, 239, 253 ], [ 96, 97, 100, 101, 222, 226, 227, 242, 244, 249, 251, 259 ], [ 106, 107, 110, 111, 228, 232, 233, 248, 250, 255, 257, 265 ], [ 116, 117, 120, 121, 234, 238, 239, 243, 245, 254, 256, 271 ], [ 126, 127, 130, 131, 240, 244, 245, 261, 263, 272, 274, 277 ], [ 136, 137, 140, 141, 246, 250, 251, 260, 262, 267, 269, 281 ], [ 146, 147, 150, 151, 252, 256, 257, 266, 268, 273, 275, 285 ], [ 156, 157, 160, 161, 181, 186, 187, 258, 262, 263, 278, 283 ], [ 164, 165, 168, 169, 189, 194, 195, 264, 268, 269, 282, 287 ], [ 172, 173, 176, 177, 197, 202, 203, 270, 274, 275, 279, 286 ], [ 180, 181, 182, 183, 290, 292, 294, 299, 301, 303, 313, 384 ], [ 188, 189, 190, 191, 298, 300, 302, 307, 309, 311, 319, 388 ], [ 196, 197, 198, 199, 291, 293, 295, 306, 308, 310, 325, 392 ], [ 204, 205, 206, 207, 288, 292, 293, 315, 317, 326, 328, 331 ], [ 210, 211, 212, 213, 296, 300, 301, 314, 316, 321, 323, 337 ], [ 216, 217, 218, 219, 304, 308, 309, 320, 322, 327, 329, 343 ], [ 222, 223, 224, 225, 312, 316, 317, 332, 334, 339, 341, 349 ], [ 228, 229, 230, 231, 318, 322, 323, 338, 340, 345, 347, 355 ], [ 234, 235, 236, 237, 324, 328, 329, 333, 335, 344, 346, 361 ], [ 240, 241, 242, 243, 330, 334, 335, 351, 353, 362, 364, 367 ], [ 246, 247, 248, 249, 336, 340, 341, 350, 352, 357, 359, 373 ], [ 252, 253, 254, 255, 342, 346, 347, 356, 358, 363, 365, 379 ], [ 258, 259, 260, 261, 348, 352, 353, 368, 370, 375, 377, 385 ], [ 264, 265, 266, 267, 354, 358, 359, 374, 376, 381, 383, 389 ], [ 270, 271, 272, 273, 360, 364, 365, 369, 371, 380, 382, 393 ], [ 276, 277, 278, 279, 289, 294, 295, 366, 370, 371, 387, 394 ], [ 280, 281, 282, 283, 297, 302, 303, 372, 376, 377, 386, 391 ], [ 284, 285, 286, 287, 305, 310, 311, 378, 382, 383, 390, 395 ], [ 288, 289, 290, 291, 399, 401, 403, 414, 416, 418, 421, 492 ], [ 296, 297, 298, 299, 398, 400, 402, 407, 409, 411, 427, 496 ], [ 304, 305, 306, 307, 406, 408, 410, 415, 417, 419, 433, 500 ], [ 312, 313, 314, 315, 396, 400, 401, 422, 424, 429, 431, 439 ], [ 318, 319, 320, 321, 404, 408, 409, 428, 430, 435, 437, 445 ], [ 324, 325, 326, 327, 412, 416, 417, 423, 425, 434, 436, 451 ], [ 330, 331, 332, 333, 420, 424, 425, 441, 443, 452, 454, 457 ], [ 336, 337, 338, 339, 426, 430, 431, 440, 442, 447, 449, 463 ], [ 342, 343, 344, 345, 432, 436, 437, 446, 448, 453, 455, 469 ], [ 348, 349, 350, 351, 438, 442, 443, 458, 460, 465, 467, 475 ], [ 354, 355, 356, 357, 444, 448, 449, 464, 466, 471, 473, 481 ], [ 360, 361, 362, 363, 450, 454, 455, 459, 461, 470, 472, 487 ], [ 366, 367, 368, 369, 456, 460, 461, 477, 479, 488, 490, 493 ], [ 372, 373, 374, 375, 462, 466, 467, 476, 478, 483, 485, 497 ], [ 378, 379, 380, 381, 468, 472, 473, 482, 484, 489, 491, 501 ], [ 384, 385, 386, 387, 397, 402, 403, 474, 478, 479, 494, 499 ], [ 388, 389, 390, 391, 405, 410, 411, 480, 484, 485, 498, 503 ], [ 392, 393, 394, 395, 413, 418, 419, 486, 490, 491, 495, 502 ], [ 396, 397, 398, 399, 506, 508, 510, 515, 517, 519, 529, 600 ], [ 404, 405, 406, 407, 514, 516, 518, 523, 525, 527, 535, 604 ], [ 412, 413, 414, 415, 507, 509, 511, 522, 524, 526, 541, 608 ], [ 420, 421, 422, 423, 504, 508, 509, 531, 533, 542, 544, 547 ], [ 426, 427, 428, 429, 512, 516, 517, 530, 532, 537, 539, 553 ], [ 432, 433, 434, 435, 520, 524, 525, 536, 538, 543, 545, 559 ], [ 438, 439, 440, 441, 528, 532, 533, 548, 550, 555, 557, 565 ], [ 444, 445, 446, 447, 534, 538, 539, 554, 556, 561, 563, 571 ], [ 450, 451, 452, 453, 540, 544, 545, 549, 551, 560, 562, 577 ], [ 456, 457, 458, 459, 546, 550, 551, 567, 569, 578, 580, 583 ], [ 462, 463, 464, 465, 552, 556, 557, 566, 568, 573, 575, 589 ], [ 468, 469, 470, 471, 558, 562, 563, 572, 574, 579, 581, 595 ], [ 474, 475, 476, 477, 564, 568, 569, 584, 586, 591, 593, 601 ], [ 480, 481, 482, 483, 570, 574, 575, 590, 592, 597, 599, 605 ], [ 486, 487, 488, 489, 576, 580, 581, 585, 587, 596, 598, 609 ], [ 492, 493, 494, 495, 505, 510, 511, 582, 586, 587, 603, 610 ], [ 496, 497, 498, 499, 513, 518, 519, 588, 592, 593, 602, 607 ], [ 500, 501, 502, 503, 521, 526, 527, 594, 598, 599, 606, 611 ], [ 2, 3, 6, 7, 504, 505, 506, 507, 613, 615, 620, 622 ], [ 14, 15, 18, 19, 512, 513, 514, 515, 612, 614, 617, 619 ], [ 26, 27, 30, 31, 520, 521, 522, 523, 616, 618, 621, 623 ], [ 38, 39, 42, 43, 528, 529, 530, 531, 612, 613, 624, 627 ], [ 48, 49, 52, 53, 534, 535, 536, 537, 616, 617, 626, 629 ], [ 58, 59, 62, 63, 540, 541, 542, 543, 620, 621, 625, 628 ], [ 68, 69, 72, 73, 546, 547, 548, 549, 624, 625, 631, 634 ], [ 78, 79, 82, 83, 552, 553, 554, 555, 626, 627, 630, 633 ], [ 88, 89, 92, 93, 558, 559, 560, 561, 628, 629, 632, 635 ], [ 98, 99, 102, 103, 564, 565, 566, 567, 630, 631, 636, 639 ], [ 108, 109, 112, 113, 570, 571, 572, 573, 632, 633, 638, 641 ], [ 118, 119, 122, 123, 576, 577, 578, 579, 634, 635, 637, 640 ], [ 128, 129, 132, 133, 582, 583, 584, 585, 636, 637, 643, 646 ], [ 138, 139, 142, 143, 588, 589, 590, 591, 638, 639, 642, 645 ], [ 148, 149, 152, 153, 594, 595, 596, 597, 640, 641, 644, 647 ], [ 158, 159, 162, 163, 600, 601, 602, 603, 614, 615, 642, 643 ], [ 166, 167, 170, 171, 604, 605, 606, 607, 618, 619, 644, 645 ], [ 174, 175, 178, 179, 608, 609, 610, 611, 622, 623, 646, 647 ] ], "Z": [ [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ], [ 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 ], [ 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35 ], [ 8, 21, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45 ], [ 20, 33, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55 ], [ 9, 32, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65 ], [ 45, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75 ], [ 44, 55, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85 ], [ 54, 65, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95 ], [ 74, 85, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105 ], [ 84, 95, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115 ], [ 75, 94, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125 ], [ 105, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135 ], [ 104, 115, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145 ], [ 114, 125, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155 ], [ 10, 23, 134, 145, 156, 157, 158, 159, 160, 161, 162, 163 ], [ 22, 35, 144, 155, 164, 165, 166, 167, 168, 169, 170, 171 ], [ 11, 34, 135, 154, 172, 173, 174, 175, 176, 177, 178, 179 ], [ 4, 17, 37, 156, 180, 181, 182, 183, 184, 185, 186, 187 ], [ 16, 29, 47, 164, 188, 189, 190, 191, 192, 193, 194, 195 ], [ 5, 28, 57, 172, 196, 197, 198, 199, 200, 201, 202, 203 ], [ 0, 41, 60, 67, 185, 200, 204, 205, 206, 207, 208, 209 ], [ 12, 40, 51, 77, 184, 193, 210, 211, 212, 213, 214, 215 ], [ 24, 50, 61, 87, 192, 201, 216, 217, 218, 219, 220, 221 ], [ 36, 70, 81, 97, 208, 215, 222, 223, 224, 225, 226, 227 ], [ 46, 80, 91, 107, 214, 221, 228, 229, 230, 231, 232, 233 ], [ 56, 71, 90, 117, 209, 220, 234, 235, 236, 237, 238, 239 ], [ 66, 101, 120, 127, 227, 238, 240, 241, 242, 243, 244, 245 ], [ 76, 100, 111, 137, 226, 233, 246, 247, 248, 249, 250, 251 ], [ 86, 110, 121, 147, 232, 239, 252, 253, 254, 255, 256, 257 ], [ 96, 130, 141, 157, 244, 251, 258, 259, 260, 261, 262, 263 ], [ 106, 140, 151, 165, 250, 257, 264, 265, 266, 267, 268, 269 ], [ 116, 131, 150, 173, 245, 256, 270, 271, 272, 273, 274, 275 ], [ 1, 126, 161, 176, 187, 202, 263, 274, 276, 277, 278, 279 ], [ 13, 136, 160, 169, 186, 195, 262, 269, 280, 281, 282, 283 ], [ 25, 146, 168, 177, 194, 203, 268, 275, 284, 285, 286, 287 ], [ 183, 198, 205, 276, 288, 289, 290, 291, 292, 293, 294, 295 ], [ 182, 191, 211, 280, 296, 297, 298, 299, 300, 301, 302, 303 ], [ 190, 199, 217, 284, 304, 305, 306, 307, 308, 309, 310, 311 ], [ 180, 206, 213, 223, 292, 301, 312, 313, 314, 315, 316, 317 ], [ 188, 212, 219, 229, 300, 309, 318, 319, 320, 321, 322, 323 ], [ 196, 207, 218, 235, 293, 308, 324, 325, 326, 327, 328, 329 ], [ 204, 225, 236, 241, 317, 328, 330, 331, 332, 333, 334, 335 ], [ 210, 224, 231, 247, 316, 323, 336, 337, 338, 339, 340, 341 ], [ 216, 230, 237, 253, 322, 329, 342, 343, 344, 345, 346, 347 ], [ 222, 242, 249, 259, 334, 341, 348, 349, 350, 351, 352, 353 ], [ 228, 248, 255, 265, 340, 347, 354, 355, 356, 357, 358, 359 ], [ 234, 243, 254, 271, 335, 346, 360, 361, 362, 363, 364, 365 ], [ 240, 261, 272, 277, 353, 364, 366, 367, 368, 369, 370, 371 ], [ 246, 260, 267, 281, 352, 359, 372, 373, 374, 375, 376, 377 ], [ 252, 266, 273, 285, 358, 365, 378, 379, 380, 381, 382, 383 ], [ 181, 258, 278, 283, 294, 303, 370, 377, 384, 385, 386, 387 ], [ 189, 264, 282, 287, 302, 311, 376, 383, 388, 389, 390, 391 ], [ 197, 270, 279, 286, 295, 310, 371, 382, 392, 393, 394, 395 ], [ 290, 299, 313, 384, 396, 397, 398, 399, 400, 401, 402, 403 ], [ 298, 307, 319, 388, 404, 405, 406, 407, 408, 409, 410, 411 ], [ 291, 306, 325, 392, 412, 413, 414, 415, 416, 417, 418, 419 ], [ 288, 315, 326, 331, 401, 416, 420, 421, 422, 423, 424, 425 ], [ 296, 314, 321, 337, 400, 409, 426, 427, 428, 429, 430, 431 ], [ 304, 320, 327, 343, 408, 417, 432, 433, 434, 435, 436, 437 ], [ 312, 332, 339, 349, 424, 431, 438, 439, 440, 441, 442, 443 ], [ 318, 338, 345, 355, 430, 437, 444, 445, 446, 447, 448, 449 ], [ 324, 333, 344, 361, 425, 436, 450, 451, 452, 453, 454, 455 ], [ 330, 351, 362, 367, 443, 454, 456, 457, 458, 459, 460, 461 ], [ 336, 350, 357, 373, 442, 449, 462, 463, 464, 465, 466, 467 ], [ 342, 356, 363, 379, 448, 455, 468, 469, 470, 471, 472, 473 ], [ 348, 368, 375, 385, 460, 467, 474, 475, 476, 477, 478, 479 ], [ 354, 374, 381, 389, 466, 473, 480, 481, 482, 483, 484, 485 ], [ 360, 369, 380, 393, 461, 472, 486, 487, 488, 489, 490, 491 ], [ 289, 366, 387, 394, 403, 418, 479, 490, 492, 493, 494, 495 ], [ 297, 372, 386, 391, 402, 411, 478, 485, 496, 497, 498, 499 ], [ 305, 378, 390, 395, 410, 419, 484, 491, 500, 501, 502, 503 ], [ 399, 414, 421, 492, 504, 505, 506, 507, 508, 509, 510, 511 ], [ 398, 407, 427, 496, 512, 513, 514, 515, 516, 517, 518, 519 ], [ 406, 415, 433, 500, 520, 521, 522, 523, 524, 525, 526, 527 ], [ 396, 422, 429, 439, 508, 517, 528, 529, 530, 531, 532, 533 ], [ 404, 428, 435, 445, 516, 525, 534, 535, 536, 537, 538, 539 ], [ 412, 423, 434, 451, 509, 524, 540, 541, 542, 543, 544, 545 ], [ 420, 441, 452, 457, 533, 544, 546, 547, 548, 549, 550, 551 ], [ 426, 440, 447, 463, 532, 539, 552, 553, 554, 555, 556, 557 ], [ 432, 446, 453, 469, 538, 545, 558, 559, 560, 561, 562, 563 ], [ 438, 458, 465, 475, 550, 557, 564, 565, 566, 567, 568, 569 ], [ 444, 464, 471, 481, 556, 563, 570, 571, 572, 573, 574, 575 ], [ 450, 459, 470, 487, 551, 562, 576, 577, 578, 579, 580, 581 ], [ 456, 477, 488, 493, 569, 580, 582, 583, 584, 585, 586, 587 ], [ 462, 476, 483, 497, 568, 575, 588, 589, 590, 591, 592, 593 ], [ 468, 482, 489, 501, 574, 581, 594, 595, 596, 597, 598, 599 ], [ 397, 474, 494, 499, 510, 519, 586, 593, 600, 601, 602, 603 ], [ 405, 480, 498, 503, 518, 527, 592, 599, 604, 605, 606, 607 ], [ 413, 486, 495, 502, 511, 526, 587, 598, 608, 609, 610, 611 ], [ 6, 19, 39, 158, 506, 515, 529, 600, 612, 613, 614, 615 ], [ 18, 31, 49, 166, 514, 523, 535, 604, 616, 617, 618, 619 ], [ 7, 30, 59, 174, 507, 522, 541, 608, 620, 621, 622, 623 ], [ 2, 43, 62, 69, 504, 531, 542, 547, 613, 620, 624, 625 ], [ 14, 42, 53, 79, 512, 530, 537, 553, 612, 617, 626, 627 ], [ 26, 52, 63, 89, 520, 536, 543, 559, 616, 621, 628, 629 ], [ 38, 72, 83, 99, 528, 548, 555, 565, 624, 627, 630, 631 ], [ 48, 82, 93, 109, 534, 554, 561, 571, 626, 629, 632, 633 ], [ 58, 73, 92, 119, 540, 549, 560, 577, 625, 628, 634, 635 ], [ 68, 103, 122, 129, 546, 567, 578, 583, 631, 634, 636, 637 ], [ 78, 102, 113, 139, 552, 566, 573, 589, 630, 633, 638, 639 ], [ 88, 112, 123, 149, 558, 572, 579, 595, 632, 635, 640, 641 ], [ 98, 132, 143, 159, 564, 584, 591, 601, 636, 639, 642, 643 ], [ 108, 142, 153, 167, 570, 590, 597, 605, 638, 641, 644, 645 ], [ 118, 133, 152, 175, 576, 585, 596, 609, 637, 640, 646, 647 ], [ 3, 128, 163, 178, 505, 582, 603, 610, 615, 622, 643, 646 ], [ 15, 138, 162, 171, 513, 588, 602, 607, 614, 619, 642, 645 ], [ 27, 148, 170, 179, 521, 594, 606, 611, 618, 623, 644, 647 ] ] }, "distance": { "d": 3, "X": { "value": 3, "confidence": "upper_bound", "witness": [ 280, 282, 302 ] }, "Z": { "value": 3, "confidence": "upper_bound", "witness": [ 561, 571, 632 ] } }, "provenance": { "authors": [ "@mathysrennela" ], "construction": "contributed via qldpc submit", "origin": "submission", "date": "2026-11-09", "model": "Beam 1.0" } }