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[[263,16,12]] d ≤
n
263
k
16
d
12
kd²/n
8.76
w
8
g
0.014
r
5.0
layers
2

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Distance

d_X 12 · witness weight 12 (claimed upper_bound)
witness operator (support, 12 qubits)
[30, 194, 201, 214, 222, 224, 227, 232, 243, 253, 254, 259]
d_Z 12 · witness weight 12 (claimed upper_bound)
witness operator (support, 12 qubits)
[12, 24, 35, 49, 82, 91, 142, 143, 151, 159, 167, 191]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 5
X checkZ checkqubit site (138)2 qubits stacked (2 layers)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

Construction & provenance

authors @FarLab
provenance submitted through the challenge
novelty novelty not audited
construction Open-boundary planar weight-8 bivariate-bicycle code, f supports {(0,0),(2,-1),(3,1),(3,-2)}, g supports {(0,0),(-2,-2),(1,-3),(-3,0)}, on a 13x11 lattice (boundary-engine build, [[278,16,12]]), then r=1 lattice grafting (arXiv:2504.08887 Sec. III E) removing 15 qubits at a d>=12 floor, and generating-set weight reduction (27 -> 8, rowspace-preserving). Bilayer grid layout: A/B sublattices stacked; kept-qubit coordinates recovered by deterministic replay of the seeded graft chains, verified by bit-exact matrix equality with the original run.
model Claude Claude Fable 5 (claimed, not verified)
builds on arXiv:2504.08887 (planar BB + grafting technique), arXiv:2410.11942 (open-boundary theory)
date 2026-07-09
notes Claimed d=12 is the lightest logical found by deep self-refutation: RIS flat at 12 across 1M/4M/16M trials/side x 2 independent seeds (~64M side-trials) with a weight-12 X witness re-validated by the pinned python stack, and the independent BP+OSD search (1M trials) also found weight-12 and nothing lighter -- unusually tight two-mechanism agreement. Upper bound only. Literature novelty of the parameter set not checked; the construction technique is from arXiv:2504.08887, the family instance and graft are ours.
family bivariate bicycle (a tag, not a ranking)
locality 2D-local bilayer (computed from the layout)
weight class weight ≤ 8 (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 127 · Z-checks 122
H_X (127 checks, sparse supports)
[2, 17, 27, 30, 137, 161, 169] [18, 28, 31, 138, 162, 170] [3, 20, 30, 33, 140, 164, 172] [4, 21, 31, 34, 134, 141, 165, 173] [5, 22, 32, 35, 135, 142, 166, 174] [6, 23, 33, 36, 143, 167, 175] [7, 27, 37, 40, 138, 147, 171, 179] [8, 28, 38, 41, 139, 148, 172, 180] [9, 29, 39, 42, 140, 149, 173, 181] [10, 30, 40, 43, 141, 150, 174, 182] [11, 31, 41, 44, 142, 151, 175, 183] [12, 32, 42, 45, 143, 152, 176, 184] [13, 33, 43, 46, 144, 153, 177, 185] [14, 34, 44, 47, 145, 154, 178, 186] [17, 38, 48, 51, 149, 158, 182, 189] [18, 39, 49, 52, 150, 159, 183, 190] [19, 40, 50, 53, 151, 160, 184, 191] [20, 41, 51, 54, 152, 161, 185, 192] [21, 42, 52, 55, 153, 162, 186, 193] [22, 43, 53, 56, 154, 163, 187, 194] [23, 44, 54, 57, 155, 164, 188, 195] [29, 50, 60, 63, 161, 170, 193, 200] [30, 51, 61, 64, 162, 171, 194, 201] [31, 52, 62, 65, 163, 172, 195, 202] [32, 53, 63, 66, 164, 173, 196, 203] [33, 54, 64, 67, 165, 174, 197, 204] [34, 55, 65, 68, 166, 175, 198, 205] [35, 56, 66, 69, 167, 176, 199, 206] [39, 60, 70, 73, 171, 180, 202, 210] [40, 61, 71, 74, 172, 181, 203, 211] [41, 62, 72, 75, 173, 182, 204, 212] [42, 63, 73, 76, 174, 183, 205, 213] [43, 64, 74, 77, 175, 184, 206, 214] [44, 65, 75, 78, 176, 185, 207, 215] [45, 66, 76, 79, 177, 186, 208, 216] [46, 67, 77, 80, 178, 187, 209, 217] [50, 71, 81, 84, 182, 190, 213, 221] [51, 72, 82, 85, 183, 191, 214, 222] [52, 73, 83, 86, 184, 192, 215, 223] [53, 74, 84, 87, 185, 193, 216, 224] [54, 75, 85, 88, 186, 194, 217, 225] [55, 76, 86, 89, 187, 195, 218, 226] [56, 77, 87, 90, 188, 196, 219, 227] [61, 82, 91, 94, 192, 200, 224, 232] [62, 83, 92, 95, 193, 201, 225, 233] [63, 84, 93, 96, 194, 202, 226, 234] [64, 85, 94, 97, 195, 203, 227, 235] [65, 86, 95, 98, 196, 204, 228, 236] [66, 87, 96, 99, 197, 205, 229, 237] [67, 88, 97, 100, 198, 206, 230, 238] [68, 89, 98, 101, 199, 207, 231, 239] [72, 92, 102, 105, 202, 211, 235, 243] [73, 93, 103, 106, 203, 212, 236, 244] [74, 94, 104, 107, 204, 213, 237, 245] [75, 95, 105, 108, 205, 214, 238, 246] [76, 96, 106, 109, 206, 215, 239, 247] [77, 97, 107, 110, 207, 216, 240, 248] [78, 98, 108, 111, 208, 217, 241, 249] [79, 99, 109, 209, 218, 242, 250] [83, 103, 112, 115, 213, 222, 246, 252] [84, 104, 113, 116, 214, 223, 247, 253] [85, 105, 114, 117, 215, 224, 248, 254] [86, 106, 115, 118, 216, 225, 249, 255] [87, 107, 116, 119, 217, 226, 250, 256] [90, 110, 119, 122, 220, 229, 251, 259] [0] [4, 139] [1, 9, 139, 147] [2, 7, 10, 140, 148] [8, 11, 141, 149] [9, 12, 142, 150] [3, 10, 13, 143, 151] [4, 11, 14, 144, 152] [12, 21, 24, 155, 163] [1, 16, 26, 29, 160, 168] [19, 29, 32, 139, 163, 171] [2, 136] [1, 137] [2, 3, 138] [5, 134, 140] [3, 6, 135, 141] [15, 18, 149, 157] [7, 16, 19, 150, 158] [8, 17, 20, 151, 159] [9, 18, 21, 152, 160] [10, 19, 22, 153, 161] [11, 20, 23, 154, 162] [13, 22, 25, 134, 156, 164] [125, 255] [126, 256] [119, 128] [130, 260] [107, 127, 238, 247] [108, 128, 239, 248] [88, 108, 117, 120, 218, 227, 257] [89, 109, 118, 121, 219, 228, 258] [129, 259] [120, 129] [116, 248, 255] [117, 249, 256] [118, 250, 257] [119, 258] [120, 259] [121, 251, 260] [105, 236, 245, 255] [106, 237, 246, 256] [127, 257] [128, 258] [109, 240, 249, 259] [110, 241, 250, 260] [111, 242, 261] [132, 262] [114, 246, 253] [115, 247, 254] [104, 124, 235, 244] [131, 261] [93, 113, 123, 126, 224, 233, 255] [94, 114, 124, 127, 225, 234, 256] [95, 115, 125, 128, 226, 235, 257] [96, 116, 126, 129, 227, 236, 258] [97, 117, 127, 130, 228, 237, 259] [98, 118, 128, 131, 229, 238, 260] [99, 119, 129, 132, 230, 239, 261] [100, 120, 130, 133, 231, 240, 262] [92, 112, 223, 232, 252, 254, 255] [103, 123, 234, 243] [113, 245, 252]
H_Z (122 checks, sparse supports)
[2, 28, 37, 136, 138, 148, 169] [3, 8, 31, 40, 138, 141, 151, 172] [4, 9, 32, 41, 139, 142, 152, 173] [5, 10, 33, 42, 140, 143, 153, 174] [6, 11, 34, 43, 141, 144, 154, 175] [12, 35, 44, 142, 145, 155, 176] [8, 15, 39, 48, 149, 159, 180] [9, 16, 40, 49, 147, 150, 160, 181] [10, 17, 41, 50, 148, 151, 161, 182] [11, 18, 42, 51, 149, 152, 162, 183] [12, 19, 43, 52, 150, 153, 163, 184] [13, 20, 44, 53, 151, 154, 164, 185] [14, 21, 45, 54, 152, 155, 165, 186] [22, 46, 55, 153, 156, 166, 187] [18, 26, 50, 157, 160, 170, 190] [19, 27, 51, 60, 158, 161, 171, 191] [20, 28, 52, 61, 159, 162, 172, 192] [21, 29, 53, 62, 160, 163, 173, 193] [22, 30, 54, 63, 161, 164, 174, 194] [23, 31, 55, 64, 162, 165, 175, 195] [24, 32, 56, 65, 163, 166, 176, 196] [25, 33, 57, 66, 164, 167, 177, 197] [29, 37, 61, 70, 168, 171, 181, 200] [30, 38, 62, 71, 169, 172, 182, 201] [31, 39, 63, 72, 170, 173, 183, 202] [32, 40, 64, 73, 171, 174, 184, 203] [33, 41, 65, 74, 172, 175, 185, 204] [34, 42, 66, 75, 173, 176, 186, 205] [35, 43, 67, 76, 174, 177, 187, 206] [36, 44, 68, 77, 175, 178, 188, 207] [40, 48, 72, 81, 179, 182, 191, 211] [41, 49, 73, 82, 180, 183, 192, 212] [42, 50, 74, 83, 181, 184, 193, 213] [43, 51, 75, 84, 182, 185, 194, 214] [44, 52, 76, 85, 183, 186, 195, 215] [45, 53, 77, 86, 184, 187, 196, 216] [46, 54, 78, 87, 185, 188, 197, 217] [47, 55, 79, 88, 186, 198, 218] [52, 60, 84, 92, 190, 193, 202, 223] [53, 61, 85, 93, 191, 194, 203, 224] [54, 62, 86, 94, 192, 195, 204, 225] [55, 63, 87, 95, 193, 196, 205, 226] [56, 64, 88, 96, 194, 197, 206, 227] [57, 65, 89, 97, 195, 198, 207, 228] [66, 90, 98, 196, 199, 208, 229] [62, 70, 93, 102, 202, 212, 233] [63, 71, 94, 103, 200, 203, 213, 234] [64, 72, 95, 104, 201, 204, 214, 235] [65, 73, 96, 105, 202, 205, 215, 236] [66, 74, 97, 106, 203, 206, 216, 237] [67, 75, 98, 107, 204, 207, 217, 238] [68, 76, 99, 108, 205, 208, 218, 239] [69, 77, 100, 109, 206, 209, 219, 240] [73, 81, 104, 112, 210, 213, 223, 244] [74, 82, 105, 113, 211, 214, 224, 245] [75, 83, 106, 114, 212, 215, 225, 246] [76, 84, 107, 115, 213, 216, 226, 247] [77, 85, 108, 116, 214, 217, 227, 248] [78, 86, 109, 117, 215, 218, 228, 249] [79, 87, 110, 118, 216, 219, 229, 250] [84, 91, 114, 123, 221, 224, 234, 253] [85, 92, 115, 124, 222, 225, 235, 254] [86, 93, 116, 125, 223, 226, 236, 255] [87, 94, 117, 126, 224, 227, 237, 256] [88, 95, 118, 127, 225, 228, 238, 257] [89, 96, 119, 128, 226, 229, 239, 258] [90, 97, 120, 129, 227, 230, 240, 259] [98, 121, 130, 228, 231, 241, 260] [16, 48, 158, 168] [27, 169, 179] [38, 70, 180, 189] [49, 81, 190] [60, 91, 200, 210] [71, 102, 211, 221] [82, 112, 222, 232] [1, 26, 27, 137, 147] [7, 37, 38, 148, 158] [17, 48, 49, 159, 169] [59] [39, 70, 71, 181, 190] [50, 81, 82, 191, 200] [146] [15, 157] [51, 83, 91, 189, 192, 201, 222] [26, 168] [37, 179] [48, 189] [28, 60, 170, 180] [70, 210] [81, 221] [61, 92, 201, 211, 232] [72, 103, 212, 222, 243] [83, 113, 223, 233, 252] [47, 145] [25, 156] [36, 69, 167] [47, 80, 178] [58] [69, 101, 199] [122, 220] [101, 133, 231] [14, 46, 144, 178] [24, 57, 155] [35, 68, 166, 199] [46, 79, 177, 209] [57, 90, 188, 220] [68, 100, 198, 231] [79, 111, 208, 242] [90, 121, 219, 251] [100, 132, 230, 262] [13, 36, 45, 143, 156, 177] [23, 47, 56, 154, 167, 188] [34, 67, 165, 178, 198] [45, 69, 78, 176, 208] [56, 80, 89, 187, 199, 219] [67, 99, 197, 209, 230] [78, 101, 110, 207, 220, 241] [99, 122, 131, 229, 242, 261] [6, 35, 135, 167] [5, 34, 134, 145, 156, 166] [91, 92, 123, 232, 233, 243] [93, 123, 124, 234, 244]
raw submission JSON