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[[171,49,7]] d ≤
n
171
k
49
d
7
kd²/n
14.0409
w
12
X/Z
1
g
0.0069
r
6.7082
layers
2
swaps
731

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Distance

X/Z asymmetry 1 · d_X ≤ 7, d_Z ≤ 7 · 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 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)
[69, 73, 76, 77, 149, 155, 156]
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)
[80, 85, 93, 95, 140, 145, 154]
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 9–12 (mean 9.656) · H_Z 9–12 (mean 9.656)
qubit degrees H_X 1–9 (mean 3.444) · H_Z 1–9 (mean 3.444)
trapping sets H_X (1,1)×19 (2,1)×21 (3,1)×7 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 19 (1,2): 21 (1,3): 56 (1,4): 42 (1,5): 21 (1,7): 10 (1,8): 1 (1,9): 1 (2,1): 21 (2,2): 126 (2,3): 203 (2,4): 441 (2,5): 315 (2,6): 322 (2,7): 72 (2,8): 236 (2,9): 211 (2,10): 186 (2,11): 45 (2,12): 10 (3,1): 7 (3,2): 308 (3,3): 980 (3,4): 2646 (3,5): 5040 (3,6): 4186 (3,7): 4771 (3,8): 3384 (3,9): 4822 (3,10): 6726 (3,11): 6351 (3,12): 4362 (3,13): 2404 (3,14): 882 (3,15): 728 (3,16): 161 (3,17): 70 (3,19): 1
trapping sets H_Z (1,1)×19 (2,1)×21 (3,1)×7 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 19 (1,2): 21 (1,3): 56 (1,4): 42 (1,5): 21 (1,7): 10 (1,8): 1 (1,9): 1 (2,1): 21 (2,2): 126 (2,3): 203 (2,4): 441 (2,5): 315 (2,6): 322 (2,7): 72 (2,8): 236 (2,9): 211 (2,10): 186 (2,11): 45 (2,12): 10 (3,1): 7 (3,2): 308 (3,3): 980 (3,4): 2646 (3,5): 5040 (3,6): 4186 (3,7): 4771 (3,8): 3384 (3,9): 4822 (3,10): 6726 (3,11): 6351 (3,12): 4362 (3,13): 2404 (3,14): 882 (3,15): 728 (3,16): 161 (3,17): 70 (3,19): 1
witness diameter X 6.3246 · Z 9.2195 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)

Circuit tier

syndrome-extraction memory circuits committed under circuits/171-49-7/ · canonical noise recipe, 7 rounds, stim 1.16.0
d_circ ≤ 7 (min over bases; penalty-only, clamped to ≤ d)
d_circ^X 7 · fault-set witness of 7 mechanisms (claimed upper_bound)
witness fault set (mechanism indices in the committed .dem, 7)
[100963, 100969, 101012, 101015, 101085, 101088, 101131]
d_circ^Z 7 · fault-set witness of 7 mechanisms (claimed upper_bound)
witness fault set (mechanism indices in the committed .dem, 7)
[101047, 101051, 101095, 101099, 101103, 101107, 101133]
no measured logical error rate yet; d_circ is a floor, and the measured tier records the prefactor it cannot see

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
layout contributed by @vprusso · Inherited from the laid-out parent codes/172-48-8.json: the parent's coordinates with the entry of the removed qubit (parent index 153) dropped, since this puncture child keeps the parent's qubit order. Radius, layer count, and class re-measured by the verifier. · 2026-11-04
r = 6.708
X checkZ checkqubit site (89)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
routing cost 731 nearest-neighbor SWAPs per round in total, at most 12 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction priced calculus E-PUNCTURE transform of codes/172-48-8.json
model Beam 1.0 (claimed, not verified)
date 2026-11-02
family other (a tag, not a ranking)
locality 2D-local bilayer (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

[[171,49,7]] — priced calculus E-PUNCTURE transform of codes/172-48-8.json

Direction & hypothesis

Weight-12 unrestricted CSS cell. Transform a connected CSS parent (codes/172-48-8.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/172-48-8.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/172-48-8.json.

Tools

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

Reproduction

Rebuild H_X/H_Z from codes/172-48-8.json by applying the E-PUNCTURE move of the priced calculus; re-run the witness search at the stated budget.

Parity checks

X-checks 61 (max weight 12) · Z-checks 61 (max weight 12)
H_X (61 checks, sparse supports)
[0, 20, 40, 60, 80, 100, 120, 140, 166] [1, 21, 41, 61, 81, 101, 121, 141, 166, 169, 170] [2, 22, 42, 62, 82, 102, 122, 142, 167, 169, 170] [3, 23, 43, 63, 83, 103, 123, 143, 166, 170] [4, 24, 44, 64, 84, 104, 124, 144, 165, 170] [5, 25, 45, 65, 85, 105, 125, 145, 167, 170] [6, 26, 46, 66, 86, 106, 126, 146, 167, 168] [7, 27, 47, 67, 87, 107, 127, 147, 165, 168, 170] [8, 28, 48, 68, 88, 108, 128, 148, 165, 169] [9, 29, 49, 69, 89, 109, 129, 149, 166, 168, 169, 170] [10, 30, 50, 70, 90, 110, 130, 150, 166, 169] [11, 31, 51, 71, 91, 111, 131, 151, 167, 168, 170] [12, 32, 52, 72, 92, 112, 132, 152, 167, 169] [14, 34, 54, 74, 94, 114, 134, 153, 167] [15, 35, 55, 75, 95, 115, 135, 154, 165, 168] [16, 36, 56, 76, 96, 116, 136, 155, 166, 168, 169] [17, 37, 57, 77, 97, 117, 137, 156, 165, 166, 167, 168] [18, 38, 58, 78, 98, 118, 138, 157, 165] [19, 39, 59, 79, 99, 119, 139, 158, 165, 169, 170] [4, 7, 8, 13, 15, 17, 18, 19, 159] [0, 1, 3, 9, 10, 13, 16, 17, 160] [2, 5, 6, 11, 12, 13, 14, 17, 161] [6, 7, 9, 11, 13, 15, 16, 17, 162] [1, 2, 8, 9, 10, 12, 16, 19, 163] [1, 2, 3, 4, 5, 7, 9, 11, 13, 19, 164] [24, 27, 28, 33, 35, 37, 38, 39, 159] [20, 21, 23, 29, 30, 33, 36, 37, 160] [22, 25, 26, 31, 32, 33, 34, 37, 161] [26, 27, 29, 31, 33, 35, 36, 37, 162] [21, 22, 28, 29, 30, 32, 36, 39, 163] [21, 22, 23, 24, 25, 27, 29, 31, 33, 39, 164] [44, 47, 48, 53, 55, 57, 58, 59, 159] [40, 41, 43, 49, 50, 53, 56, 57, 160] [42, 45, 46, 51, 52, 53, 54, 57, 161] [46, 47, 49, 51, 53, 55, 56, 57, 162] [41, 42, 48, 49, 50, 52, 56, 59, 163] [41, 42, 43, 44, 45, 47, 49, 51, 53, 59, 164] [64, 67, 68, 73, 75, 77, 78, 79, 159] [60, 61, 63, 69, 70, 73, 76, 77, 160] [62, 65, 66, 71, 72, 73, 74, 77, 161] [66, 67, 69, 71, 73, 75, 76, 77, 162] [61, 62, 68, 69, 70, 72, 76, 79, 163] [61, 62, 63, 64, 65, 67, 69, 71, 73, 79, 164] [84, 87, 88, 93, 95, 97, 98, 99, 159] [80, 81, 83, 89, 90, 93, 96, 97, 160] [82, 85, 86, 91, 92, 93, 94, 97, 161] [86, 87, 89, 91, 93, 95, 96, 97, 162] [81, 82, 88, 89, 90, 92, 96, 99, 163] [81, 82, 83, 84, 85, 87, 89, 91, 93, 99, 164] [104, 107, 108, 113, 115, 117, 118, 119, 159] [100, 101, 103, 109, 110, 113, 116, 117, 160] [102, 105, 106, 111, 112, 113, 114, 117, 161] [106, 107, 109, 111, 113, 115, 116, 117, 162] [101, 102, 108, 109, 110, 112, 116, 119, 163] [101, 102, 103, 104, 105, 107, 109, 111, 113, 119, 164] [124, 127, 128, 133, 135, 137, 138, 139, 159] [120, 121, 123, 129, 130, 133, 136, 137, 160] [122, 125, 126, 131, 132, 133, 134, 137, 161] [126, 127, 129, 131, 133, 135, 136, 137, 162] [121, 122, 128, 129, 130, 132, 136, 139, 163] [121, 122, 123, 124, 125, 127, 129, 131, 133, 139, 164]
H_Z (61 checks, sparse supports)
[0, 20, 40, 60, 80, 100, 120, 140, 160] [1, 21, 41, 61, 81, 101, 121, 141, 160, 163, 164] [2, 22, 42, 62, 82, 102, 122, 142, 161, 163, 164] [3, 23, 43, 63, 83, 103, 123, 143, 160, 164] [4, 24, 44, 64, 84, 104, 124, 144, 159, 164] [5, 25, 45, 65, 85, 105, 125, 145, 161, 164] [6, 26, 46, 66, 86, 106, 126, 146, 161, 162] [7, 27, 47, 67, 87, 107, 127, 147, 159, 162, 164] [8, 28, 48, 68, 88, 108, 128, 148, 159, 163] [9, 29, 49, 69, 89, 109, 129, 149, 160, 162, 163, 164] [10, 30, 50, 70, 90, 110, 130, 150, 160, 163] [11, 31, 51, 71, 91, 111, 131, 151, 161, 162, 164] [12, 32, 52, 72, 92, 112, 132, 152, 161, 163] [14, 34, 54, 74, 94, 114, 134, 153, 161] [15, 35, 55, 75, 95, 115, 135, 154, 159, 162] [16, 36, 56, 76, 96, 116, 136, 155, 160, 162, 163] [17, 37, 57, 77, 97, 117, 137, 156, 159, 160, 161, 162] [18, 38, 58, 78, 98, 118, 138, 157, 159] [19, 39, 59, 79, 99, 119, 139, 158, 159, 163, 164] [4, 7, 8, 13, 15, 17, 18, 19, 165] [0, 1, 3, 9, 10, 13, 16, 17, 166] [2, 5, 6, 11, 12, 13, 14, 17, 167] [6, 7, 9, 11, 13, 15, 16, 17, 168] [1, 2, 8, 9, 10, 12, 16, 19, 169] [1, 2, 3, 4, 5, 7, 9, 11, 13, 19, 170] [24, 27, 28, 33, 35, 37, 38, 39, 165] [20, 21, 23, 29, 30, 33, 36, 37, 166] [22, 25, 26, 31, 32, 33, 34, 37, 167] [26, 27, 29, 31, 33, 35, 36, 37, 168] [21, 22, 28, 29, 30, 32, 36, 39, 169] [21, 22, 23, 24, 25, 27, 29, 31, 33, 39, 170] [44, 47, 48, 53, 55, 57, 58, 59, 165] [40, 41, 43, 49, 50, 53, 56, 57, 166] [42, 45, 46, 51, 52, 53, 54, 57, 167] [46, 47, 49, 51, 53, 55, 56, 57, 168] [41, 42, 48, 49, 50, 52, 56, 59, 169] [41, 42, 43, 44, 45, 47, 49, 51, 53, 59, 170] [64, 67, 68, 73, 75, 77, 78, 79, 165] [60, 61, 63, 69, 70, 73, 76, 77, 166] [62, 65, 66, 71, 72, 73, 74, 77, 167] [66, 67, 69, 71, 73, 75, 76, 77, 168] [61, 62, 68, 69, 70, 72, 76, 79, 169] [61, 62, 63, 64, 65, 67, 69, 71, 73, 79, 170] [84, 87, 88, 93, 95, 97, 98, 99, 165] [80, 81, 83, 89, 90, 93, 96, 97, 166] [82, 85, 86, 91, 92, 93, 94, 97, 167] [86, 87, 89, 91, 93, 95, 96, 97, 168] [81, 82, 88, 89, 90, 92, 96, 99, 169] [81, 82, 83, 84, 85, 87, 89, 91, 93, 99, 170] [104, 107, 108, 113, 115, 117, 118, 119, 165] [100, 101, 103, 109, 110, 113, 116, 117, 166] [102, 105, 106, 111, 112, 113, 114, 117, 167] [106, 107, 109, 111, 113, 115, 116, 117, 168] [101, 102, 108, 109, 110, 112, 116, 119, 169] [101, 102, 103, 104, 105, 107, 109, 111, 113, 119, 170] [124, 127, 128, 133, 135, 137, 138, 139, 165] [120, 121, 123, 129, 130, 133, 136, 137, 166] [122, 125, 126, 131, 132, 133, 134, 137, 167] [126, 127, 129, 131, 133, 135, 136, 137, 168] [121, 122, 128, 129, 130, 132, 136, 139, 169] [121, 122, 123, 124, 125, 127, 129, 131, 133, 139, 170]
Code ID 171-49-7 · download JSON · raw on GitHub