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[[50,6,4]] d =
n
50
k
6
d
4
kd²/n
1.92
w
6
g
0.0768
r
2.2361
layers
2

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Distance

d_X 4 · witness weight 4 (claimed exact)
witness operator (support, 4 qubits)
[0, 20, 31, 40]
d_Z 4 · witness weight 4 (claimed exact)
witness operator (support, 4 qubits)
[11, 13, 36, 38]
certificate exact, d = 4 · scipy/HiGHS cutoff IP
X: no logical < 4 exists; Z: no logical < 4 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 = 2.236
X checkZ checkqubit site (25)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, (5,5) 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 23 · Z-checks 23
H_X (23 checks, sparse supports)
[2, 5, 11, 25, 32, 36] [3, 6, 12, 26, 33, 37] [4, 7, 13, 27, 34, 38] [7, 10, 16, 30, 37, 41] [8, 11, 17, 31, 38, 42] [9, 12, 18, 32, 39, 43] [12, 15, 21, 35, 42, 46] [13, 16, 22, 36, 43, 47] [14, 17, 23, 37, 44, 48] [0, 25] [1, 26] [2, 27] [3, 28] [4, 29] [22, 45] [23, 46] [24, 47] [6, 25, 27, 31] [7, 26, 28, 32] [8, 27, 29, 33] [17, 20, 40, 47] [18, 21, 41, 48] [19, 22, 42, 49]
H_Z (23 checks, sparse supports)
[1, 5, 12, 26, 32, 35] [2, 6, 13, 27, 33, 36] [3, 7, 14, 28, 34, 37] [6, 10, 17, 31, 37, 40] [7, 11, 18, 32, 38, 41] [8, 12, 19, 33, 39, 42] [11, 15, 22, 36, 42, 45] [12, 16, 23, 37, 43, 46] [13, 17, 24, 38, 44, 47] [10, 30] [15, 35] [20, 40] [9, 39] [14, 44] [19, 49] [0, 11, 25, 31] [5, 16, 30, 36] [10, 21, 35, 41] [13, 34, 39, 43] [18, 39, 44, 48] [4, 8, 29, 38] [9, 13, 34, 43] [14, 18, 39, 48]
raw submission JSON