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[[107,33,7]] d ≤
n
107
k
33
d
7
kd²/n
15.1121
w
26
X/Z
1.43

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Distance

X/Z asymmetry 1.43 · d_X ≤ 10, d_Z ≤ 7 · w_X = 26, w_Z = 26 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 10 · witness weight 10 (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, 10 qubits)
[11, 19, 22, 33, 57, 60, 63, 74, 75, 76]
d_Z 7 · witness weight 7 (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, 7 qubits)
[19, 47, 53, 56, 61, 72, 101]
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 26 · H_Z 26
qubit degrees H_X 2–14 (mean 7.776) · H_Z 4–17 (mean 10.206)
trapping sets H_X (1,2)×2 (2,2)×3 (3,2)×5 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 2 (1,3): 6 (1,4): 14 (1,5): 18 (1,6): 12 (1,7): 3 (1,8): 2 (1,9): 5 (1,10): 12 (1,11): 16 (1,12): 11 (1,13): 2 (1,14): 4 (2,2): 3 (2,3): 7 (2,4): 19 (2,5): 64 (2,6): 135 (2,7): 186 (2,8): 240 (2,9): 287 (2,10): 322 (2,11): 505 (2,12): 600 (2,13): 640 (2,14): 544 (2,15): 367 (2,16): 261 (2,17): 176 (2,18): 89 (2,19): 50 (2,20): 31 (2,21): 4 (2,22): 2 (3,2): 5 (3,3): 16 (3,4): 68 (3,5): 248 (3,6): 616 (3,7): 1442 (3,8): 2926 (3,9): 5330 (3,10): 8931 (3,11): 13216 (3,12): 17564 (3,13): 21437 (3,14): 23236 (3,15): 22423 (3,16): 18822 (3,17): 14204 (3,18): 9294 (3,19): 5551 (3,20): 3005 (3,21): 1480 (3,22): 659 (3,23): 281 (3,24): 94 (3,25): 25 (3,26): 5
trapping sets H_Z (1,4)×3 (2,3)×1 (3,4)×1 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,4): 3 (1,5): 7 (1,6): 17 (1,7): 21 (1,8): 5 (1,10): 1 (1,12): 8 (1,13): 7 (1,14): 18 (1,15): 14 (1,16): 5 (1,17): 1 (2,3): 1 (2,4): 1 (2,5): 7 (2,6): 14 (2,7): 45 (2,8): 75 (2,9): 145 (2,10): 223 (2,11): 261 (2,12): 251 (2,13): 254 (2,14): 316 (2,15): 466 (2,16): 573 (2,17): 612 (2,18): 549 (2,19): 425 (2,20): 280 (2,21): 168 (2,22): 125 (2,23): 71 (2,24): 36 (2,25): 19 (2,26): 7 (2,27): 2 (3,4): 1 (3,5): 9 (3,6): 41 (3,7): 113 (3,8): 249 (3,9): 604 (3,10): 1170 (3,11): 2157 (3,12): 3750 (3,13): 6265 (3,14): 9340 (3,15): 12717 (3,16): 15954 (3,17): 18974 (3,18): 21149 (3,19): 21787 (3,20): 20386 (3,21): 17099 (3,22): 12716 (3,23): 8637 (3,24): 5238 (3,25): 3114 (3,26): 1689 (3,27): 868 (3,28): 469 (3,29): 224 (3,30): 99 (3,31): 30 (3,32): 14 (3,33): 1

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction priced calculus E-PUNCTURE transform of codes/108-8-12.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

[[107,33,7]] — priced calculus E-PUNCTURE transform of codes/108-8-12.json

Direction & hypothesis

Weight-26 unrestricted CSS cell. Transform a connected CSS parent (codes/108-8-12.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-PUNCTURE. Parent: codes/108-8-12.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/108-8-12.json.

Tools

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

Reproduction

Rebuild H_X/H_Z from codes/108-8-12.json by applying the E-PUNCTURE move of the priced calculus; re-run the witness search at the stated budget.

Parity checks

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