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[[968,8,23]] d ≤
n
968
k
8
d
23
kd²/n
4.372
w
6
X/Z
1.17
g
0.0683
r
4.0
layers
1
swaps
6920

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Distance

X/Z asymmetry 1.17 · d_X ≤ 27, d_Z ≤ 23 · w_X = 6, w_Z = 6 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 27 · witness weight 27 (claimed upper_bound)
witness operator (support, 27 qubits)
[48, 93, 94, 198, 242, 243, 286, 287, 308, 309, 397, 442, 463, 488, 620, 622, 640, 642, 660, 664, 682, 706, 748, 771, 815, 837, 925]
d_Z 23 · witness weight 23 (claimed upper_bound)
witness operator (support, 23 qubits)
[247, 249, 269, 275, 284, 289, 297, 326, 328, 348, 368, 726, 733, 734, 757, 758, 759, 760, 771, 779, 804, 805, 850]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 6 · H_Z 6 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 2–6 (mean 5.5) · H_Z 2–6 (mean 5.5)
qubit degrees H_X 1–3 (mean 2.727) · H_Z 1–3 (mean 2.727)
trapping sets H_X (1,1)×88 (2,0)×20 (3,0)×60 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 88 (1,2): 88 (1,3): 792 (2,0): 20 (2,1): 123 (2,2): 377 (2,3): 463 (2,4): 5277 (3,0): 60 (3,1): 256 (3,2): 945 (3,3): 3492 (3,4): 4438 (3,5): 46297 (3,6): 428 (3,7): 6617
trapping sets H_Z (1,1)×88 (2,0)×20 (3,0)×58 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 88 (1,2): 88 (1,3): 792 (2,0): 20 (2,1): 125 (2,2): 377 (2,3): 461 (2,4): 5277 (3,0): 58 (3,1): 264 (3,2): 939 (3,3): 3498 (3,4): 4426 (3,5): 46298 (3,6): 425 (3,7): 6617
witness diameter X 30.8058 · Z 28.0179 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 4
X checkZ checkqubit site (968)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release
routing cost 6920 nearest-neighbor SWAPs per round in total, at most 8 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction Open-boundary planar bivariate-bicycle code (arXiv:2504.08887) with f = x + x2 + y2 and g = 1 + x2 y + x2 y2 on a 22 x 22 grid (research/local2d/planar.py build_open_directional(22, 22)).
model MiMo-V2.6-Flash (claimed, not verified)
date 2026-09-27
notes Checked against the board: no same-parameter or WL-equivalent entry; see notes/968-8-23.md.
family bivariate bicycle (a tag, not a ranking)
locality 2D-local single (computed from the layout)
weight class weight ≤ 6 (computed)

How this code was found

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

[[968,8,23]] open-boundary planar bivariate-bicycle code, L = 22

Direction & hypothesis

Third rung of the planar extension (siblings [[800,8,21]] and [[882,8,22]]): the weight-6 x local-2d-single flagship ladder held d = L + 1 through L = 17..21, so L = 22 (raw n = 968, still inside the n <= 1000 admissibility window for w <= 8 with d <= 40) was expected to witness d = 23. This rung took the k = 8 frontier of the cell to its highest d at any n.

What was searched

Targeted build, no sweep: research/local2d/planar.py build_open_directional(22, 22) — n = 968, k = 8, max check weight 6, single layer at (i + j, j - i + c), interaction radius exactly 4. Confirmation ladder on the bit-packed RIS accelerator (research/kit/surrogate.py distance_rand, fresh seed per rung):

  • 300,000 trials (seed 1154) -> lightest logical 23
  • 1,500,000 trials (seed 1155) -> lightest logical 23

Evidence trail

Claim: witness-backed upper bound d <= 23 (upper_bound), not exact. The document carries a weight-23 Z-side witness and a weight-27 X-side witness (d = min = 23); 1.5M fresh-seed trials found nothing lighter, and the submission gate's refutation found no lighter logical in 8,000 RIS trials (seed 1330972760). Dedup against the board: no exact duplicate, no WL-equivalent entry. Verifier-computed classes: local-2d-single / weight-6; non-dominated in weight-6, weight-8 and weight-9plus of that cell.

Dead ends

  • Tooling: the portable NumPy witness search in research/kit/submit.py is

    • unaffordable near n = 1000 (measured ~121 s per 5,000 trials at n = 800); the accelerator-backed witness path replaced it for all three rungs.

  • L = 23 (raw n = 1046) would leave the n <= 1000 admissibility window, so

    • the ladder stops here for the unrestricted-weight window; deeper raw rungs were not attempted.

Tools

MiMo-V2.6-Flash (matches provenance.model) under the Zed agent harness, on a 10-core MacBook. research/kit ladder utilities and the gf2_fast bit-packed accelerator; no decoders. Roughly 10 minutes of compute for the ladder plus gate.

Reproduction

import sys; sys.path[:0] = ["research/kit", "research/local2d"] from planar import build_open_directional HX, HZ = build_open_directional(22, 22) # n = 968, k = 8, w = 6

Then research/kit/surrogate.py `distance_rand(prepared=prepare_distance_search(HX, HZ), trials=300_000, seed=1154, backend="auto", threads=4)` returns 23; seeds 1154/1155 are the ladder above. The staged witnesses live in the submission JSON itself.

Parity checks

X-checks 480 (max weight 6) · Z-checks 480 (max weight 6)
H_X (480 checks, sparse supports)
[0, 485, 486] [1, 486, 487] [2, 487, 488] [3, 488, 489] [4, 489, 490] [5, 490, 491] [6, 491, 492] [7, 492, 493] [8, 493, 494] [9, 494, 495] [10, 495, 496] [11, 496, 497] [12, 497, 498] [13, 498, 499] [14, 499, 500] [15, 500, 501] [16, 501, 502] [17, 502, 503] [18, 503, 504] [19, 504, 505] [0, 22, 507, 508] [1, 23, 508, 509] [2, 24, 509, 510] [3, 25, 510, 511] [4, 26, 511, 512] [5, 27, 512, 513] [6, 28, 513, 514] [7, 29, 514, 515] [8, 30, 515, 516] [9, 31, 516, 517] [10, 32, 517, 518] [11, 33, 518, 519] [12, 34, 519, 520] [13, 35, 520, 521] [14, 36, 521, 522] [15, 37, 522, 523] [16, 38, 523, 524] [17, 39, 524, 525] [18, 40, 525, 526] [19, 41, 526, 527] [2, 22, 44, 484, 529, 530] [3, 23, 45, 485, 530, 531] [4, 24, 46, 486, 531, 532] [5, 25, 47, 487, 532, 533] [6, 26, 48, 488, 533, 534] [7, 27, 49, 489, 534, 535] [8, 28, 50, 490, 535, 536] [9, 29, 51, 491, 536, 537] [10, 30, 52, 492, 537, 538] [11, 31, 53, 493, 538, 539] [12, 32, 54, 494, 539, 540] [13, 33, 55, 495, 540, 541] [14, 34, 56, 496, 541, 542] [15, 35, 57, 497, 542, 543] [16, 36, 58, 498, 543, 544] [17, 37, 59, 499, 544, 545] [18, 38, 60, 500, 545, 546] [19, 39, 61, 501, 546, 547] [20, 40, 62, 502, 547, 548] [21, 41, 63, 503, 548, 549] [24, 44, 66, 506, 551, 552] [25, 45, 67, 507, 552, 553] [26, 46, 68, 508, 553, 554] [27, 47, 69, 509, 554, 555] [28, 48, 70, 510, 555, 556] [29, 49, 71, 511, 556, 557] [30, 50, 72, 512, 557, 558] [31, 51, 73, 513, 558, 559] [32, 52, 74, 514, 559, 560] [33, 53, 75, 515, 560, 561] [34, 54, 76, 516, 561, 562] [35, 55, 77, 517, 562, 563] [36, 56, 78, 518, 563, 564] [37, 57, 79, 519, 564, 565] [38, 58, 80, 520, 565, 566] [39, 59, 81, 521, 566, 567] [40, 60, 82, 522, 567, 568] [41, 61, 83, 523, 568, 569] [42, 62, 84, 524, 569, 570] [43, 63, 85, 525, 570, 571] [46, 66, 88, 528, 573, 574] [47, 67, 89, 529, 574, 575] [48, 68, 90, 530, 575, 576] [49, 69, 91, 531, 576, 577] [50, 70, 92, 532, 577, 578] [51, 71, 93, 533, 578, 579] [52, 72, 94, 534, 579, 580] [53, 73, 95, 535, 580, 581] [54, 74, 96, 536, 581, 582] [55, 75, 97, 537, 582, 583] [56, 76, 98, 538, 583, 584] [57, 77, 99, 539, 584, 585] [58, 78, 100, 540, 585, 586] [59, 79, 101, 541, 586, 587] [60, 80, 102, 542, 587, 588] [61, 81, 103, 543, 588, 589] [62, 82, 104, 544, 589, 590] [63, 83, 105, 545, 590, 591] [64, 84, 106, 546, 591, 592] [65, 85, 107, 547, 592, 593] [68, 88, 110, 550, 595, 596] [69, 89, 111, 551, 596, 597] [70, 90, 112, 552, 597, 598] [71, 91, 113, 553, 598, 599] [72, 92, 114, 554, 599, 600] [73, 93, 115, 555, 600, 601] [74, 94, 116, 556, 601, 602] [75, 95, 117, 557, 602, 603] [76, 96, 118, 558, 603, 604] [77, 97, 119, 559, 604, 605] [78, 98, 120, 560, 605, 606] [79, 99, 121, 561, 606, 607] [80, 100, 122, 562, 607, 608] [81, 101, 123, 563, 608, 609] [82, 102, 124, 564, 609, 610] [83, 103, 125, 565, 610, 611] [84, 104, 126, 566, 611, 612] [85, 105, 127, 567, 612, 613] [86, 106, 128, 568, 613, 614] [87, 107, 129, 569, 614, 615] [90, 110, 132, 572, 617, 618] [91, 111, 133, 573, 618, 619] [92, 112, 134, 574, 619, 620] [93, 113, 135, 575, 620, 621] [94, 114, 136, 576, 621, 622] [95, 115, 137, 577, 622, 623] [96, 116, 138, 578, 623, 624] [97, 117, 139, 579, 624, 625] [98, 118, 140, 580, 625, 626] [99, 119, 141, 581, 626, 627] [100, 120, 142, 582, 627, 628] [101, 121, 143, 583, 628, 629] [102, 122, 144, 584, 629, 630] [103, 123, 145, 585, 630, 631] [104, 124, 146, 586, 631, 632] [105, 125, 147, 587, 632, 633] [106, 126, 148, 588, 633, 634] [107, 127, 149, 589, 634, 635] [108, 128, 150, 590, 635, 636] [109, 129, 151, 591, 636, 637] [112, 132, 154, 594, 639, 640] [113, 133, 155, 595, 640, 641] [114, 134, 156, 596, 641, 642] [115, 135, 157, 597, 642, 643] [116, 136, 158, 598, 643, 644] [117, 137, 159, 599, 644, 645] [118, 138, 160, 600, 645, 646] [119, 139, 161, 601, 646, 647] [120, 140, 162, 602, 647, 648] [121, 141, 163, 603, 648, 649] [122, 142, 164, 604, 649, 650] [123, 143, 165, 605, 650, 651] [124, 144, 166, 606, 651, 652] [125, 145, 167, 607, 652, 653] [126, 146, 168, 608, 653, 654] [127, 147, 169, 609, 654, 655] [128, 148, 170, 610, 655, 656] [129, 149, 171, 611, 656, 657] [130, 150, 172, 612, 657, 658] [131, 151, 173, 613, 658, 659] [134, 154, 176, 616, 661, 662] [135, 155, 177, 617, 662, 663] [136, 156, 178, 618, 663, 664] [137, 157, 179, 619, 664, 665] [138, 158, 180, 620, 665, 666] [139, 159, 181, 621, 666, 667] [140, 160, 182, 622, 667, 668] [141, 161, 183, 623, 668, 669] [142, 162, 184, 624, 669, 670] [143, 163, 185, 625, 670, 671] [144, 164, 186, 626, 671, 672] [145, 165, 187, 627, 672, 673] [146, 166, 188, 628, 673, 674] [147, 167, 189, 629, 674, 675] [148, 168, 190, 630, 675, 676] [149, 169, 191, 631, 676, 677] [150, 170, 192, 632, 677, 678] [151, 171, 193, 633, 678, 679] [152, 172, 194, 634, 679, 680] [153, 173, 195, 635, 680, 681] [156, 176, 198, 638, 683, 684] [157, 177, 199, 639, 684, 685] [158, 178, 200, 640, 685, 686] [159, 179, 201, 641, 686, 687] [160, 180, 202, 642, 687, 688] [161, 181, 203, 643, 688, 689] [162, 182, 204, 644, 689, 690] [163, 183, 205, 645, 690, 691] [164, 184, 206, 646, 691, 692] [165, 185, 207, 647, 692, 693] [166, 186, 208, 648, 693, 694] [167, 187, 209, 649, 694, 695] [168, 188, 210, 650, 695, 696] [169, 189, 211, 651, 696, 697] [170, 190, 212, 652, 697, 698] [171, 191, 213, 653, 698, 699] [172, 192, 214, 654, 699, 700] [173, 193, 215, 655, 700, 701] [174, 194, 216, 656, 701, 702] [175, 195, 217, 657, 702, 703] [178, 198, 220, 660, 705, 706] [179, 199, 221, 661, 706, 707] [180, 200, 222, 662, 707, 708] [181, 201, 223, 663, 708, 709] [182, 202, 224, 664, 709, 710] [183, 203, 225, 665, 710, 711] [184, 204, 226, 666, 711, 712] [185, 205, 227, 667, 712, 713] [186, 206, 228, 668, 713, 714] [187, 207, 229, 669, 714, 715] [188, 208, 230, 670, 715, 716] [189, 209, 231, 671, 716, 717] [190, 210, 232, 672, 717, 718] [191, 211, 233, 673, 718, 719] [192, 212, 234, 674, 719, 720] [193, 213, 235, 675, 720, 721] [194, 214, 236, 676, 721, 722] [195, 215, 237, 677, 722, 723] [196, 216, 238, 678, 723, 724] [197, 217, 239, 679, 724, 725] [200, 220, 242, 682, 727, 728] [201, 221, 243, 683, 728, 729] [202, 222, 244, 684, 729, 730] [203, 223, 245, 685, 730, 731] [204, 224, 246, 686, 731, 732] [205, 225, 247, 687, 732, 733] [206, 226, 248, 688, 733, 734] [207, 227, 249, 689, 734, 735] [208, 228, 250, 690, 735, 736] [209, 229, 251, 691, 736, 737] [210, 230, 252, 692, 737, 738] [211, 231, 253, 693, 738, 739] [212, 232, 254, 694, 739, 740] [213, 233, 255, 695, 740, 741] [214, 234, 256, 696, 741, 742] [215, 235, 257, 697, 742, 743] [216, 236, 258, 698, 743, 744] [217, 237, 259, 699, 744, 745] [218, 238, 260, 700, 745, 746] [219, 239, 261, 701, 746, 747] [222, 242, 264, 704, 749, 750] [223, 243, 265, 705, 750, 751] [224, 244, 266, 706, 751, 752] [225, 245, 267, 707, 752, 753] [226, 246, 268, 708, 753, 754] [227, 247, 269, 709, 754, 755] [228, 248, 270, 710, 755, 756] [229, 249, 271, 711, 756, 757] [230, 250, 272, 712, 757, 758] [231, 251, 273, 713, 758, 759] [232, 252, 274, 714, 759, 760] [233, 253, 275, 715, 760, 761] [234, 254, 276, 716, 761, 762] [235, 255, 277, 717, 762, 763] [236, 256, 278, 718, 763, 764] [237, 257, 279, 719, 764, 765] [238, 258, 280, 720, 765, 766] [239, 259, 281, 721, 766, 767] [240, 260, 282, 722, 767, 768] [241, 261, 283, 723, 768, 769] [244, 264, 286, 726, 771, 772] [245, 265, 287, 727, 772, 773] [246, 266, 288, 728, 773, 774] [247, 267, 289, 729, 774, 775] [248, 268, 290, 730, 775, 776] [249, 269, 291, 731, 776, 777] [250, 270, 292, 732, 777, 778] [251, 271, 293, 733, 778, 779] [252, 272, 294, 734, 779, 780] [253, 273, 295, 735, 780, 781] [254, 274, 296, 736, 781, 782] [255, 275, 297, 737, 782, 783] [256, 276, 298, 738, 783, 784] [257, 277, 299, 739, 784, 785] [258, 278, 300, 740, 785, 786] [259, 279, 301, 741, 786, 787] [260, 280, 302, 742, 787, 788] [261, 281, 303, 743, 788, 789] [262, 282, 304, 744, 789, 790] [263, 283, 305, 745, 790, 791] [266, 286, 308, 748, 793, 794] [267, 287, 309, 749, 794, 795] [268, 288, 310, 750, 795, 796] [269, 289, 311, 751, 796, 797] [270, 290, 312, 752, 797, 798] [271, 291, 313, 753, 798, 799] [272, 292, 314, 754, 799, 800] [273, 293, 315, 755, 800, 801] [274, 294, 316, 756, 801, 802] [275, 295, 317, 757, 802, 803] [276, 296, 318, 758, 803, 804] [277, 297, 319, 759, 804, 805] [278, 298, 320, 760, 805, 806] [279, 299, 321, 761, 806, 807] [280, 300, 322, 762, 807, 808] [281, 301, 323, 763, 808, 809] [282, 302, 324, 764, 809, 810] [283, 303, 325, 765, 810, 811] [284, 304, 326, 766, 811, 812] [285, 305, 327, 767, 812, 813] [288, 308, 330, 770, 815, 816] [289, 309, 331, 771, 816, 817] [290, 310, 332, 772, 817, 818] [291, 311, 333, 773, 818, 819] [292, 312, 334, 774, 819, 820] [293, 313, 335, 775, 820, 821] [294, 314, 336, 776, 821, 822] [295, 315, 337, 777, 822, 823] [296, 316, 338, 778, 823, 824] [297, 317, 339, 779, 824, 825] [298, 318, 340, 780, 825, 826] [299, 319, 341, 781, 826, 827] [300, 320, 342, 782, 827, 828] [301, 321, 343, 783, 828, 829] [302, 322, 344, 784, 829, 830] [303, 323, 345, 785, 830, 831] [304, 324, 346, 786, 831, 832] [305, 325, 347, 787, 832, 833] [306, 326, 348, 788, 833, 834] [307, 327, 349, 789, 834, 835] [310, 330, 352, 792, 837, 838] [311, 331, 353, 793, 838, 839] [312, 332, 354, 794, 839, 840] [313, 333, 355, 795, 840, 841] [314, 334, 356, 796, 841, 842] [315, 335, 357, 797, 842, 843] [316, 336, 358, 798, 843, 844] [317, 337, 359, 799, 844, 845] [318, 338, 360, 800, 845, 846] [319, 339, 361, 801, 846, 847] [320, 340, 362, 802, 847, 848] [321, 341, 363, 803, 848, 849] [322, 342, 364, 804, 849, 850] [323, 343, 365, 805, 850, 851] [324, 344, 366, 806, 851, 852] [325, 345, 367, 807, 852, 853] [326, 346, 368, 808, 853, 854] [327, 347, 369, 809, 854, 855] [328, 348, 370, 810, 855, 856] [329, 349, 371, 811, 856, 857] [332, 352, 374, 814, 859, 860] [333, 353, 375, 815, 860, 861] [334, 354, 376, 816, 861, 862] [335, 355, 377, 817, 862, 863] [336, 356, 378, 818, 863, 864] [337, 357, 379, 819, 864, 865] [338, 358, 380, 820, 865, 866] [339, 359, 381, 821, 866, 867] [340, 360, 382, 822, 867, 868] [341, 361, 383, 823, 868, 869] [342, 362, 384, 824, 869, 870] [343, 363, 385, 825, 870, 871] [344, 364, 386, 826, 871, 872] [345, 365, 387, 827, 872, 873] [346, 366, 388, 828, 873, 874] [347, 367, 389, 829, 874, 875] [348, 368, 390, 830, 875, 876] [349, 369, 391, 831, 876, 877] [350, 370, 392, 832, 877, 878] [351, 371, 393, 833, 878, 879] [354, 374, 396, 836, 881, 882] [355, 375, 397, 837, 882, 883] [356, 376, 398, 838, 883, 884] [357, 377, 399, 839, 884, 885] [358, 378, 400, 840, 885, 886] [359, 379, 401, 841, 886, 887] [360, 380, 402, 842, 887, 888] [361, 381, 403, 843, 888, 889] [362, 382, 404, 844, 889, 890] [363, 383, 405, 845, 890, 891] [364, 384, 406, 846, 891, 892] [365, 385, 407, 847, 892, 893] [366, 386, 408, 848, 893, 894] [367, 387, 409, 849, 894, 895] [368, 388, 410, 850, 895, 896] [369, 389, 411, 851, 896, 897] [370, 390, 412, 852, 897, 898] [371, 391, 413, 853, 898, 899] [372, 392, 414, 854, 899, 900] [373, 393, 415, 855, 900, 901] [376, 396, 418, 858, 903, 904] [377, 397, 419, 859, 904, 905] [378, 398, 420, 860, 905, 906] [379, 399, 421, 861, 906, 907] [380, 400, 422, 862, 907, 908] [381, 401, 423, 863, 908, 909] [382, 402, 424, 864, 909, 910] [383, 403, 425, 865, 910, 911] [384, 404, 426, 866, 911, 912] [385, 405, 427, 867, 912, 913] [386, 406, 428, 868, 913, 914] [387, 407, 429, 869, 914, 915] [388, 408, 430, 870, 915, 916] [389, 409, 431, 871, 916, 917] [390, 410, 432, 872, 917, 918] [391, 411, 433, 873, 918, 919] [392, 412, 434, 874, 919, 920] [393, 413, 435, 875, 920, 921] [394, 414, 436, 876, 921, 922] [395, 415, 437, 877, 922, 923] [398, 418, 440, 880, 925, 926] [399, 419, 441, 881, 926, 927] [400, 420, 442, 882, 927, 928] [401, 421, 443, 883, 928, 929] [402, 422, 444, 884, 929, 930] [403, 423, 445, 885, 930, 931] [404, 424, 446, 886, 931, 932] [405, 425, 447, 887, 932, 933] [406, 426, 448, 888, 933, 934] [407, 427, 449, 889, 934, 935] [408, 428, 450, 890, 935, 936] [409, 429, 451, 891, 936, 937] [410, 430, 452, 892, 937, 938] [411, 431, 453, 893, 938, 939] [412, 432, 454, 894, 939, 940] [413, 433, 455, 895, 940, 941] [414, 434, 456, 896, 941, 942] [415, 435, 457, 897, 942, 943] [416, 436, 458, 898, 943, 944] [417, 437, 459, 899, 944, 945] [420, 440, 462, 902, 947, 948] [421, 441, 463, 903, 948, 949] [422, 442, 464, 904, 949, 950] [423, 443, 465, 905, 950, 951] [424, 444, 466, 906, 951, 952] [425, 445, 467, 907, 952, 953] [426, 446, 468, 908, 953, 954] [427, 447, 469, 909, 954, 955] [428, 448, 470, 910, 955, 956] [429, 449, 471, 911, 956, 957] [430, 450, 472, 912, 957, 958] [431, 451, 473, 913, 958, 959] [432, 452, 474, 914, 959, 960] [433, 453, 475, 915, 960, 961] [434, 454, 476, 916, 961, 962] [435, 455, 477, 917, 962, 963] [436, 456, 478, 918, 963, 964] [437, 457, 479, 919, 964, 965] [438, 458, 480, 920, 965, 966] [439, 459, 481, 921, 966, 967] [442, 462, 924] [443, 463, 925] [444, 464, 926] [445, 465, 927] [446, 466, 928] [447, 467, 929] [448, 468, 930] [449, 469, 931] [450, 470, 932] [451, 471, 933] [452, 472, 934] [453, 473, 935] [454, 474, 936] [455, 475, 937] [456, 476, 938] [457, 477, 939] [458, 478, 940] [459, 479, 941] [460, 480, 942] [461, 481, 943] [464, 946] [465, 947] [466, 948] [467, 949] [468, 950] [469, 951] [470, 952] [471, 953] [472, 954] [473, 955] [474, 956] [475, 957] [476, 958] [477, 959] [478, 960] [479, 961] [480, 962] [481, 963] [482, 964] [483, 965]
H_Z (480 checks, sparse supports)
[44, 484, 506] [0, 45, 485, 507] [0, 1, 46, 486, 508, 528] [1, 2, 47, 487, 509, 529] [2, 3, 48, 488, 510, 530] [3, 4, 49, 489, 511, 531] [4, 5, 50, 490, 512, 532] [5, 6, 51, 491, 513, 533] [6, 7, 52, 492, 514, 534] [7, 8, 53, 493, 515, 535] [8, 9, 54, 494, 516, 536] [9, 10, 55, 495, 517, 537] [10, 11, 56, 496, 518, 538] [11, 12, 57, 497, 519, 539] [12, 13, 58, 498, 520, 540] [13, 14, 59, 499, 521, 541] [14, 15, 60, 500, 522, 542] [15, 16, 61, 501, 523, 543] [16, 17, 62, 502, 524, 544] [17, 18, 63, 503, 525, 545] [18, 19, 64, 504, 526, 546] [19, 20, 65, 505, 527, 547] [20, 21, 548] [21, 549] [66, 506, 528] [22, 67, 507, 529] [22, 23, 68, 508, 530, 550] [23, 24, 69, 509, 531, 551] [24, 25, 70, 510, 532, 552] [25, 26, 71, 511, 533, 553] [26, 27, 72, 512, 534, 554] [27, 28, 73, 513, 535, 555] [28, 29, 74, 514, 536, 556] [29, 30, 75, 515, 537, 557] [30, 31, 76, 516, 538, 558] [31, 32, 77, 517, 539, 559] [32, 33, 78, 518, 540, 560] [33, 34, 79, 519, 541, 561] [34, 35, 80, 520, 542, 562] [35, 36, 81, 521, 543, 563] [36, 37, 82, 522, 544, 564] [37, 38, 83, 523, 545, 565] [38, 39, 84, 524, 546, 566] [39, 40, 85, 525, 547, 567] [40, 41, 86, 526, 548, 568] [41, 42, 87, 527, 549, 569] [42, 43, 570] [43, 571] [88, 528, 550] [44, 89, 529, 551] [44, 45, 90, 530, 552, 572] [45, 46, 91, 531, 553, 573] [46, 47, 92, 532, 554, 574] [47, 48, 93, 533, 555, 575] [48, 49, 94, 534, 556, 576] [49, 50, 95, 535, 557, 577] [50, 51, 96, 536, 558, 578] [51, 52, 97, 537, 559, 579] [52, 53, 98, 538, 560, 580] [53, 54, 99, 539, 561, 581] [54, 55, 100, 540, 562, 582] [55, 56, 101, 541, 563, 583] [56, 57, 102, 542, 564, 584] [57, 58, 103, 543, 565, 585] [58, 59, 104, 544, 566, 586] [59, 60, 105, 545, 567, 587] [60, 61, 106, 546, 568, 588] [61, 62, 107, 547, 569, 589] [62, 63, 108, 548, 570, 590] [63, 64, 109, 549, 571, 591] [64, 65, 592] [65, 593] [110, 550, 572] [66, 111, 551, 573] [66, 67, 112, 552, 574, 594] [67, 68, 113, 553, 575, 595] [68, 69, 114, 554, 576, 596] [69, 70, 115, 555, 577, 597] [70, 71, 116, 556, 578, 598] [71, 72, 117, 557, 579, 599] [72, 73, 118, 558, 580, 600] [73, 74, 119, 559, 581, 601] [74, 75, 120, 560, 582, 602] [75, 76, 121, 561, 583, 603] [76, 77, 122, 562, 584, 604] [77, 78, 123, 563, 585, 605] [78, 79, 124, 564, 586, 606] [79, 80, 125, 565, 587, 607] [80, 81, 126, 566, 588, 608] [81, 82, 127, 567, 589, 609] [82, 83, 128, 568, 590, 610] [83, 84, 129, 569, 591, 611] [84, 85, 130, 570, 592, 612] [85, 86, 131, 571, 593, 613] [86, 87, 614] [87, 615] [132, 572, 594] [88, 133, 573, 595] [88, 89, 134, 574, 596, 616] [89, 90, 135, 575, 597, 617] [90, 91, 136, 576, 598, 618] [91, 92, 137, 577, 599, 619] [92, 93, 138, 578, 600, 620] [93, 94, 139, 579, 601, 621] [94, 95, 140, 580, 602, 622] [95, 96, 141, 581, 603, 623] [96, 97, 142, 582, 604, 624] [97, 98, 143, 583, 605, 625] [98, 99, 144, 584, 606, 626] [99, 100, 145, 585, 607, 627] [100, 101, 146, 586, 608, 628] [101, 102, 147, 587, 609, 629] [102, 103, 148, 588, 610, 630] [103, 104, 149, 589, 611, 631] [104, 105, 150, 590, 612, 632] [105, 106, 151, 591, 613, 633] [106, 107, 152, 592, 614, 634] [107, 108, 153, 593, 615, 635] [108, 109, 636] [109, 637] [154, 594, 616] [110, 155, 595, 617] [110, 111, 156, 596, 618, 638] [111, 112, 157, 597, 619, 639] [112, 113, 158, 598, 620, 640] [113, 114, 159, 599, 621, 641] [114, 115, 160, 600, 622, 642] [115, 116, 161, 601, 623, 643] [116, 117, 162, 602, 624, 644] [117, 118, 163, 603, 625, 645] [118, 119, 164, 604, 626, 646] [119, 120, 165, 605, 627, 647] [120, 121, 166, 606, 628, 648] [121, 122, 167, 607, 629, 649] [122, 123, 168, 608, 630, 650] [123, 124, 169, 609, 631, 651] [124, 125, 170, 610, 632, 652] [125, 126, 171, 611, 633, 653] [126, 127, 172, 612, 634, 654] [127, 128, 173, 613, 635, 655] [128, 129, 174, 614, 636, 656] [129, 130, 175, 615, 637, 657] [130, 131, 658] [131, 659] [176, 616, 638] [132, 177, 617, 639] [132, 133, 178, 618, 640, 660] [133, 134, 179, 619, 641, 661] [134, 135, 180, 620, 642, 662] [135, 136, 181, 621, 643, 663] [136, 137, 182, 622, 644, 664] [137, 138, 183, 623, 645, 665] [138, 139, 184, 624, 646, 666] [139, 140, 185, 625, 647, 667] [140, 141, 186, 626, 648, 668] [141, 142, 187, 627, 649, 669] [142, 143, 188, 628, 650, 670] [143, 144, 189, 629, 651, 671] [144, 145, 190, 630, 652, 672] [145, 146, 191, 631, 653, 673] [146, 147, 192, 632, 654, 674] [147, 148, 193, 633, 655, 675] [148, 149, 194, 634, 656, 676] [149, 150, 195, 635, 657, 677] [150, 151, 196, 636, 658, 678] [151, 152, 197, 637, 659, 679] [152, 153, 680] [153, 681] [198, 638, 660] [154, 199, 639, 661] [154, 155, 200, 640, 662, 682] [155, 156, 201, 641, 663, 683] [156, 157, 202, 642, 664, 684] [157, 158, 203, 643, 665, 685] [158, 159, 204, 644, 666, 686] [159, 160, 205, 645, 667, 687] [160, 161, 206, 646, 668, 688] [161, 162, 207, 647, 669, 689] [162, 163, 208, 648, 670, 690] [163, 164, 209, 649, 671, 691] [164, 165, 210, 650, 672, 692] [165, 166, 211, 651, 673, 693] [166, 167, 212, 652, 674, 694] [167, 168, 213, 653, 675, 695] [168, 169, 214, 654, 676, 696] [169, 170, 215, 655, 677, 697] [170, 171, 216, 656, 678, 698] [171, 172, 217, 657, 679, 699] [172, 173, 218, 658, 680, 700] [173, 174, 219, 659, 681, 701] [174, 175, 702] [175, 703] [220, 660, 682] [176, 221, 661, 683] [176, 177, 222, 662, 684, 704] [177, 178, 223, 663, 685, 705] [178, 179, 224, 664, 686, 706] [179, 180, 225, 665, 687, 707] [180, 181, 226, 666, 688, 708] [181, 182, 227, 667, 689, 709] [182, 183, 228, 668, 690, 710] [183, 184, 229, 669, 691, 711] [184, 185, 230, 670, 692, 712] [185, 186, 231, 671, 693, 713] [186, 187, 232, 672, 694, 714] [187, 188, 233, 673, 695, 715] [188, 189, 234, 674, 696, 716] [189, 190, 235, 675, 697, 717] [190, 191, 236, 676, 698, 718] [191, 192, 237, 677, 699, 719] [192, 193, 238, 678, 700, 720] [193, 194, 239, 679, 701, 721] [194, 195, 240, 680, 702, 722] [195, 196, 241, 681, 703, 723] [196, 197, 724] [197, 725] [242, 682, 704] [198, 243, 683, 705] [198, 199, 244, 684, 706, 726] [199, 200, 245, 685, 707, 727] [200, 201, 246, 686, 708, 728] [201, 202, 247, 687, 709, 729] [202, 203, 248, 688, 710, 730] [203, 204, 249, 689, 711, 731] [204, 205, 250, 690, 712, 732] [205, 206, 251, 691, 713, 733] [206, 207, 252, 692, 714, 734] [207, 208, 253, 693, 715, 735] [208, 209, 254, 694, 716, 736] [209, 210, 255, 695, 717, 737] [210, 211, 256, 696, 718, 738] [211, 212, 257, 697, 719, 739] [212, 213, 258, 698, 720, 740] [213, 214, 259, 699, 721, 741] [214, 215, 260, 700, 722, 742] [215, 216, 261, 701, 723, 743] [216, 217, 262, 702, 724, 744] [217, 218, 263, 703, 725, 745] [218, 219, 746] [219, 747] [264, 704, 726] [220, 265, 705, 727] [220, 221, 266, 706, 728, 748] [221, 222, 267, 707, 729, 749] [222, 223, 268, 708, 730, 750] [223, 224, 269, 709, 731, 751] [224, 225, 270, 710, 732, 752] [225, 226, 271, 711, 733, 753] [226, 227, 272, 712, 734, 754] [227, 228, 273, 713, 735, 755] [228, 229, 274, 714, 736, 756] [229, 230, 275, 715, 737, 757] [230, 231, 276, 716, 738, 758] [231, 232, 277, 717, 739, 759] [232, 233, 278, 718, 740, 760] [233, 234, 279, 719, 741, 761] [234, 235, 280, 720, 742, 762] [235, 236, 281, 721, 743, 763] [236, 237, 282, 722, 744, 764] [237, 238, 283, 723, 745, 765] [238, 239, 284, 724, 746, 766] [239, 240, 285, 725, 747, 767] [240, 241, 768] [241, 769] [286, 726, 748] [242, 287, 727, 749] [242, 243, 288, 728, 750, 770] [243, 244, 289, 729, 751, 771] [244, 245, 290, 730, 752, 772] [245, 246, 291, 731, 753, 773] [246, 247, 292, 732, 754, 774] [247, 248, 293, 733, 755, 775] [248, 249, 294, 734, 756, 776] [249, 250, 295, 735, 757, 777] [250, 251, 296, 736, 758, 778] [251, 252, 297, 737, 759, 779] [252, 253, 298, 738, 760, 780] [253, 254, 299, 739, 761, 781] [254, 255, 300, 740, 762, 782] [255, 256, 301, 741, 763, 783] [256, 257, 302, 742, 764, 784] [257, 258, 303, 743, 765, 785] [258, 259, 304, 744, 766, 786] [259, 260, 305, 745, 767, 787] [260, 261, 306, 746, 768, 788] [261, 262, 307, 747, 769, 789] [262, 263, 790] [263, 791] [308, 748, 770] [264, 309, 749, 771] [264, 265, 310, 750, 772, 792] [265, 266, 311, 751, 773, 793] [266, 267, 312, 752, 774, 794] [267, 268, 313, 753, 775, 795] [268, 269, 314, 754, 776, 796] [269, 270, 315, 755, 777, 797] [270, 271, 316, 756, 778, 798] [271, 272, 317, 757, 779, 799] [272, 273, 318, 758, 780, 800] [273, 274, 319, 759, 781, 801] [274, 275, 320, 760, 782, 802] [275, 276, 321, 761, 783, 803] [276, 277, 322, 762, 784, 804] [277, 278, 323, 763, 785, 805] [278, 279, 324, 764, 786, 806] [279, 280, 325, 765, 787, 807] [280, 281, 326, 766, 788, 808] [281, 282, 327, 767, 789, 809] [282, 283, 328, 768, 790, 810] [283, 284, 329, 769, 791, 811] [284, 285, 812] [285, 813] [330, 770, 792] [286, 331, 771, 793] [286, 287, 332, 772, 794, 814] [287, 288, 333, 773, 795, 815] [288, 289, 334, 774, 796, 816] [289, 290, 335, 775, 797, 817] [290, 291, 336, 776, 798, 818] [291, 292, 337, 777, 799, 819] [292, 293, 338, 778, 800, 820] [293, 294, 339, 779, 801, 821] [294, 295, 340, 780, 802, 822] [295, 296, 341, 781, 803, 823] [296, 297, 342, 782, 804, 824] [297, 298, 343, 783, 805, 825] [298, 299, 344, 784, 806, 826] [299, 300, 345, 785, 807, 827] [300, 301, 346, 786, 808, 828] [301, 302, 347, 787, 809, 829] [302, 303, 348, 788, 810, 830] [303, 304, 349, 789, 811, 831] [304, 305, 350, 790, 812, 832] [305, 306, 351, 791, 813, 833] [306, 307, 834] [307, 835] [352, 792, 814] [308, 353, 793, 815] [308, 309, 354, 794, 816, 836] [309, 310, 355, 795, 817, 837] [310, 311, 356, 796, 818, 838] [311, 312, 357, 797, 819, 839] [312, 313, 358, 798, 820, 840] [313, 314, 359, 799, 821, 841] [314, 315, 360, 800, 822, 842] [315, 316, 361, 801, 823, 843] [316, 317, 362, 802, 824, 844] [317, 318, 363, 803, 825, 845] [318, 319, 364, 804, 826, 846] [319, 320, 365, 805, 827, 847] [320, 321, 366, 806, 828, 848] [321, 322, 367, 807, 829, 849] [322, 323, 368, 808, 830, 850] [323, 324, 369, 809, 831, 851] [324, 325, 370, 810, 832, 852] [325, 326, 371, 811, 833, 853] [326, 327, 372, 812, 834, 854] [327, 328, 373, 813, 835, 855] [328, 329, 856] [329, 857] [374, 814, 836] [330, 375, 815, 837] [330, 331, 376, 816, 838, 858] [331, 332, 377, 817, 839, 859] [332, 333, 378, 818, 840, 860] [333, 334, 379, 819, 841, 861] [334, 335, 380, 820, 842, 862] [335, 336, 381, 821, 843, 863] [336, 337, 382, 822, 844, 864] [337, 338, 383, 823, 845, 865] [338, 339, 384, 824, 846, 866] [339, 340, 385, 825, 847, 867] [340, 341, 386, 826, 848, 868] [341, 342, 387, 827, 849, 869] [342, 343, 388, 828, 850, 870] [343, 344, 389, 829, 851, 871] [344, 345, 390, 830, 852, 872] [345, 346, 391, 831, 853, 873] [346, 347, 392, 832, 854, 874] [347, 348, 393, 833, 855, 875] [348, 349, 394, 834, 856, 876] [349, 350, 395, 835, 857, 877] [350, 351, 878] [351, 879] [396, 836, 858] [352, 397, 837, 859] [352, 353, 398, 838, 860, 880] [353, 354, 399, 839, 861, 881] [354, 355, 400, 840, 862, 882] [355, 356, 401, 841, 863, 883] [356, 357, 402, 842, 864, 884] [357, 358, 403, 843, 865, 885] [358, 359, 404, 844, 866, 886] [359, 360, 405, 845, 867, 887] [360, 361, 406, 846, 868, 888] [361, 362, 407, 847, 869, 889] [362, 363, 408, 848, 870, 890] [363, 364, 409, 849, 871, 891] [364, 365, 410, 850, 872, 892] [365, 366, 411, 851, 873, 893] [366, 367, 412, 852, 874, 894] [367, 368, 413, 853, 875, 895] [368, 369, 414, 854, 876, 896] [369, 370, 415, 855, 877, 897] [370, 371, 416, 856, 878, 898] [371, 372, 417, 857, 879, 899] [372, 373, 900] [373, 901] [418, 858, 880] [374, 419, 859, 881] [374, 375, 420, 860, 882, 902] [375, 376, 421, 861, 883, 903] [376, 377, 422, 862, 884, 904] [377, 378, 423, 863, 885, 905] [378, 379, 424, 864, 886, 906] [379, 380, 425, 865, 887, 907] [380, 381, 426, 866, 888, 908] [381, 382, 427, 867, 889, 909] [382, 383, 428, 868, 890, 910] [383, 384, 429, 869, 891, 911] [384, 385, 430, 870, 892, 912] [385, 386, 431, 871, 893, 913] [386, 387, 432, 872, 894, 914] [387, 388, 433, 873, 895, 915] [388, 389, 434, 874, 896, 916] [389, 390, 435, 875, 897, 917] [390, 391, 436, 876, 898, 918] [391, 392, 437, 877, 899, 919] [392, 393, 438, 878, 900, 920] [393, 394, 439, 879, 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953] [426, 427, 472, 912, 934, 954] [427, 428, 473, 913, 935, 955] [428, 429, 474, 914, 936, 956] [429, 430, 475, 915, 937, 957] [430, 431, 476, 916, 938, 958] [431, 432, 477, 917, 939, 959] [432, 433, 478, 918, 940, 960] [433, 434, 479, 919, 941, 961] [434, 435, 480, 920, 942, 962] [435, 436, 481, 921, 943, 963] [436, 437, 482, 922, 944, 964] [437, 438, 483, 923, 945, 965] [438, 439, 966] [439, 967]
Code ID 968-8-23 · download JSON · raw on GitHub