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[[140,92,2]] d ≤
n
140
k
92
d
2
kd²/n
2.62857
w
12
X/Z
1.5

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Distance

X/Z asymmetry 1.5 · d_X ≤ 2, 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 2 · witness weight 2 (claimed upper_bound)
witness operator (support, 2 qubits)
[24, 55]
d_Z 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[73, 87, 102]
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 12
qubit degrees H_X 1–3 (mean 2.057) · H_Z 1–3 (mean 2.057)
trapping sets H_X (1,1)×31 (2,0)×30 (3,0)×161 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 31 (1,2): 70 (1,3): 39 (2,0): 30 (2,1): 213 (2,2): 516 (2,3): 550 (2,4): 181 (3,0): 161 (3,1): 1452 (3,2): 4532 (3,3): 7200 (3,4): 5852 (3,5): 2345 (3,6): 658 (3,7): 128
trapping sets H_Z (1,1)×30 (2,0)×27 (3,0)×158 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 30 (1,2): 72 (1,3): 38 (2,0): 27 (2,1): 232 (2,2): 510 (2,3): 532 (2,4): 189 (3,0): 158 (3,1): 1464 (3,2): 4553 (3,3): 7132 (3,4): 5741 (3,5): 2370 (3,6): 679 (3,7): 147

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction code-calculus v0.2rc E-PUNCTURE
model Beam 1.0 (claimed, not verified)
date 2026-11-13
notes Generated by the priced construction calculus. Distance is reported only with witness-backed upper bounds; lower interval bounds are kept in the separate local ledger.
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

[[140,92,2]] greedy 2 from 143-79-2

Direction & hypothesis

Unrestricted-weight CSS parents with 99 <= n <= 400, searched with the priced construction calculus (code-calculus v0.2rc) greedy multi-step composition. The rule used on this step is E-PUNCTURE.

What was searched

Greedy multi-step composition of C-DELETE-CHECK / E-PEEL / E-PUNCTURE with sector-targeted planning, sector swap, bounded support search, and Pareto ranking. This candidate is step 2 of a chain from codes/143-79-2.json (target sector X).

Evidence trail

Staged deep-verify (2k -> 20k -> 200k -> 2M trials, multi-seed) kept the screened distance unchanged; the witness-backed upper bound is d_X <= 2, d_Z <= 2. No downgrade at any depth.

Dead ends

Parents whose display carries a dependent generator produce no derivable child; candidates whose deep-verified slug collides with an existing board entry are skipped.

Tools

Model: Beam 1.0. Harness: code-calculus v0.2rc greedy gated campaign with the verifier's staged deep-verify used before submission.

Reproduction

Start from codes/143-79-2.json, apply E-PUNCTURE on the target sector, and repeat greedily with Pareto ranking and staged deep-verify.

Parity checks

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