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[[91,5,7]] d =
n
91
k
5
d
7
kd²/n
2.692
w
6
g
0.0269
r
3.1623
layers
2

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Distance

d_X 7 · witness weight 7 (claimed exact)
witness operator (support, 7 qubits)
[12, 26, 32, 55, 62, 68, 88]
d_Z 7 · witness weight 7 (claimed exact)
witness operator (support, 7 qubits)
[0, 4, 5, 12, 45, 46, 50]
certificate exact, d = 7 · scipy/HiGHS cutoff IP
X: no logical < 7 exists; Z: no logical < 7 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 (49)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, (7,7) open-boundary lattice.
model Claude Claude Opus 4.8 (claimed, not verified)
date 2026-06-16
notes 2D-local bilayer layout (reconstructed 2026-07-02): A/B sublattices of 7x7 and 6x7 rows on one grid, physical row = (+i+1) mod 7 on A and (+i+0) mod 6 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 41 · Z-checks 47
H_X (41 checks, sparse supports)
[0, 8, 15, 50, 51, 56] [1, 9, 16, 51, 52, 57] [2, 10, 17, 52, 53, 58] [3, 11, 18, 53, 54, 59] [4, 12, 19, 54, 55, 60] [7, 15, 22, 57, 58, 63] [8, 16, 23, 58, 59, 64] [9, 17, 24, 59, 60, 65] [10, 18, 25, 60, 61, 66] [11, 19, 26, 61, 62, 67] [14, 22, 29, 64, 65, 70] [15, 23, 30, 65, 66, 71] [16, 24, 31, 66, 67, 72] [17, 25, 32, 67, 68, 73] [18, 26, 33, 68, 69, 74] [21, 29, 36, 71, 72, 77] [22, 30, 37, 72, 73, 78] [23, 31, 38, 73, 74, 79] [24, 32, 39, 74, 75, 80] [25, 33, 40, 75, 76, 81] [1, 42] [2, 43] [3, 44] [4, 45] [5, 46] [6, 47] [35, 85, 86] [36, 86, 87] [37, 87, 88] [38, 88, 89] [39, 89, 90] [8, 42, 43, 44, 49] [9, 43, 44, 45, 50] [10, 44, 45, 46, 51] [11, 45, 46, 47, 52] [12, 46, 47, 48, 53] [28, 36, 78, 79, 84] [29, 37, 79, 80, 85] [30, 38, 80, 81, 86] [31, 39, 81, 82, 87] [32, 40, 82, 83, 88]
H_Z (47 checks, sparse supports)
[2, 7, 8, 43, 50, 58] [3, 8, 9, 44, 51, 59] [4, 9, 10, 45, 52, 60] [5, 10, 11, 46, 53, 61] [6, 11, 12, 47, 54, 62] [9, 14, 15, 50, 57, 65] [10, 15, 16, 51, 58, 66] [11, 16, 17, 52, 59, 67] [12, 17, 18, 53, 60, 68] [13, 18, 19, 54, 61, 69] [16, 21, 22, 57, 64, 72] [17, 22, 23, 58, 65, 73] [18, 23, 24, 59, 66, 74] [19, 24, 25, 60, 67, 75] [20, 25, 26, 61, 68, 76] [23, 28, 29, 64, 71, 79] [24, 29, 30, 65, 72, 80] [25, 30, 31, 66, 73, 81] [26, 31, 32, 67, 74, 82] [27, 32, 33, 68, 75, 83] [30, 35, 36, 71, 78, 86] [31, 36, 37, 72, 79, 87] [32, 37, 38, 73, 80, 88] [33, 38, 39, 74, 81, 89] [34, 39, 40, 75, 82, 90] [13] [20] [27] [34] [41] [0, 56] [7, 63] [14, 70] [21, 77] [28, 84] [12, 48, 55] [19, 55, 62] [26, 62, 69] [33, 69, 76] [40, 76, 83] [1, 42, 49, 57, 63] [8, 49, 56, 64, 70] [15, 56, 63, 71, 77] [22, 63, 70, 78, 84] [0, 7, 15, 21, 71] [7, 14, 22, 28, 78] [14, 21, 29, 35, 85]