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[[630,126,20]] d ≤
n
630
k
126
d
20
kd²/n
80.0
w
9

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Distance

d_X 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[281, 289, 299, 332, 335, 348, 383, 393, 414, 430, 432, 434, 438, 454, 458, 461, 463, 471, 487, 489]
d_Z 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[5, 10, 31, 35, 41, 50, 82, 87, 93, 254, 290, 291, 315, 325, 333, 347, 353, 358, 359, 364]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors Bhardwaj, Aditya and Ma, Muzhou and Meister, Nadine and King, Robbie and Bluvstein, Dolev and Preskill, John and Cain, Madelyn and Xu, Qian and Huang, Hsin-Yuan
provenance literature baseline
construction Mitten code (arXiv:2607.28795, Definition 4): lifted product LP(A,B) over F2[G], G = GAP SmallGroup(126,1) = C7 : C18, base matrices A = [a0|a1], B = [b0|b1] from Table XIII, entries as 0-based indices into Elements(G): a0=[50, 117, 123], a1=[0, 62, 104], b0=[4, 39, 82], b1=[0, 67, 87]. Block form H_X = [[L(a0),0,L(a1),0,R(b0*)],[0,L(a0),0,L(a1),R(b1*)]], H_Z = [[R(b0),R(b1),0,0,L(a0*)],[0,0,R(b0),R(b1),L(a1*)]] with L(g)b(h)=b(gh), R(g)b(h)=b(h g-1) and * the g->g-1 involution (paper Definition 8). Check matrices taken from the authors' repository (github.com/a7b/yarn @ 82fb695a1e40, processor_codes/mitten). Independent reconstruction from Table XIII + GAP Elements ordering reproduces the published H_X/H_Z bit-for-bit.
model classical construction (no AI model)
reference arXiv:2607.28795
date 2026
notes Literature baseline. Paper claims d = 20 (upper bound estimate from >50M sQetch + >50k BP+OSD iterations). Seeded per issue #377.
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

[[630,126,≤20]] — literature baseline (mitten code, Bhardwaj–Ma et al.)

Why this entry exists

Baseline seeding per issue #377: arXiv:2607.28795 introduces mitten codes, a family of non-abelian lifted product codes with guaranteed 20% encoding rate and check weight 9. This is the sixth of the paper's eight processor codes (Table I). None of the family was on the board.

Reproduction (the actual work)

Mitten code = LP(A,B) per the paper's Definition 4: G a non-abelian group, A = [a0|a1], B = [b0|b1] over F2[G] with a1, b1 containing the identity; H_X = [[L(a0),0,L(a1),0,R(b0*)],[0,L(a0),0,L(a1),R(b1*)]], H_Z = [[R(b0),R(b1),0,0,L(a0*)],[0,0,R(b0),R(b1),L(a1*)]], where L(g)b(h)=b(gh), R(g)b(h)=b(hg⁻¹) (Definition 8) and * inverts each group element. n = 5|G|, k = |G|.

For this code G = SmallGroup(126,1) = C7⋊C18 and Table XIII lists a0={50,117,123}, a1={0,62,104}, b0={4,39,82}, b1={0,67,87} as 0-based indices into Elements(G). Rebuilding from these generators under the GAP Elements(SmallGroup(126,1)) ordering (libgap/GAP 4.x) reproduces the authors' published check matrices bit-for-bit (github.com/a7b/yarn @ 82fb695, processor_codes/mitten/[[630,126,20]]/), which are the matrices used here.

Cross-checks: CSS holds, k = 126, max check weight 9, and the repo's shipped canonical logical basis Lx/Lz commutes with the checks with row weights exactly Table I's wt(Lx)/wt(Lz) = 28/44.

Evidence trail

Paper claims d <= 20 (estimate tier: >50M sQetch + >50k BP+OSD iterations; the paper does not certify this code's distance). Local witnesses land at exactly weight 20 both sides (kit RIS via make_submission, 12000 trials/side); independent BP+OSD decoder pass (80k trials): nothing lighter. validate_candidate: passed, refutation found nothing lighter. Board entry carries the witness-backed d <= 20.

Dead ends / tips

  • pdftotext garbles Table XIII's ‖ separators; the numbers themselves are

    • clean (page 92 of the v1 PDF).

  • The yarn repo also ships the five surgery gadgets per code

    • (gadgets/*.npz) — not used here, but useful for future circuit-level verification (the issue's Level-II discussion).

Parity checks

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