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[[45,5,4]] d =
n
45
k
5
d
4
kd²/n
1.778
w
6
g
0.0219
r
3.0
layers
2

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Distance

d_X 4 · witness weight 4 (claimed exact)
witness operator (support, 4 qubits)
[3, 18, 33, 39]
d_Z 4 · witness weight 4 (claimed exact)
witness operator (support, 4 qubits)
[28, 29, 31, 35]
certificate exact, d = 4 · scipy/HiGHS MILP
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 = 3
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 Generalized weight-6, (5,5) open-boundary lattice. New instance of the Liang-Eberhardt-Chen open-boundary family (arXiv:2504.08887); the paper has no k=5 family.
model Claude Claude Opus 4.8 (claimed, not verified)
builds on arXiv:2504.08887
date 2026-06-19
notes Distance proven exact by cutoff MILP (scipy/HiGHS); no lighter logical exists on either side. 2D-local bilayer layout (reconstructed 2026-07-02): A/B sublattices of 5x5 and 4x5 rows on one grid, physical row = (-i+3) mod 5 on A and (-i+3) mod 4 on B; interaction radius 3.000.
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 19 · Z-checks 23
H_X (19 checks, sparse supports)
[0, 6, 11, 26, 27, 30] [1, 7, 12, 27, 28, 31] [2, 8, 13, 28, 29, 32] [5, 11, 16, 31, 32, 35] [6, 12, 17, 32, 33, 36] [7, 13, 18, 33, 34, 37] [1, 20] [2, 21] [3, 22] [4, 23] [15, 41, 42] [16, 42, 43] [17, 43, 44] [6, 20, 21, 22, 25] [7, 21, 22, 23, 26] [8, 22, 23, 24, 27] [10, 16, 36, 37, 40] [11, 17, 37, 38, 41] [12, 18, 38, 39, 42]
H_Z (23 checks, sparse supports)
[2, 5, 6, 21, 26, 32] [3, 6, 7, 22, 27, 33] [4, 7, 8, 23, 28, 34] [7, 10, 11, 26, 31, 37] [8, 11, 12, 27, 32, 38] [9, 12, 13, 28, 33, 39] [12, 15, 16, 31, 36, 42] [13, 16, 17, 32, 37, 43] [14, 17, 18, 33, 38, 44] [9] [14] [19] [0, 30] [5, 35] [10, 40] [8, 24, 29] [13, 29, 34] [18, 34, 39] [1, 20, 25, 31, 35] [6, 25, 30, 36, 40] [1, 5, 20, 25, 31] [6, 10, 25, 30, 36] [11, 15, 30, 35, 41]
raw submission JSON