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[[120,5,8]] d =
n
120
k
5
d
8
kd²/n
2.667
w
6
g
0.0267
r
3.1623
layers
2

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Distance

d_X 8 · witness weight 8 (claimed exact)
witness operator (support, 8 qubits)
[30, 46, 53, 62, 70, 87, 95, 102]
d_Z 8 · witness weight 8 (claimed exact)
witness operator (support, 8 qubits)
[18, 19, 27, 36, 73, 74, 102, 103]
certificate exact, d = 8 · scipy/HiGHS cutoff IP
X: no logical < 8 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 = 3.162
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 Generalized weight-6, (8,8) open-boundary lattice.
model Claude Claude Opus 4.8 (claimed, not verified)
builds on arXiv:2504.08887
date 2026-06-16
notes 2D-local bilayer layout (reconstructed 2026-07-02): A/B sublattices of 8x8 and 7x8 rows on one grid, physical row = (+i+1) mod 8 on A and (+i+0) mod 7 on B; interaction radius 3.162.
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 55 · Z-checks 63
H_X (55 checks, sparse supports)
[0, 9, 17, 65, 66, 72] [1, 10, 18, 66, 67, 73] [2, 11, 19, 67, 68, 74] [3, 12, 20, 68, 69, 75] [4, 13, 21, 69, 70, 76] [5, 14, 22, 70, 71, 77] [8, 17, 25, 73, 74, 80] [9, 18, 26, 74, 75, 81] [10, 19, 27, 75, 76, 82] [11, 20, 28, 76, 77, 83] [12, 21, 29, 77, 78, 84] [13, 22, 30, 78, 79, 85] [16, 25, 33, 81, 82, 88] [17, 26, 34, 82, 83, 89] [18, 27, 35, 83, 84, 90] [19, 28, 36, 84, 85, 91] [20, 29, 37, 85, 86, 92] [21, 30, 38, 86, 87, 93] [24, 33, 41, 89, 90, 96] [25, 34, 42, 90, 91, 97] [26, 35, 43, 91, 92, 98] [27, 36, 44, 92, 93, 99] [28, 37, 45, 93, 94, 100] [29, 38, 46, 94, 95, 101] [32, 41, 49, 97, 98, 104] [33, 42, 50, 98, 99, 105] [34, 43, 51, 99, 100, 106] [35, 44, 52, 100, 101, 107] [36, 45, 53, 101, 102, 108] [37, 46, 54, 102, 103, 109] [1, 56] [2, 57] [3, 58] [4, 59] [5, 60] [6, 61] [7, 62] [48, 113, 114] [49, 114, 115] [50, 115, 116] [51, 116, 117] [52, 117, 118] [53, 118, 119] [9, 56, 57, 58, 64] [10, 57, 58, 59, 65] [11, 58, 59, 60, 66] [12, 59, 60, 61, 67] [13, 60, 61, 62, 68] [14, 61, 62, 63, 69] [40, 49, 105, 106, 112] [41, 50, 106, 107, 113] [42, 51, 107, 108, 114] [43, 52, 108, 109, 115] [44, 53, 109, 110, 116] [45, 54, 110, 111, 117]
H_Z (63 checks, sparse supports)
[2, 8, 9, 57, 65, 74] [3, 9, 10, 58, 66, 75] [4, 10, 11, 59, 67, 76] [5, 11, 12, 60, 68, 77] [6, 12, 13, 61, 69, 78] [7, 13, 14, 62, 70, 79] [10, 16, 17, 65, 73, 82] [11, 17, 18, 66, 74, 83] [12, 18, 19, 67, 75, 84] [13, 19, 20, 68, 76, 85] [14, 20, 21, 69, 77, 86] [15, 21, 22, 70, 78, 87] [18, 24, 25, 73, 81, 90] [19, 25, 26, 74, 82, 91] [20, 26, 27, 75, 83, 92] [21, 27, 28, 76, 84, 93] [22, 28, 29, 77, 85, 94] [23, 29, 30, 78, 86, 95] [26, 32, 33, 81, 89, 98] [27, 33, 34, 82, 90, 99] [28, 34, 35, 83, 91, 100] [29, 35, 36, 84, 92, 101] [30, 36, 37, 85, 93, 102] [31, 37, 38, 86, 94, 103] [34, 40, 41, 89, 97, 106] [35, 41, 42, 90, 98, 107] [36, 42, 43, 91, 99, 108] [37, 43, 44, 92, 100, 109] [38, 44, 45, 93, 101, 110] [39, 45, 46, 94, 102, 111] [42, 48, 49, 97, 105, 114] [43, 49, 50, 98, 106, 115] [44, 50, 51, 99, 107, 116] [45, 51, 52, 100, 108, 117] [46, 52, 53, 101, 109, 118] [47, 53, 54, 102, 110, 119] [15] [23] [31] [39] [47] [55] [0, 72] [8, 80] [16, 88] [24, 96] [32, 104] [40, 112] [14, 63, 71] [22, 71, 79] [30, 79, 87] [38, 87, 95] [46, 95, 103] [54, 103, 111] [1, 56, 64, 73, 80] [9, 64, 72, 81, 88] [17, 72, 80, 89, 96] [25, 80, 88, 97, 104] [33, 88, 96, 105, 112] [0, 8, 17, 24, 89] [8, 16, 25, 32, 97] [16, 24, 33, 40, 105] [24, 32, 41, 48, 113]
raw submission JSON