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[[516,178,20]] d ≤
n
516
k
178
d
20
kd²/n
137.984
w
12

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Distance

d_X 20 · witness weight 20 (claimed exact)
witness operator (support, 20 qubits)
[1, 29, 122, 140, 148, 150, 162, 221, 262, 277, 300, 324, 373, 380, 383, 426, 437, 442, 447, 489]
d_Z 20 · witness weight 20 (claimed exact)
witness operator (support, 20 qubits)
[6, 17, 32, 48, 98, 99, 107, 131, 190, 222, 265, 271, 281, 293, 334, 339, 414, 430, 445, 465]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors Okada, Koki and Kasai, Kenta
provenance literature baseline
construction Pair-partition CPM CSS (Okada-Kasai arXiv:2607.14091): J=4 column weight, L=12 row weight, prime lift P=43, girth 6. Exact distance d=20 certified by 14148 exhaustive lower-bound certificates and verified X/Z affine isomorphism.
model classical construction (no AI model)
reference arXiv:2607.14091
date 2026
notes Literature baseline (arXiv:2607.14091). Exact distance d=20: 14148 X-side lower-bound certificates exclude through weight 18; verified CPM-affine X/Z isomorphism transfers exclusion to Z side. X weight-20 witness and isomorphism data published at kasai.ict.eng.isct.ac.jp/pair_partition_cpm_css_codes_20260714.html. The paper's catalogue also includes [[492,170,20]] (eff=117.5), [[584,150,18]] girth-8 (eff=84.1), [[472,122,16]] girth-8 (eff=64.2), and [[970,392,16]] (eff=125.9) with exact distances, but their witness data is in tar.gz archives not embedded here.
family lifted product (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight > 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[516,178,20]] — pair-partition CPM CSS (Okada-Kasai arXiv:2607.14091)

Author: @mathysrennela Date: 2026-08-02 Status: Literature baseline — exact distance certified

Source

Exact-distance CPM-based pair-partition CSS code from the paper's catalogue, published on Kasai's supplementary page (updated 2026-08-01):

https://kasai.ict.eng.isct.ac.jp/pair_partition_cpm_css_codes_20260714.html

Parameters: J=4, L=12, P=43, girth 6, rate 0.345.

Distance certification (per Kasai)

  • X side: 14,148 independently verified branch certificates completely

    • exclude logical vectors through weight 18 (third-branch search).

  • X weight-20 witness: Published at

    • distance_records/qc_516_178_20/distance_X_witness_w20.json.

  • Z side: A verified CPM-affine X/Z coordinate isomorphism transfers

    • the complete exclusion from X to Z. Published at distance_records/qc_516_178_20/xz_affine_isomorphism.json.

  • Conclusion per paper: d = 20 exactly on both CSS sides.

Reconstruction

CPM exponent files downloaded from Kasai's website were expanded to binary H_X, H_Z using the CPM construction: H_X = (C(e_jl)), H_Z = (C(d_jl)) where C(s) is a P×P circulant permutation matrix with 1 at row i, column ((i - s) mod P). Row blocks follow the J×L CPM array convention.

Verifier confirmation:

  • CSS orthogonality H_X H_Z^T = 0: PASS
  • Rank H_X = 169, rank H_Z = 169, k = 516 - 169 - 169 = 178: PASS
  • X weight-20 witness in ker(H_Z), outside rowspace(H_X): PASS
  • Z weight-20 witness in ker(H_X), outside rowspace(H_Z): PASS
  • Refutation (8000 RIS trials): no lighter logical found: PASS

Other exact-distance PP codes in the paper's catalogue

The same paper reports exact distances (certified via exhaustive lower-bound search) for: [[492,170,20]] (eff 117.5), [[584,150,18]] girth-8 (eff 84.1), [[472,122,16]] girth-8 (eff 64.2), [[970,392,16]] (eff 125.9), and others. Their witness data is in tar.gz archives on Kasai's site; only [[516,178,20]] has a cleanly published witness JSON.

Parity checks

X-checks 172 · Z-checks 172
H_X (172 checks, sparse supports)
[12, 114, 135, 226, 227, 229, 248, 333, 367, 398, 401, 424] [24, 126, 147, 238, 239, 241, 260, 345, 379, 410, 413, 436] [36, 138, 159, 250, 251, 253, 272, 357, 391, 422, 425, 448] [48, 150, 171, 262, 263, 265, 284, 369, 403, 434, 437, 460] [60, 162, 183, 274, 275, 277, 296, 381, 415, 446, 449, 472] [72, 174, 195, 286, 287, 289, 308, 393, 427, 458, 461, 484] [84, 186, 207, 298, 299, 301, 320, 405, 439, 470, 473, 496] [96, 198, 219, 310, 311, 313, 332, 417, 451, 482, 485, 508] [4, 108, 210, 231, 322, 323, 325, 344, 429, 463, 494, 497] [16, 120, 222, 243, 334, 335, 337, 356, 441, 475, 506, 509] [2, 5, 28, 132, 234, 255, 346, 347, 349, 368, 453, 487] [14, 17, 40, 144, 246, 267, 358, 359, 361, 380, 465, 499] [26, 29, 52, 156, 258, 279, 370, 371, 373, 392, 477, 511] [7, 38, 41, 64, 168, 270, 291, 382, 383, 385, 404, 489] [19, 50, 53, 76, 180, 282, 303, 394, 395, 397, 416, 501] [31, 62, 65, 88, 192, 294, 315, 406, 407, 409, 428, 513] [9, 43, 74, 77, 100, 204, 306, 327, 418, 419, 421, 440] [21, 55, 86, 89, 112, 216, 318, 339, 430, 431, 433, 452] [33, 67, 98, 101, 124, 228, 330, 351, 442, 443, 445, 464] [45, 79, 110, 113, 136, 240, 342, 363, 454, 455, 457, 476] [57, 91, 122, 125, 148, 252, 354, 375, 466, 467, 469, 488] [69, 103, 134, 137, 160, 264, 366, 387, 478, 479, 481, 500] [81, 115, 146, 149, 172, 276, 378, 399, 490, 491, 493, 512] [8, 93, 127, 158, 161, 184, 288, 390, 411, 502, 503, 505] [1, 20, 105, 139, 170, 173, 196, 300, 402, 423, 514, 515] [10, 11, 13, 32, 117, 151, 182, 185, 208, 312, 414, 435] [22, 23, 25, 44, 129, 163, 194, 197, 220, 324, 426, 447] [34, 35, 37, 56, 141, 175, 206, 209, 232, 336, 438, 459] [46, 47, 49, 68, 153, 187, 218, 221, 244, 348, 450, 471] [58, 59, 61, 80, 165, 199, 230, 233, 256, 360, 462, 483] [70, 71, 73, 92, 177, 211, 242, 245, 268, 372, 474, 495] [82, 83, 85, 104, 189, 223, 254, 257, 280, 384, 486, 507] [3, 94, 95, 97, 116, 201, 235, 266, 269, 292, 396, 498] [15, 106, 107, 109, 128, 213, 247, 278, 281, 304, 408, 510] [6, 27, 118, 119, 121, 140, 225, 259, 290, 293, 316, 420] [18, 39, 130, 131, 133, 152, 237, 271, 302, 305, 328, 432] [30, 51, 142, 143, 145, 164, 249, 283, 314, 317, 340, 444] [42, 63, 154, 155, 157, 176, 261, 295, 326, 329, 352, 456] [54, 75, 166, 167, 169, 188, 273, 307, 338, 341, 364, 468] [66, 87, 178, 179, 181, 200, 285, 319, 350, 353, 376, 480] [78, 99, 190, 191, 193, 212, 297, 331, 362, 365, 388, 492] [90, 111, 202, 203, 205, 224, 309, 343, 374, 377, 400, 504] [0, 102, 123, 214, 215, 217, 236, 321, 355, 386, 389, 412] [2, 11, 92, 94, 184, 282, 421, 437, 441, 444, 451, 483] [14, 23, 104, 106, 196, 294, 433, 449, 453, 456, 463, 495] [26, 35, 116, 118, 208, 306, 445, 461, 465, 468, 475, 507] [3, 38, 47, 128, 130, 220, 318, 457, 473, 477, 480, 487] [15, 50, 59, 140, 142, 232, 330, 469, 485, 489, 492, 499] [27, 62, 71, 152, 154, 244, 342, 481, 497, 501, 504, 511] [0, 7, 39, 74, 83, 164, 166, 256, 354, 493, 509, 513] [5, 9, 12, 19, 51, 86, 95, 176, 178, 268, 366, 505] [1, 17, 21, 24, 31, 63, 98, 107, 188, 190, 280, 378] [13, 29, 33, 36, 43, 75, 110, 119, 200, 202, 292, 390] [25, 41, 45, 48, 55, 87, 122, 131, 212, 214, 304, 402] [37, 53, 57, 60, 67, 99, 134, 143, 224, 226, 316, 414] [49, 65, 69, 72, 79, 111, 146, 155, 236, 238, 328, 426] [61, 77, 81, 84, 91, 123, 158, 167, 248, 250, 340, 438] [73, 89, 93, 96, 103, 135, 170, 179, 260, 262, 352, 450] [85, 101, 105, 108, 115, 147, 182, 191, 272, 274, 364, 462] [97, 113, 117, 120, 127, 159, 194, 203, 284, 286, 376, 474] [109, 125, 129, 132, 139, 171, 206, 215, 296, 298, 388, 486] [121, 137, 141, 144, 151, 183, 218, 227, 308, 310, 400, 498] [133, 149, 153, 156, 163, 195, 230, 239, 320, 322, 412, 510] [6, 145, 161, 165, 168, 175, 207, 242, 251, 332, 334, 424] [18, 157, 173, 177, 180, 187, 219, 254, 263, 344, 346, 436] [30, 169, 185, 189, 192, 199, 231, 266, 275, 356, 358, 448] [42, 181, 197, 201, 204, 211, 243, 278, 287, 368, 370, 460] [54, 193, 209, 213, 216, 223, 255, 290, 299, 380, 382, 472] [66, 205, 221, 225, 228, 235, 267, 302, 311, 392, 394, 484] [78, 217, 233, 237, 240, 247, 279, 314, 323, 404, 406, 496] [90, 229, 245, 249, 252, 259, 291, 326, 335, 416, 418, 508] [4, 102, 241, 257, 261, 264, 271, 303, 338, 347, 428, 430] [16, 114, 253, 269, 273, 276, 283, 315, 350, 359, 440, 442] [28, 126, 265, 281, 285, 288, 295, 327, 362, 371, 452, 454] [40, 138, 277, 293, 297, 300, 307, 339, 374, 383, 464, 466] [52, 150, 289, 305, 309, 312, 319, 351, 386, 395, 476, 478] [64, 162, 301, 317, 321, 324, 331, 363, 398, 407, 488, 490] [76, 174, 313, 329, 333, 336, 343, 375, 410, 419, 500, 502] [88, 186, 325, 341, 345, 348, 355, 387, 422, 431, 512, 514] [8, 10, 100, 198, 337, 353, 357, 360, 367, 399, 434, 443] [20, 22, 112, 210, 349, 365, 369, 372, 379, 411, 446, 455] [32, 34, 124, 222, 361, 377, 381, 384, 391, 423, 458, 467] [44, 46, 136, 234, 373, 389, 393, 396, 403, 435, 470, 479] [56, 58, 148, 246, 385, 401, 405, 408, 415, 447, 482, 491] [68, 70, 160, 258, 397, 413, 417, 420, 427, 459, 494, 503] [80, 82, 172, 270, 409, 425, 429, 432, 439, 471, 506, 515] [7, 58, 159, 176, 222, 300, 313, 328, 341, 347, 434, 465] [19, 70, 171, 188, 234, 312, 325, 340, 353, 359, 446, 477] [31, 82, 183, 200, 246, 324, 337, 352, 365, 371, 458, 489] [43, 94, 195, 212, 258, 336, 349, 364, 377, 383, 470, 501] [55, 106, 207, 224, 270, 348, 361, 376, 389, 395, 482, 513] [9, 67, 118, 219, 236, 282, 360, 373, 388, 401, 407, 494] [21, 79, 130, 231, 248, 294, 372, 385, 400, 413, 419, 506] [2, 33, 91, 142, 243, 260, 306, 384, 397, 412, 425, 431] [14, 45, 103, 154, 255, 272, 318, 396, 409, 424, 437, 443] [26, 57, 115, 166, 267, 284, 330, 408, 421, 436, 449, 455] [38, 69, 127, 178, 279, 296, 342, 420, 433, 448, 461, 467] [50, 81, 139, 190, 291, 308, 354, 432, 445, 460, 473, 479] [62, 93, 151, 202, 303, 320, 366, 444, 457, 472, 485, 491] [74, 105, 163, 214, 315, 332, 378, 456, 469, 484, 497, 503] [86, 117, 175, 226, 327, 344, 390, 468, 481, 496, 509, 515] [5, 11, 98, 129, 187, 238, 339, 356, 402, 480, 493, 508] [4, 17, 23, 110, 141, 199, 250, 351, 368, 414, 492, 505] [1, 16, 29, 35, 122, 153, 211, 262, 363, 380, 426, 504] [0, 13, 28, 41, 47, 134, 165, 223, 274, 375, 392, 438] [12, 25, 40, 53, 59, 146, 177, 235, 286, 387, 404, 450] [24, 37, 52, 65, 71, 158, 189, 247, 298, 399, 416, 462] [36, 49, 64, 77, 83, 170, 201, 259, 310, 411, 428, 474] [48, 61, 76, 89, 95, 182, 213, 271, 322, 423, 440, 486] [60, 73, 88, 101, 107, 194, 225, 283, 334, 435, 452, 498] [72, 85, 100, 113, 119, 206, 237, 295, 346, 447, 464, 510] [6, 84, 97, 112, 125, 131, 218, 249, 307, 358, 459, 476] [18, 96, 109, 124, 137, 143, 230, 261, 319, 370, 471, 488] [30, 108, 121, 136, 149, 155, 242, 273, 331, 382, 483, 500] [42, 120, 133, 148, 161, 167, 254, 285, 343, 394, 495, 512] [8, 54, 132, 145, 160, 173, 179, 266, 297, 355, 406, 507] [3, 20, 66, 144, 157, 172, 185, 191, 278, 309, 367, 418] [15, 32, 78, 156, 169, 184, 197, 203, 290, 321, 379, 430] [27, 44, 90, 168, 181, 196, 209, 215, 302, 333, 391, 442] [39, 56, 102, 180, 193, 208, 221, 227, 314, 345, 403, 454] [51, 68, 114, 192, 205, 220, 233, 239, 326, 357, 415, 466] [63, 80, 126, 204, 217, 232, 245, 251, 338, 369, 427, 478] [75, 92, 138, 216, 229, 244, 257, 263, 350, 381, 439, 490] [87, 104, 150, 228, 241, 256, 269, 275, 362, 393, 451, 502] [99, 116, 162, 240, 253, 268, 281, 287, 374, 405, 463, 514] [10, 111, 128, 174, 252, 265, 280, 293, 299, 386, 417, 475] [22, 123, 140, 186, 264, 277, 292, 305, 311, 398, 429, 487] [34, 135, 152, 198, 276, 289, 304, 317, 323, 410, 441, 499] [46, 147, 164, 210, 288, 301, 316, 329, 335, 422, 453, 511] [12, 30, 147, 170, 263, 353, 368, 394, 412, 427, 469, 513] [9, 24, 42, 159, 182, 275, 365, 380, 406, 424, 439, 481] [21, 36, 54, 171, 194, 287, 377, 392, 418, 436, 451, 493] [33, 48, 66, 183, 206, 299, 389, 404, 430, 448, 463, 505] [1, 45, 60, 78, 195, 218, 311, 401, 416, 442, 460, 475] [13, 57, 72, 90, 207, 230, 323, 413, 428, 454, 472, 487] [25, 69, 84, 102, 219, 242, 335, 425, 440, 466, 484, 499] [37, 81, 96, 114, 231, 254, 347, 437, 452, 478, 496, 511] [7, 49, 93, 108, 126, 243, 266, 359, 449, 464, 490, 508] [4, 19, 61, 105, 120, 138, 255, 278, 371, 461, 476, 502] [16, 31, 73, 117, 132, 150, 267, 290, 383, 473, 488, 514] [10, 28, 43, 85, 129, 144, 162, 279, 302, 395, 485, 500] [22, 40, 55, 97, 141, 156, 174, 291, 314, 407, 497, 512] [8, 34, 52, 67, 109, 153, 168, 186, 303, 326, 419, 509] [5, 20, 46, 64, 79, 121, 165, 180, 198, 315, 338, 431] [17, 32, 58, 76, 91, 133, 177, 192, 210, 327, 350, 443] [29, 44, 70, 88, 103, 145, 189, 204, 222, 339, 362, 455] [41, 56, 82, 100, 115, 157, 201, 216, 234, 351, 374, 467] [53, 68, 94, 112, 127, 169, 213, 228, 246, 363, 386, 479] [65, 80, 106, 124, 139, 181, 225, 240, 258, 375, 398, 491] [77, 92, 118, 136, 151, 193, 237, 252, 270, 387, 410, 503] [89, 104, 130, 148, 163, 205, 249, 264, 282, 399, 422, 515] [11, 101, 116, 142, 160, 175, 217, 261, 276, 294, 411, 434] [23, 113, 128, 154, 172, 187, 229, 273, 288, 306, 423, 446] [35, 125, 140, 166, 184, 199, 241, 285, 300, 318, 435, 458] [47, 137, 152, 178, 196, 211, 253, 297, 312, 330, 447, 470] [59, 149, 164, 190, 208, 223, 265, 309, 324, 342, 459, 482] [71, 161, 176, 202, 220, 235, 277, 321, 336, 354, 471, 494] [83, 173, 188, 214, 232, 247, 289, 333, 348, 366, 483, 506] [2, 95, 185, 200, 226, 244, 259, 301, 345, 360, 378, 495] [14, 107, 197, 212, 238, 256, 271, 313, 357, 372, 390, 507] [3, 26, 119, 209, 224, 250, 268, 283, 325, 369, 384, 402] [15, 38, 131, 221, 236, 262, 280, 295, 337, 381, 396, 414] [27, 50, 143, 233, 248, 274, 292, 307, 349, 393, 408, 426] [39, 62, 155, 245, 260, 286, 304, 319, 361, 405, 420, 438] [51, 74, 167, 257, 272, 298, 316, 331, 373, 417, 432, 450] [63, 86, 179, 269, 284, 310, 328, 343, 385, 429, 444, 462] [75, 98, 191, 281, 296, 322, 340, 355, 397, 441, 456, 474] [87, 110, 203, 293, 308, 334, 352, 367, 409, 453, 468, 486] [99, 122, 215, 305, 320, 346, 364, 379, 421, 465, 480, 498] [111, 134, 227, 317, 332, 358, 376, 391, 433, 477, 492, 510] [6, 123, 146, 239, 329, 344, 370, 388, 403, 445, 489, 504] [0, 18, 135, 158, 251, 341, 356, 382, 400, 415, 457, 501]
H_Z (172 checks, sparse supports)
[108, 115, 126, 146, 155, 157, 177, 245, 327, 344, 418, 436] [120, 127, 138, 158, 167, 169, 189, 257, 339, 356, 430, 448] [132, 139, 150, 170, 179, 181, 201, 269, 351, 368, 442, 460] [144, 151, 162, 182, 191, 193, 213, 281, 363, 380, 454, 472] [156, 163, 174, 194, 203, 205, 225, 293, 375, 392, 466, 484] [168, 175, 186, 206, 215, 217, 237, 305, 387, 404, 478, 496] [180, 187, 198, 218, 227, 229, 249, 317, 399, 416, 490, 508] [4, 192, 199, 210, 230, 239, 241, 261, 329, 411, 428, 502] [16, 204, 211, 222, 242, 251, 253, 273, 341, 423, 440, 514] [10, 28, 216, 223, 234, 254, 263, 265, 285, 353, 435, 452] [22, 40, 228, 235, 246, 266, 275, 277, 297, 365, 447, 464] [34, 52, 240, 247, 258, 278, 287, 289, 309, 377, 459, 476] [46, 64, 252, 259, 270, 290, 299, 301, 321, 389, 471, 488] [58, 76, 264, 271, 282, 302, 311, 313, 333, 401, 483, 500] [70, 88, 276, 283, 294, 314, 323, 325, 345, 413, 495, 512] [8, 82, 100, 288, 295, 306, 326, 335, 337, 357, 425, 507] [3, 20, 94, 112, 300, 307, 318, 338, 347, 349, 369, 437] [15, 32, 106, 124, 312, 319, 330, 350, 359, 361, 381, 449] [27, 44, 118, 136, 324, 331, 342, 362, 371, 373, 393, 461] [39, 56, 130, 148, 336, 343, 354, 374, 383, 385, 405, 473] [51, 68, 142, 160, 348, 355, 366, 386, 395, 397, 417, 485] [63, 80, 154, 172, 360, 367, 378, 398, 407, 409, 429, 497] [75, 92, 166, 184, 372, 379, 390, 410, 419, 421, 441, 509] [5, 87, 104, 178, 196, 384, 391, 402, 422, 431, 433, 453] [17, 99, 116, 190, 208, 396, 403, 414, 434, 443, 445, 465] [29, 111, 128, 202, 220, 408, 415, 426, 446, 455, 457, 477] [41, 123, 140, 214, 232, 420, 427, 438, 458, 467, 469, 489] [53, 135, 152, 226, 244, 432, 439, 450, 470, 479, 481, 501] [65, 147, 164, 238, 256, 444, 451, 462, 482, 491, 493, 513] [9, 77, 159, 176, 250, 268, 456, 463, 474, 494, 503, 505] [1, 21, 89, 171, 188, 262, 280, 468, 475, 486, 506, 515] [2, 11, 13, 33, 101, 183, 200, 274, 292, 480, 487, 498] [14, 23, 25, 45, 113, 195, 212, 286, 304, 492, 499, 510] [6, 26, 35, 37, 57, 125, 207, 224, 298, 316, 504, 511] [0, 7, 18, 38, 47, 49, 69, 137, 219, 236, 310, 328] [12, 19, 30, 50, 59, 61, 81, 149, 231, 248, 322, 340] [24, 31, 42, 62, 71, 73, 93, 161, 243, 260, 334, 352] [36, 43, 54, 74, 83, 85, 105, 173, 255, 272, 346, 364] [48, 55, 66, 86, 95, 97, 117, 185, 267, 284, 358, 376] [60, 67, 78, 98, 107, 109, 129, 197, 279, 296, 370, 388] [72, 79, 90, 110, 119, 121, 141, 209, 291, 308, 382, 400] [84, 91, 102, 122, 131, 133, 153, 221, 303, 320, 394, 412] [96, 103, 114, 134, 143, 145, 165, 233, 315, 332, 406, 424] [42, 52, 189, 204, 231, 254, 329, 344, 419, 478, 481, 511] [7, 54, 64, 201, 216, 243, 266, 341, 356, 431, 490, 493] [19, 66, 76, 213, 228, 255, 278, 353, 368, 443, 502, 505] [1, 31, 78, 88, 225, 240, 267, 290, 365, 380, 455, 514] [10, 13, 43, 90, 100, 237, 252, 279, 302, 377, 392, 467] [22, 25, 55, 102, 112, 249, 264, 291, 314, 389, 404, 479] [34, 37, 67, 114, 124, 261, 276, 303, 326, 401, 416, 491] [46, 49, 79, 126, 136, 273, 288, 315, 338, 413, 428, 503] [58, 61, 91, 138, 148, 285, 300, 327, 350, 425, 440, 515] [11, 70, 73, 103, 150, 160, 297, 312, 339, 362, 437, 452] [23, 82, 85, 115, 162, 172, 309, 324, 351, 374, 449, 464] [35, 94, 97, 127, 174, 184, 321, 336, 363, 386, 461, 476] [47, 106, 109, 139, 186, 196, 333, 348, 375, 398, 473, 488] [59, 118, 121, 151, 198, 208, 345, 360, 387, 410, 485, 500] [71, 130, 133, 163, 210, 220, 357, 372, 399, 422, 497, 512] [8, 83, 142, 145, 175, 222, 232, 369, 384, 411, 434, 509] [5, 20, 95, 154, 157, 187, 234, 244, 381, 396, 423, 446] [17, 32, 107, 166, 169, 199, 246, 256, 393, 408, 435, 458] [29, 44, 119, 178, 181, 211, 258, 268, 405, 420, 447, 470] [41, 56, 131, 190, 193, 223, 270, 280, 417, 432, 459, 482] [53, 68, 143, 202, 205, 235, 282, 292, 429, 444, 471, 494] [65, 80, 155, 214, 217, 247, 294, 304, 441, 456, 483, 506] [2, 77, 92, 167, 226, 229, 259, 306, 316, 453, 468, 495] [14, 89, 104, 179, 238, 241, 271, 318, 328, 465, 480, 507] [3, 26, 101, 116, 191, 250, 253, 283, 330, 340, 477, 492] [15, 38, 113, 128, 203, 262, 265, 295, 342, 352, 489, 504] [0, 27, 50, 125, 140, 215, 274, 277, 307, 354, 364, 501] [12, 39, 62, 137, 152, 227, 286, 289, 319, 366, 376, 513] [9, 24, 51, 74, 149, 164, 239, 298, 301, 331, 378, 388] [21, 36, 63, 86, 161, 176, 251, 310, 313, 343, 390, 400] [33, 48, 75, 98, 173, 188, 263, 322, 325, 355, 402, 412] [45, 60, 87, 110, 185, 200, 275, 334, 337, 367, 414, 424] [57, 72, 99, 122, 197, 212, 287, 346, 349, 379, 426, 436] [69, 84, 111, 134, 209, 224, 299, 358, 361, 391, 438, 448] [81, 96, 123, 146, 221, 236, 311, 370, 373, 403, 450, 460] [93, 108, 135, 158, 233, 248, 323, 382, 385, 415, 462, 472] [105, 120, 147, 170, 245, 260, 335, 394, 397, 427, 474, 484] [117, 132, 159, 182, 257, 272, 347, 406, 409, 439, 486, 496] [129, 144, 171, 194, 269, 284, 359, 418, 421, 451, 498, 508] [4, 141, 156, 183, 206, 281, 296, 371, 430, 433, 463, 510] [6, 16, 153, 168, 195, 218, 293, 308, 383, 442, 445, 475] [18, 28, 165, 180, 207, 230, 305, 320, 395, 454, 457, 487] [30, 40, 177, 192, 219, 242, 317, 332, 407, 466, 469, 499] [55, 106, 207, 240, 304, 323, 332, 342, 405, 433, 482, 497] [67, 118, 219, 252, 316, 335, 344, 354, 417, 445, 494, 509] [5, 79, 130, 231, 264, 328, 347, 356, 366, 429, 457, 506] [2, 17, 91, 142, 243, 276, 340, 359, 368, 378, 441, 469] [14, 29, 103, 154, 255, 288, 352, 371, 380, 390, 453, 481] [26, 41, 115, 166, 267, 300, 364, 383, 392, 402, 465, 493] [38, 53, 127, 178, 279, 312, 376, 395, 404, 414, 477, 505] [1, 50, 65, 139, 190, 291, 324, 388, 407, 416, 426, 489] [13, 62, 77, 151, 202, 303, 336, 400, 419, 428, 438, 501] [25, 74, 89, 163, 214, 315, 348, 412, 431, 440, 450, 513] [9, 37, 86, 101, 175, 226, 327, 360, 424, 443, 452, 462] [21, 49, 98, 113, 187, 238, 339, 372, 436, 455, 464, 474] [33, 61, 110, 125, 199, 250, 351, 384, 448, 467, 476, 486] [45, 73, 122, 137, 211, 262, 363, 396, 460, 479, 488, 498] [57, 85, 134, 149, 223, 274, 375, 408, 472, 491, 500, 510] [6, 69, 97, 146, 161, 235, 286, 387, 420, 484, 503, 512] [8, 18, 81, 109, 158, 173, 247, 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raw submission JSON