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[[153,5,9]] d =
n
153
k
5
d
9
kd²/n
2.647
w
6
g
0.0265
r
3.1623
layers
2

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Distance

d_X 9 · witness weight 9 (claimed exact)
witness operator (support, 9 qubits)
[33, 41, 42, 49, 77, 96, 106, 139, 149]
d_Z 9 · witness weight 9 (claimed exact)
witness operator (support, 9 qubits)
[18, 30, 31, 40, 50, 101, 102, 133, 134]
certificate exact, d = 9 · scipy/HiGHS MILP
X: no logical < 9 exists; Z: no logical < 9 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 (81)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, (9,9) 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 9x9 and 8x9 rows on one grid, physical row = (+i+1) mod 9 on A and (+i+0) mod 8 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 71 · Z-checks 81
H_X (71 checks, sparse supports)
[0, 10, 19, 82, 83, 90] [1, 11, 20, 83, 84, 91] [2, 12, 21, 84, 85, 92] [3, 13, 22, 85, 86, 93] [4, 14, 23, 86, 87, 94] [5, 15, 24, 87, 88, 95] [6, 16, 25, 88, 89, 96] [9, 19, 28, 91, 92, 99] [10, 20, 29, 92, 93, 100] [11, 21, 30, 93, 94, 101] [12, 22, 31, 94, 95, 102] [13, 23, 32, 95, 96, 103] [14, 24, 33, 96, 97, 104] [15, 25, 34, 97, 98, 105] [18, 28, 37, 100, 101, 108] [19, 29, 38, 101, 102, 109] [20, 30, 39, 102, 103, 110] [21, 31, 40, 103, 104, 111] [22, 32, 41, 104, 105, 112] [23, 33, 42, 105, 106, 113] [24, 34, 43, 106, 107, 114] [27, 37, 46, 109, 110, 117] [28, 38, 47, 110, 111, 118] [29, 39, 48, 111, 112, 119] [30, 40, 49, 112, 113, 120] [31, 41, 50, 113, 114, 121] [32, 42, 51, 114, 115, 122] [33, 43, 52, 115, 116, 123] [36, 46, 55, 118, 119, 126] [37, 47, 56, 119, 120, 127] [38, 48, 57, 120, 121, 128] [39, 49, 58, 121, 122, 129] [40, 50, 59, 122, 123, 130] [41, 51, 60, 123, 124, 131] [42, 52, 61, 124, 125, 132] [45, 55, 64, 127, 128, 135] [46, 56, 65, 128, 129, 136] [47, 57, 66, 129, 130, 137] [48, 58, 67, 130, 131, 138] [49, 59, 68, 131, 132, 139] [50, 60, 69, 132, 133, 140] [51, 61, 70, 133, 134, 141] [1, 72] [2, 73] [3, 74] [4, 75] [5, 76] [6, 77] [7, 78] [8, 79] [63, 145, 146] [64, 146, 147] [65, 147, 148] [66, 148, 149] [67, 149, 150] [68, 150, 151] [69, 151, 152] [10, 72, 73, 74, 81] [11, 73, 74, 75, 82] [12, 74, 75, 76, 83] [13, 75, 76, 77, 84] [14, 76, 77, 78, 85] [15, 77, 78, 79, 86] [16, 78, 79, 80, 87] [54, 64, 136, 137, 144] [55, 65, 137, 138, 145] [56, 66, 138, 139, 146] [57, 67, 139, 140, 147] [58, 68, 140, 141, 148] [59, 69, 141, 142, 149] [60, 70, 142, 143, 150]
H_Z (81 checks, sparse supports)
[2, 9, 10, 73, 82, 92] [3, 10, 11, 74, 83, 93] [4, 11, 12, 75, 84, 94] [5, 12, 13, 76, 85, 95] [6, 13, 14, 77, 86, 96] [7, 14, 15, 78, 87, 97] [8, 15, 16, 79, 88, 98] [11, 18, 19, 82, 91, 101] [12, 19, 20, 83, 92, 102] [13, 20, 21, 84, 93, 103] [14, 21, 22, 85, 94, 104] [15, 22, 23, 86, 95, 105] [16, 23, 24, 87, 96, 106] [17, 24, 25, 88, 97, 107] [20, 27, 28, 91, 100, 110] [21, 28, 29, 92, 101, 111] [22, 29, 30, 93, 102, 112] [23, 30, 31, 94, 103, 113] [24, 31, 32, 95, 104, 114] [25, 32, 33, 96, 105, 115] [26, 33, 34, 97, 106, 116] [29, 36, 37, 100, 109, 119] [30, 37, 38, 101, 110, 120] [31, 38, 39, 102, 111, 121] [32, 39, 40, 103, 112, 122] [33, 40, 41, 104, 113, 123] [34, 41, 42, 105, 114, 124] [35, 42, 43, 106, 115, 125] [38, 45, 46, 109, 118, 128] [39, 46, 47, 110, 119, 129] [40, 47, 48, 111, 120, 130] [41, 48, 49, 112, 121, 131] [42, 49, 50, 113, 122, 132] [43, 50, 51, 114, 123, 133] [44, 51, 52, 115, 124, 134] [47, 54, 55, 118, 127, 137] [48, 55, 56, 119, 128, 138] [49, 56, 57, 120, 129, 139] [50, 57, 58, 121, 130, 140] [51, 58, 59, 122, 131, 141] [52, 59, 60, 123, 132, 142] [53, 60, 61, 124, 133, 143] [56, 63, 64, 127, 136, 146] [57, 64, 65, 128, 137, 147] [58, 65, 66, 129, 138, 148] [59, 66, 67, 130, 139, 149] [60, 67, 68, 131, 140, 150] [61, 68, 69, 132, 141, 151] [62, 69, 70, 133, 142, 152] [17] [26] [35] [44] [53] [62] [71] [0, 90] [9, 99] [18, 108] [27, 117] [36, 126] [45, 135] [54, 144] [16, 80, 89] [25, 89, 98] [34, 98, 107] [43, 107, 116] [52, 116, 125] [61, 125, 134] [70, 134, 143] [1, 72, 81, 91, 99] [10, 81, 90, 100, 108] [19, 90, 99, 109, 117] [28, 99, 108, 118, 126] [37, 108, 117, 127, 135] [46, 117, 126, 136, 144] [0, 9, 19, 27, 109] [9, 18, 28, 36, 118] [18, 27, 37, 45, 127] [27, 36, 46, 54, 136] [36, 45, 55, 63, 145]
raw submission JSON