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[[112,6,7]] d =
n
112
k
6
d
7
kd²/n
2.625
w
6
g
0.0091
r
4.1231
layers
2

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Distance

d_X 7 · witness weight 7 (claimed exact)
witness operator (support, 7 qubits)
[4, 10, 20, 27, 50, 69, 98]
d_Z 8 · witness weight 8 (claimed exact)
witness operator (support, 8 qubits)
[2, 4, 6, 17, 58, 60, 62, 65]
certificate exact, d = 7 · scipy/HiGHS cutoff IP
X: no logical < 7 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 (56)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, (7,8) 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 60 · Z-checks 57
H_X (60 checks, sparse supports)
[2, 8, 17, 56, 66, 73] [3, 9, 18, 57, 67, 74] [4, 10, 19, 58, 68, 75] [5, 11, 20, 59, 69, 76] [6, 12, 21, 60, 70, 77] [7, 13, 22, 61, 71, 78] [10, 16, 25, 64, 74, 81] [11, 17, 26, 65, 75, 82] [12, 18, 27, 66, 76, 83] [13, 19, 28, 67, 77, 84] [14, 20, 29, 68, 78, 85] [15, 21, 30, 69, 79, 86] [18, 24, 33, 72, 82, 89] [19, 25, 34, 73, 83, 90] [20, 26, 35, 74, 84, 91] [21, 27, 36, 75, 85, 92] [22, 28, 37, 76, 86, 93] [23, 29, 38, 77, 87, 94] [26, 32, 41, 80, 90, 97] [27, 33, 42, 81, 91, 98] [28, 34, 43, 82, 92, 99] [29, 35, 44, 83, 93, 100] [30, 36, 45, 84, 94, 101] [31, 37, 46, 85, 95, 102] [34, 40, 49, 88, 98, 105] [35, 41, 50, 89, 99, 106] [36, 42, 51, 90, 100, 107] [37, 43, 52, 91, 101, 108] [38, 44, 53, 92, 102, 109] [39, 45, 54, 93, 103, 110] [0, 56] [1, 57] [2, 58] [3, 59] [4, 60] [5, 61] [6, 62] [7, 63] [50, 104] [51, 105] [52, 106] [53, 107] [54, 108] [55, 109] [9, 56, 58, 65] [10, 57, 59, 66] [11, 58, 60, 67] [12, 59, 61, 68] [13, 60, 62, 69] [14, 61, 63, 70] [44, 98, 104, 108] [45, 99, 105, 109] [46, 100, 106, 110] [47, 101, 107, 111] [42, 48, 96, 106] [43, 49, 97, 107] [44, 50, 98, 108] [45, 51, 99, 109] [46, 52, 100, 110] [47, 53, 101, 111]
H_Z (57 checks, sparse supports)
[1, 8, 18, 57, 66, 72] [2, 9, 19, 58, 67, 73] [3, 10, 20, 59, 68, 74] [4, 11, 21, 60, 69, 75] [5, 12, 22, 61, 70, 76] [6, 13, 23, 62, 71, 77] [9, 16, 26, 65, 74, 80] [10, 17, 27, 66, 75, 81] [11, 18, 28, 67, 76, 82] [12, 19, 29, 68, 77, 83] [13, 20, 30, 69, 78, 84] [14, 21, 31, 70, 79, 85] [17, 24, 34, 73, 82, 88] [18, 25, 35, 74, 83, 89] [19, 26, 36, 75, 84, 90] [20, 27, 37, 76, 85, 91] [21, 28, 38, 77, 86, 92] [22, 29, 39, 78, 87, 93] [25, 32, 42, 81, 90, 96] [26, 33, 43, 82, 91, 97] [27, 34, 44, 83, 92, 98] [28, 35, 45, 84, 93, 99] [29, 36, 46, 85, 94, 100] [30, 37, 47, 86, 95, 101] [33, 40, 50, 89, 98, 104] [34, 41, 51, 90, 99, 105] [35, 42, 52, 91, 100, 106] [36, 43, 53, 92, 101, 107] [37, 44, 54, 93, 102, 108] [38, 45, 55, 94, 103, 109] [16, 64] [24, 72] [32, 80] [40, 88] [48, 96] [15, 79] [23, 87] [31, 95] [39, 103] [47, 111] [33, 64, 72, 81] [41, 72, 80, 89] [49, 80, 88, 97] [0, 17, 56, 65] [8, 25, 64, 73] [16, 33, 72, 81] [24, 41, 80, 89] [32, 49, 88, 97] [22, 71, 79, 86] [30, 79, 87, 94] [38, 87, 95, 102] [46, 95, 103, 110] [7, 14, 63, 78] [15, 22, 71, 86] [23, 30, 79, 94] [31, 38, 87, 102] [39, 46, 95, 110]
raw submission JSON