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[[89,49,3]] d ≤
n
89
k
49
d
3
kd²/n
4.95506
w
31
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 3, d_Z ≤ 3 · w_X = 31, w_Z = 31 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 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)
[76, 79, 80]
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)
[23, 24, 27]
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 31 · H_Z 31
qubit degrees H_X 4–14 (mean 8.011) · H_Z 1–11 (mean 5.921)
trapping sets H_X (1,4)×7 (2,1)×1 (3,0)×2 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,4): 7 (1,5): 6 (1,6): 13 (1,7): 15 (1,8): 16 (1,9): 7 (1,10): 10 (1,11): 6 (1,12): 4 (1,13): 3 (1,14): 2 (2,1): 1 (2,2): 3 (2,3): 8 (2,4): 32 (2,5): 67 (2,6): 128 (2,7): 210 (2,8): 309 (2,9): 468 (2,10): 579 (2,11): 568 (2,12): 503 (2,13): 350 (2,14): 217 (2,15): 92 (2,16): 37 (2,17): 6 (2,18): 1 (3,0): 2 (3,1): 12 (3,2): 38 (3,3): 93 (3,4): 292 (3,5): 785 (3,6): 1753 (3,7): 3783 (3,8): 6961 (3,9): 11386 (3,10): 15514 (3,11): 18327 (3,12): 17924 (3,13): 14417 (3,14): 9387 (3,15): 4898 (3,16): 2324 (3,17): 938 (3,18): 336 (3,19): 106 (3,20): 39 (3,21): 7 (3,23): 1
trapping sets H_Z (1,1)×1 (2,1)×7 (3,0)×11 (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): 5 (1,3): 10 (1,4): 10 (1,5): 10 (1,6): 17 (1,7): 12 (1,8): 11 (1,9): 9 (1,10): 3 (1,11): 1 (2,1): 7 (2,2): 28 (2,3): 59 (2,4): 133 (2,5): 253 (2,6): 424 (2,7): 584 (2,8): 634 (2,9): 570 (2,10): 327 (2,11): 177 (2,12): 67 (2,13): 22 (2,14): 4 (2,15): 2 (3,0): 11 (3,1): 55 (3,2): 235 (3,3): 806 (3,4): 2316 (3,5): 5527 (3,6): 10549 (3,7): 16421 (3,8): 19752 (3,9): 18600 (3,10): 13713 (3,11): 7978 (3,12): 3659 (3,13): 1273 (3,14): 418 (3,15): 99 (3,16): 16 (3,17): 1

Circuit tier

syndrome-extraction memory circuits committed under circuits/89-49-3/ · canonical noise recipe, 3 rounds, stim 1.16.0
d_circ ≤ 3 (min over bases; penalty-only, clamped to ≤ d)
d_circ^X 3 · fault-set witness of 3 mechanisms (claimed upper_bound)
witness fault set (mechanism indices in the committed .dem, 3)
[40140, 40142, 40333]
d_circ^Z 3 · fault-set witness of 3 mechanisms (claimed upper_bound)
witness fault set (mechanism indices in the committed .dem, 3)
[206, 1741, 5030]
no measured logical error rate yet; d_circ is a floor, and the measured tier records the prefactor it cannot see

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction priced calculus E-PUNCTURE transform of codes/90-20-7.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

[[89,49,3]] — priced calculus E-PUNCTURE transform of codes/90-20-7.json

Direction & hypothesis

Weight-31 unrestricted CSS cell. Transform a connected CSS parent (codes/90-20-7.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/90-20-7.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/90-20-7.json.

Tools

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

Reproduction

Rebuild H_X/H_Z from codes/90-20-7.json by applying the E-PUNCTURE move of the priced calculus; re-run the witness search at the stated budget.

Parity checks

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