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[[656,114,3]] d =
n
656
k
114
d
3
kd²/n
1.564
w
4
X/Z
1
g
1.56
r
1.4142
layers
1
swaps
0

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Distance

X/Z asymmetry 1 · d_X = 3, d_Z = 3 · w_X = 4, w_Z = 4 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[298, 325, 351]
d_Z 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[623, 624, 648]
certificate exact, d = 3 · CryptoMiniSat 5.14.7 SAT
X: no logical < 3 exists; Z: no logical < 3 exists

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 8 · H_Z 8 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 2–4 (mean 3.845) · H_Z 2–4 (mean 3.86)
qubit degrees H_X 1–2 (mean 1.588) · H_Z 1–2 (mean 1.595)
trapping sets H_X (1,1)×270 (2,0)×19 (3,0)×349 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 270 (1,2): 386 (2,0): 19 (2,1): 736 (2,2): 766 (3,0): 349 (3,1): 1456 (3,2): 1563 (3,3): 680 (3,4): 282
trapping sets H_Z (1,1)×266 (2,0)×21 (3,0)×332 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 266 (1,2): 390 (2,0): 21 (2,1): 722 (2,2): 788 (3,0): 332 (3,1): 1458 (3,2): 1636 (3,3): 663 (3,4): 303
witness diameter X 2.2361 · Z 2.2361 (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 = 1.414
X checkZ checkqubit site (656)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 0 nearest-neighbor SWAPs per round in total, at most 0 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 @npdeep
provenance submitted through the challenge
novelty novelty not audited
construction 25x25-cell checkerboard plaquette/exposed-boundary code with a length-6 top-right chamfer and bottom-right Young diagram (8,6); exact d=3 independently audited
model Magic State Labs (Custom) v0.1 (claimed, not verified)
date 2026-08-13
notes Connected single-layer local 2D code. Exact d=3 was established by exhaustive weight-1/2 exclusion and explicit nontrivial weight-3 logicals on both CSS sides.
family topological (a tag, not a ranking)
locality 2D-local single (computed from the layout)
weight class weight ≤ 4 (computed)

How this code was found

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

X-checks 271 (max weight 4) · Z-checks 271 (max weight 4)
H_X (271 checks, sparse supports)
[0, 1, 26, 27] [2, 3, 28, 29] [6, 7, 32, 33] [8, 9, 34, 35] [10, 11, 36, 37] [12, 13, 38, 39] [16, 17, 42, 43] [18, 19, 44, 45] [20, 21, 46, 47] [22, 23, 48, 49] [24, 25, 50, 51] [27, 28, 53, 54] [29, 30, 55, 56] [31, 32, 57, 58] [33, 34, 59, 60] [35, 36, 61, 62] [37, 38, 63, 64] [39, 40, 65, 66] [41, 42, 67, 68] [43, 44, 69, 70] [45, 46, 71, 72] [47, 48, 73, 74] [49, 50, 75, 76] [54, 55, 80, 81] [56, 57, 82, 83] [58, 59, 84, 85] [60, 61, 86, 87] [64, 65, 90, 91] [66, 67, 92, 93] [68, 69, 94, 95] [70, 71, 96, 97] [74, 75, 100, 101] [79, 80, 105, 106] [83, 84, 109, 110] [85, 86, 111, 112] [87, 88, 113, 114] [89, 90, 115, 116] [93, 94, 119, 120] [95, 96, 121, 122] [97, 98, 123, 124] [99, 100, 125, 126] [101, 102, 127, 128] [104, 105, 130, 131] [106, 107, 132, 133] [108, 109, 134, 135] [112, 113, 138, 139] [114, 115, 140, 141] [116, 117, 142, 143] [118, 119, 144, 145] [122, 123, 148, 149] [124, 125, 150, 151] [126, 127, 152, 153] [128, 129, 154, 155] [131, 132, 157, 158] [133, 134, 159, 160] [135, 136, 161, 162] [137, 138, 163, 164] [141, 142, 167, 168] [143, 144, 169, 170] [145, 146, 171, 172] [147, 148, 173, 174] [151, 152, 177, 178] [153, 154, 179, 180] [156, 157, 182, 183] [160, 161, 186, 187] [162, 163, 188, 189] [164, 165, 190, 191] [166, 167, 192, 193] [170, 171, 196, 197] [172, 173, 198, 199] [174, 175, 200, 201] [176, 177, 202, 203] [180, 181, 206, 207] [183, 184, 209, 210] [185, 186, 211, 212] [189, 190, 215, 216] [191, 192, 217, 218] [193, 194, 219, 220] [195, 196, 221, 222] [199, 200, 225, 226] [201, 202, 227, 228] [203, 204, 229, 230] [205, 206, 231, 232] [208, 209, 234, 235] [210, 211, 236, 237] [212, 213, 238, 239] [214, 215, 240, 241] [218, 219, 244, 245] [220, 221, 246, 247] [222, 223, 248, 249] [224, 225, 250, 251] [228, 229, 254, 255] [230, 231, 256, 257] [232, 233, 258, 259] [235, 236, 261, 262] [237, 238, 263, 264] [239, 240, 265, 266] [241, 242, 267, 268] [243, 244, 269, 270] [247, 248, 273, 274] [249, 250, 275, 276] [251, 252, 277, 278] [253, 254, 279, 280] [257, 258, 283, 284] [260, 261, 286, 287] [262, 263, 288, 289] [266, 267, 292, 293] [268, 269, 294, 295] [270, 271, 296, 297] [272, 273, 298, 299] [276, 277, 302, 303] [278, 279, 304, 305] [280, 281, 306, 307] [282, 283, 308, 309] [287, 288, 313, 314] [289, 290, 315, 316] [291, 292, 317, 318] [295, 296, 321, 322] [297, 298, 323, 324] [299, 300, 325, 326] [301, 302, 327, 328] [305, 306, 331, 332] [307, 308, 333, 334] [309, 310, 335, 336] [314, 315, 340, 341] [316, 317, 342, 343] [318, 319, 344, 345] [320, 321, 346, 347] [324, 325, 350, 351] [326, 327, 352, 353] [328, 329, 354, 355] [330, 331, 356, 357] [334, 335, 360, 361] [336, 337, 362, 363] [339, 340, 365, 366] [343, 344, 369, 370] [345, 346, 371, 372] [347, 348, 373, 374] [349, 350, 375, 376] [353, 354, 379, 380] [355, 356, 381, 382] [357, 358, 383, 384] [359, 360, 385, 386] [364, 365, 390, 391] [366, 367, 392, 393] [368, 369, 394, 395] [372, 373, 398, 399] [374, 375, 400, 401] [376, 377, 402, 403] [378, 379, 404, 405] [382, 383, 408, 409] [384, 385, 410, 411] [386, 387, 412, 413] [388, 389, 414, 415] [391, 392, 417, 418] [393, 394, 419, 420] [395, 396, 421, 422] [397, 398, 423, 424] [401, 402, 427, 428] [403, 404, 429, 430] [405, 406, 431, 432] [407, 408, 433, 434] [411, 412, 437, 438] [413, 414, 439, 440] [416, 417, 442, 443] [420, 421, 446, 447] [422, 423, 448, 449] [424, 425, 450, 451] [426, 427, 452, 453] [430, 431, 456, 457] [432, 433, 458, 459] [434, 435, 460, 461] [436, 437, 462, 463] [440, 441, 466, 467] [443, 444, 468, 469] [445, 446, 470, 471] [449, 450, 474, 475] [451, 452, 476, 477] [453, 454, 478, 479] [455, 456, 480, 481] [459, 460, 484, 485] [461, 462, 486, 487] [463, 464, 488, 489] [465, 466, 490, 491] [469, 470, 494, 495] [471, 472, 496, 497] [473, 474, 498, 499] [477, 478, 502, 503] [479, 480, 504, 505] [481, 482, 506, 507] [483, 484, 508, 509] [487, 488, 512, 513] [489, 490, 514, 515] [491, 492, 516, 517] [495, 496, 519, 520] [497, 498, 521, 522] [499, 500, 523, 524] [501, 502, 525, 526] [505, 506, 529, 530] [507, 508, 531, 532] [509, 510, 533, 534] [511, 512, 535, 536] [515, 516, 539, 540] [518, 519, 541, 542] [522, 523, 545, 546] [524, 525, 547, 548] [526, 527, 549, 550] [528, 529, 551, 552] [532, 533, 555, 556] [534, 535, 557, 558] [536, 537, 559, 560] [538, 539, 561, 562] [542, 543, 565, 566] [544, 545, 567, 568] [548, 549, 571, 572] [550, 551, 573, 574] [552, 553, 575, 576] [554, 555, 577, 578] [558, 559, 581, 582] [560, 561, 583, 584] [562, 563, 585, 586] [564, 565, 587, 588] [566, 567, 589, 590] [568, 569, 591, 592] [570, 571, 593, 594] [574, 575, 597, 598] [576, 577, 599, 600] [578, 579, 601, 602] [580, 581, 603, 604] [584, 585, 607, 608] [588, 589, 611, 612] [590, 591, 613, 614] [592, 593, 615, 616] [594, 595, 617, 618] [596, 597, 619, 620] [598, 599, 621, 622] [600, 601, 623, 624] [602, 603, 625, 626] [604, 605, 627, 628] [606, 607, 629, 630] [608, 609, 631, 632] [610, 611, 633, 634] [614, 615, 637, 638] [616, 617, 639, 640] [618, 619, 641, 642] [620, 621, 643, 644] [624, 625, 647, 648] [626, 627, 649, 650] [628, 629, 651, 652] [630, 631, 653, 654] [3, 4] [5, 6] [13, 14] [15, 16] [26, 52] [51, 77] [78, 104] [103, 129] [259, 285] [286, 312] [311, 337] [338, 364] [363, 389] [415, 441] [468, 493] [541, 564] [634, 635] [636, 637] [644, 645] [646, 647] [654, 655]
H_Z (271 checks, sparse supports)
[1, 2, 27, 28] [3, 4, 29, 30] [5, 6, 31, 32] [7, 8, 33, 34] [11, 12, 37, 38] [13, 14, 39, 40] [15, 16, 41, 42] [17, 18, 43, 44] [21, 22, 47, 48] [23, 24, 49, 50] [26, 27, 52, 53] [28, 29, 54, 55] [30, 31, 56, 57] [32, 33, 58, 59] [34, 35, 60, 61] [36, 37, 62, 63] [38, 39, 64, 65] [40, 41, 66, 67] [42, 43, 68, 69] [44, 45, 70, 71] [46, 47, 72, 73] [50, 51, 76, 77] [53, 54, 79, 80] [55, 56, 81, 82] [59, 60, 85, 86] [61, 62, 87, 88] [63, 64, 89, 90] [65, 66, 91, 92] [69, 70, 95, 96] [71, 72, 97, 98] [73, 74, 99, 100] [75, 76, 101, 102] [78, 79, 104, 105] [82, 83, 108, 109] [84, 85, 110, 111] [86, 87, 112, 113] [88, 89, 114, 115] [92, 93, 118, 119] [94, 95, 120, 121] [96, 97, 122, 123] [98, 99, 124, 125] [100, 101, 126, 127] [102, 103, 128, 129] [105, 106, 131, 132] [107, 108, 133, 134] [109, 110, 135, 136] [111, 112, 137, 138] [115, 116, 141, 142] [117, 118, 143, 144] [119, 120, 145, 146] [121, 122, 147, 148] [125, 126, 151, 152] [127, 128, 153, 154] [130, 131, 156, 157] [132, 133, 158, 159] [134, 135, 160, 161] [138, 139, 164, 165] [140, 141, 166, 167] [142, 143, 168, 169] [144, 145, 170, 171] [148, 149, 174, 175] [150, 151, 176, 177] [154, 155, 180, 181] [157, 158, 183, 184] [161, 162, 187, 188] [163, 164, 189, 190] [165, 166, 191, 192] [167, 168, 193, 194] [171, 172, 197, 198] [173, 174, 199, 200] [175, 176, 201, 202] [177, 178, 203, 204] [179, 180, 205, 206] [184, 185, 210, 211] [186, 187, 212, 213] [188, 189, 214, 215] [190, 191, 216, 217] [194, 195, 220, 221] [196, 197, 222, 223] [198, 199, 224, 225] [200, 201, 226, 227] [202, 203, 228, 229] [204, 205, 230, 231] [206, 207, 232, 233] [209, 210, 235, 236] [211, 212, 237, 238] [213, 214, 239, 240] [217, 218, 243, 244] [219, 220, 245, 246] [221, 222, 247, 248] [223, 224, 249, 250] [227, 228, 253, 254] [231, 232, 257, 258] [234, 235, 260, 261] [236, 237, 262, 263] [240, 241, 266, 267] [242, 243, 268, 269] [244, 245, 270, 271] [246, 247, 272, 273] [250, 251, 276, 277] [252, 253, 278, 279] [254, 255, 280, 281] [256, 257, 282, 283] [258, 259, 284, 285] [261, 262, 287, 288] [263, 264, 289, 290] [265, 266, 291, 292] [267, 268, 293, 294] [269, 270, 295, 296] [273, 274, 299, 300] [275, 276, 301, 302] [277, 278, 303, 304] [279, 280, 305, 306] [281, 282, 307, 308] [283, 284, 309, 310] [286, 287, 312, 313] [288, 289, 314, 315] [290, 291, 316, 317] [292, 293, 318, 319] [296, 297, 322, 323] [298, 299, 324, 325] [300, 301, 326, 327] [302, 303, 328, 329] [306, 307, 332, 333] [310, 311, 336, 337] [313, 314, 339, 340] [315, 316, 341, 342] [319, 320, 345, 346] [321, 322, 347, 348] [323, 324, 349, 350] [325, 326, 351, 352] [329, 330, 355, 356] [331, 332, 357, 358] [333, 334, 359, 360] [335, 336, 361, 362] [338, 339, 364, 365] [342, 343, 368, 369] [344, 345, 370, 371] [346, 347, 372, 373] [348, 349, 374, 375] [352, 353, 378, 379] [354, 355, 380, 381] [356, 357, 382, 383] [358, 359, 384, 385] [360, 361, 386, 387] [362, 363, 388, 389] [365, 366, 391, 392] [367, 368, 393, 394] [369, 370, 395, 396] [371, 372, 397, 398] [375, 376, 401, 402] [377, 378, 403, 404] [379, 380, 405, 406] [381, 382, 407, 408] [385, 386, 411, 412] [387, 388, 413, 414] [390, 391, 416, 417] [392, 393, 418, 419] [394, 395, 420, 421] [398, 399, 424, 425] [400, 401, 426, 427] [402, 403, 428, 429] [404, 405, 430, 431] [408, 409, 434, 435] [410, 411, 436, 437] [414, 415, 440, 441] [417, 418, 443, 444] [421, 422, 447, 448] [423, 424, 449, 450] [425, 426, 451, 452] [427, 428, 453, 454] [431, 432, 457, 458] [433, 434, 459, 460] [435, 436, 461, 462] [437, 438, 463, 464] [439, 440, 465, 466] [444, 445, 469, 470] [446, 447, 471, 472] [448, 449, 473, 474] [450, 451, 475, 476] [454, 455, 479, 480] [456, 457, 481, 482] [458, 459, 483, 484] [460, 461, 485, 486] [462, 463, 487, 488] [464, 465, 489, 490] [466, 467, 491, 492] [468, 469, 493, 494] [470, 471, 495, 496] [472, 473, 497, 498] [476, 477, 501, 502] [478, 479, 503, 504] [480, 481, 505, 506] [482, 483, 507, 508] [486, 487, 511, 512] [490, 491, 515, 516] [494, 495, 518, 519] [498, 499, 522, 523] [500, 501, 524, 525] [502, 503, 526, 527] [504, 505, 528, 529] [508, 509, 532, 533] [510, 511, 534, 535] [512, 513, 536, 537] [514, 515, 538, 539] [519, 520, 542, 543] [521, 522, 544, 545] [523, 524, 546, 547] [525, 526, 548, 549] [529, 530, 552, 553] [531, 532, 554, 555] [533, 534, 556, 557] [535, 536, 558, 559] [537, 538, 560, 561] [539, 540, 562, 563] [541, 542, 564, 565] [543, 544, 566, 567] [545, 546, 568, 569] [549, 550, 572, 573] [551, 552, 574, 575] [553, 554, 576, 577] [555, 556, 578, 579] [557, 558, 580, 581] [561, 562, 584, 585] [565, 566, 588, 589] [569, 570, 592, 593] [571, 572, 594, 595] [573, 574, 596, 597] [575, 576, 598, 599] [579, 580, 602, 603] [581, 582, 604, 605] [583, 584, 606, 607] [587, 588, 610, 611] [589, 590, 612, 613] [591, 592, 614, 615] [593, 594, 616, 617] [595, 596, 618, 619] [597, 598, 620, 621] [599, 600, 622, 623] [601, 602, 624, 625] [603, 604, 626, 627] [605, 606, 628, 629] [607, 608, 630, 631] [611, 612, 634, 635] [613, 614, 636, 637] [615, 616, 638, 639] [619, 620, 642, 643] [621, 622, 644, 645] [623, 624, 646, 647] [625, 626, 648, 649] [629, 630, 652, 653] [631, 632, 654, 655] [0, 1] [8, 9] [10, 11] [18, 19] [20, 21] [22, 23] [24, 25] [156, 182] [181, 207] [208, 234] [416, 442] [492, 517] [563, 586] [609, 632] [610, 633] [639, 640] [641, 642] [649, 650] [651, 652]
Code ID 656-114-3 · download JSON · raw on GitHub