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[[128,6,8]] d =
n
128
k
6
d
8
kd²/n
3.0
w
6
g
0.0104
r
4.1231
layers
2

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Distance

d_X 9 · witness weight 9 (claimed exact)
witness operator (support, 9 qubits)
[10, 26, 33, 41, 82, 89, 97, 98, 120]
d_Z 8 · witness weight 8 (claimed exact)
witness operator (support, 8 qubits)
[1, 3, 5, 14, 65, 67, 69, 86]
certificate exact, d = 8 · scipy/HiGHS cutoff IP
X: no logical < 9 exists; Z: no logical < 8 exists

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 4.123
X checkZ checkqubit site (64)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 and @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction f = 1 + xy + x-1 y2, g = 1 + x-1 y + x-2 y-1; annulus-type boundary engine, (8,8) lattice.
model Claude Claude Opus 4.8 (claimed, not verified)
builds on arXiv:2504.08887
date 2026-06-16
family bivariate bicycle (a tag, not a ranking)
locality 2D-local bilayer (computed from the layout)
weight class weight ≤ 6 (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 66 · Z-checks 69
H_X (66 checks, sparse supports)
[2, 8, 17, 64, 74, 81] [3, 9, 18, 65, 75, 82] [4, 10, 19, 66, 76, 83] [5, 11, 20, 67, 77, 84] [6, 12, 21, 68, 78, 85] [7, 13, 22, 69, 79, 86] [10, 16, 25, 72, 82, 89] [11, 17, 26, 73, 83, 90] [12, 18, 27, 74, 84, 91] [13, 19, 28, 75, 85, 92] [14, 20, 29, 76, 86, 93] [15, 21, 30, 77, 87, 94] [18, 24, 33, 80, 90, 97] [19, 25, 34, 81, 91, 98] [20, 26, 35, 82, 92, 99] [21, 27, 36, 83, 93, 100] [22, 28, 37, 84, 94, 101] [23, 29, 38, 85, 95, 102] [26, 32, 41, 88, 98, 105] [27, 33, 42, 89, 99, 106] [28, 34, 43, 90, 100, 107] [29, 35, 44, 91, 101, 108] [30, 36, 45, 92, 102, 109] [31, 37, 46, 93, 103, 110] [34, 40, 49, 96, 106, 113] [35, 41, 50, 97, 107, 114] [36, 42, 51, 98, 108, 115] [37, 43, 52, 99, 109, 116] [38, 44, 53, 100, 110, 117] [39, 45, 54, 101, 111, 118] [42, 48, 57, 104, 114, 121] [43, 49, 58, 105, 115, 122] [44, 50, 59, 106, 116, 123] [45, 51, 60, 107, 117, 124] [46, 52, 61, 108, 118, 125] [47, 53, 62, 109, 119, 126] [0, 64] [1, 65] [2, 66] [3, 67] [4, 68] [5, 69] [6, 70] [7, 71] [58, 120] [59, 121] [60, 122] [61, 123] [62, 124] [63, 125] [9, 64, 66, 73] [10, 65, 67, 74] [11, 66, 68, 75] [12, 67, 69, 76] [13, 68, 70, 77] [14, 69, 71, 78] [52, 114, 120, 124] [53, 115, 121, 125] [54, 116, 122, 126] [55, 117, 123, 127] [50, 56, 112, 122] [51, 57, 113, 123] [52, 58, 114, 124] [53, 59, 115, 125] [54, 60, 116, 126] [55, 61, 117, 127]
H_Z (69 checks, sparse supports)
[1, 8, 18, 65, 74, 80] [2, 9, 19, 66, 75, 81] [3, 10, 20, 67, 76, 82] [4, 11, 21, 68, 77, 83] [5, 12, 22, 69, 78, 84] [6, 13, 23, 70, 79, 85] [9, 16, 26, 73, 82, 88] [10, 17, 27, 74, 83, 89] [11, 18, 28, 75, 84, 90] [12, 19, 29, 76, 85, 91] [13, 20, 30, 77, 86, 92] [14, 21, 31, 78, 87, 93] [17, 24, 34, 81, 90, 96] [18, 25, 35, 82, 91, 97] [19, 26, 36, 83, 92, 98] [20, 27, 37, 84, 93, 99] [21, 28, 38, 85, 94, 100] [22, 29, 39, 86, 95, 101] [25, 32, 42, 89, 98, 104] [26, 33, 43, 90, 99, 105] [27, 34, 44, 91, 100, 106] [28, 35, 45, 92, 101, 107] [29, 36, 46, 93, 102, 108] [30, 37, 47, 94, 103, 109] [33, 40, 50, 97, 106, 112] [34, 41, 51, 98, 107, 113] [35, 42, 52, 99, 108, 114] [36, 43, 53, 100, 109, 115] [37, 44, 54, 101, 110, 116] [38, 45, 55, 102, 111, 117] [41, 48, 58, 105, 114, 120] [42, 49, 59, 106, 115, 121] [43, 50, 60, 107, 116, 122] [44, 51, 61, 108, 117, 123] [45, 52, 62, 109, 118, 124] [46, 53, 63, 110, 119, 125] [16, 72] [24, 80] [32, 88] [40, 96] [48, 104] [56, 112] [15, 87] [23, 95] [31, 103] [39, 111] [47, 119] [55, 127] [33, 72, 80, 89] [41, 80, 88, 97] [49, 88, 96, 105] [57, 96, 104, 113] [0, 17, 64, 73] [8, 25, 72, 81] [16, 33, 80, 89] [24, 41, 88, 97] [32, 49, 96, 105] [40, 57, 104, 113] [22, 79, 87, 94] [30, 87, 95, 102] [38, 95, 103, 110] [46, 103, 111, 118] [54, 111, 119, 126] [7, 14, 71, 86] [15, 22, 79, 94] [23, 30, 87, 102] [31, 38, 95, 110] [39, 46, 103, 118] [47, 54, 111, 126]
raw submission JSON