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[[72,6,6]] d =
n
72
k
6
d
6
kd²/n
3.0
w
6
g
0.0104
r
4.1231
layers
2

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Distance

d_X 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[10, 23, 41, 65, 69, 70]
d_Z 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[16, 25, 29, 47, 48, 63]
certificate exact, d = 6 · scipy/HiGHS cutoff IP
X: no logical < 6 exists; Z: no logical < 6 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 (36)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, (6,6) 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 36 · Z-checks 37
H_X (36 checks, sparse supports)
[2, 6, 13, 36, 44, 49] [3, 7, 14, 37, 45, 50] [4, 8, 15, 38, 46, 51] [5, 9, 16, 39, 47, 52] [8, 12, 19, 42, 50, 55] [9, 13, 20, 43, 51, 56] [10, 14, 21, 44, 52, 57] [11, 15, 22, 45, 53, 58] [14, 18, 25, 48, 56, 61] [15, 19, 26, 49, 57, 62] [16, 20, 27, 50, 58, 63] [17, 21, 28, 51, 59, 64] [20, 24, 31, 54, 62, 67] [21, 25, 32, 55, 63, 68] [22, 26, 33, 56, 64, 69] [23, 27, 34, 57, 65, 70] [0, 36] [1, 37] [2, 38] [3, 39] [4, 40] [5, 41] [32, 66] [33, 67] [34, 68] [35, 69] [7, 36, 38, 43] [8, 37, 39, 44] [9, 38, 40, 45] [10, 39, 41, 46] [28, 62, 66, 70] [29, 63, 67, 71] [26, 30, 60, 68] [27, 31, 61, 69] [28, 32, 62, 70] [29, 33, 63, 71]
H_Z (37 checks, sparse supports)
[1, 6, 14, 37, 44, 48] [2, 7, 15, 38, 45, 49] [3, 8, 16, 39, 46, 50] [4, 9, 17, 40, 47, 51] [7, 12, 20, 43, 50, 54] [8, 13, 21, 44, 51, 55] [9, 14, 22, 45, 52, 56] [10, 15, 23, 46, 53, 57] [13, 18, 26, 49, 56, 60] [14, 19, 27, 50, 57, 61] [15, 20, 28, 51, 58, 62] [16, 21, 29, 52, 59, 63] [19, 24, 32, 55, 62, 66] [20, 25, 33, 56, 63, 67] [21, 26, 34, 57, 64, 68] [22, 27, 35, 58, 65, 69] [12, 42] [18, 48] [24, 54] [30, 60] [11, 53] [17, 59] [23, 65] [29, 71] [25, 42, 48, 55] [31, 48, 54, 61] [0, 13, 36, 43] [6, 19, 42, 49] [12, 25, 48, 55] [18, 31, 54, 61] [16, 47, 53, 58] [22, 53, 59, 64] [28, 59, 65, 70] [5, 10, 41, 52] [11, 16, 47, 58] [17, 22, 53, 64] [23, 28, 59, 70]
raw submission JSON