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[[107,58,3]] d ≤
n
107
k
58
d
3
kd²/n
4.8785
w
12
X/Z
1.33

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Distance

X/Z asymmetry 1.33 · d_X ≤ 4, d_Z ≤ 3 · w_X = 12, w_Z = 12 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 4 · witness weight 4 (claimed upper_bound)
witness found by @mathys · research/kit/surrogate.lightest_logical · found at 1000 trials · survived 1000 trials · 2026-11-02
witness operator (support, 4 qubits)
[7, 78, 88, 95]
d_Z 3 · witness weight 3 (claimed upper_bound)
witness found by @mathys · research/kit/surrogate.lightest_logical · found at 1000 trials · survived 1000 trials · 2026-11-02
witness operator (support, 3 qubits)
[55, 69, 72]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 12 · H_Z 11–12 (mean 11.88)
qubit degrees H_X 1–3 (mean 2.692) · H_Z 1–3 (mean 2.776)
trapping sets H_X (1,1)×2 (2,1)×42 (3,0)×6 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 2 (1,2): 29 (1,3): 76 (2,1): 42 (2,2): 218 (2,3): 434 (2,4): 715 (3,0): 6 (3,1): 145 (3,2): 1224 (3,3): 4583 (3,4): 7664 (3,5): 9540 (3,6): 1039 (3,7): 900
trapping sets H_Z (1,1)×1 (2,1)×30 (3,1)×64 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 1 (1,2): 22 (1,3): 84 (2,1): 30 (2,2): 198 (2,3): 361 (2,4): 842 (3,1): 64 (3,2): 982 (3,3): 4121 (3,4): 6765 (3,5): 11794 (3,6): 943 (3,7): 1140

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction priced calculus E-PEEL transform of codes/108-58-4.json
model Beam 1.0 (claimed, not verified)
date 2026-11-02
family other (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight > 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[107,58,3]] — priced calculus E-PEEL transform of codes/108-58-4.json

Direction & hypothesis

Weight-12 unrestricted CSS cell. Transform a connected CSS parent (codes/108-58-4.json, a board entry) with the priced construction calculus to obtain a connected child that is not dominated by any existing entry in its track cell.

What was searched

Gap-targeted search: all priced calculus moves (peel, puncture, deletion, rebase) applied to board codes. Targets Pareto frontier gaps. Rule used: E-PEEL. Parent: codes/108-58-4.json. Connected children only; bare-qubit children and dominated candidates dropped. Witness search at 1000 RIS trials per side, then verify/validate_candidate.py with full refutation.

Evidence trail

The submitted distance is a witness-backed upper bound: d = min(d_X, d_Z) with explicit X and Z logical witnesses carried in the JSON. Parent entry: codes/108-58-4.json.

Tools

Model: Beam 1.0. Harness: research/kit (coordination, submit, prescreen), code-calculus consumer.

Reproduction

Rebuild H_X/H_Z from codes/108-58-4.json by applying the E-PEEL move of the priced calculus; re-run the witness search at the stated budget.

Parity checks

X-checks 24 (max weight 12) · Z-checks 25 (max weight 12)
H_X (24 checks, sparse supports)
[5, 17, 18, 26, 36, 46, 53, 64, 76, 86, 90, 98] [3, 15, 19, 27, 37, 44, 54, 62, 74, 87, 91, 99] [7, 13, 20, 31, 38, 48, 58, 66, 78, 85, 92, 103] [8, 14, 21, 29, 39, 49, 56, 67, 79, 83, 93, 101] [6, 12, 22, 30, 40, 47, 57, 65, 77, 84, 94, 102] [1, 10, 23, 34, 41, 51, 61, 69, 72, 82, 95, 106] [2, 11, 24, 32, 42, 52, 59, 70, 73, 80, 96, 104] [0, 9, 25, 33, 43, 50, 60, 68, 71, 81, 97, 105] [1, 13, 24, 26, 37, 44, 55, 64, 72, 84, 97, 98] [2, 14, 25, 27, 35, 45, 53, 62, 73, 85, 95, 99] [0, 12, 23, 28, 36, 46, 54, 63, 71, 83, 96, 100] [4, 16, 21, 29, 40, 47, 58, 67, 75, 87, 94, 101] [5, 17, 22, 30, 38, 48, 56, 65, 76, 88, 92, 102] [3, 15, 20, 31, 39, 49, 57, 66, 74, 86, 93, 103] [7, 10, 18, 32, 43, 50, 61, 70, 78, 81, 91, 104] [8, 11, 19, 33, 41, 51, 59, 68, 79, 82, 89, 105] [0, 10, 21, 33, 35, 46, 53, 64, 73, 81, 93, 106] [1, 11, 22, 34, 36, 44, 54, 62, 71, 82, 94, 104] [2, 9, 20, 32, 37, 45, 55, 63, 72, 80, 92, 105] [3, 13, 24, 30, 38, 49, 56, 67, 76, 84, 96, 103] [4, 14, 25, 31, 39, 47, 57, 65, 74, 85, 97, 101] [5, 12, 23, 29, 40, 48, 58, 66, 75, 83, 95, 102] [6, 16, 18, 27, 41, 52, 59, 70, 79, 87, 90, 100] [7, 17, 19, 28, 42, 50, 60, 68, 77, 88, 91, 98]
H_Z (25 checks, sparse supports)
[1, 10, 33, 43, 46, 61, 64, 71, 81, 89, 106] [2, 11, 18, 34, 41, 44, 59, 62, 72, 82, 90, 104] [0, 9, 19, 32, 42, 45, 60, 63, 73, 80, 91, 105] [4, 13, 20, 30, 37, 49, 55, 67, 74, 84, 92, 103] [5, 14, 21, 31, 35, 47, 53, 65, 75, 85, 93, 101] [3, 12, 22, 29, 36, 48, 54, 66, 76, 83, 94, 102] [7, 16, 23, 27, 40, 52, 58, 70, 77, 87, 95, 100] [8, 17, 24, 28, 38, 50, 56, 68, 78, 88, 96, 98] [6, 15, 25, 26, 39, 51, 57, 69, 79, 86, 97, 99] [2, 10, 18, 26, 42, 52, 61, 70, 73, 80, 90, 98] [0, 11, 19, 27, 43, 50, 59, 68, 71, 81, 91, 99] [1, 9, 28, 41, 51, 60, 69, 72, 82, 89, 100] [5, 13, 21, 29, 39, 46, 58, 64, 76, 83, 93, 101] [3, 14, 22, 30, 40, 44, 56, 62, 74, 84, 94, 102] [4, 12, 20, 31, 38, 45, 57, 63, 75, 85, 92, 103] [8, 16, 24, 32, 36, 49, 55, 67, 79, 86, 96, 104] [6, 17, 25, 33, 37, 47, 53, 65, 77, 87, 97, 105] [8, 11, 18, 27, 35, 51, 53, 70, 79, 82, 89, 99] [6, 9, 19, 28, 36, 52, 54, 68, 77, 80, 90, 100] [7, 10, 26, 37, 50, 55, 69, 78, 81, 91, 98] [2, 14, 21, 30, 38, 48, 56, 67, 73, 85, 92, 102] [0, 12, 22, 31, 39, 49, 57, 65, 71, 83, 93, 103] [1, 13, 20, 29, 40, 47, 58, 66, 72, 84, 94, 101] [5, 17, 24, 33, 41, 45, 59, 64, 76, 88, 95, 105] [3, 15, 25, 34, 42, 46, 60, 62, 74, 86, 96, 106]
Code ID 107-58-3 · download JSON · raw on GitHub