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[[139,94,2]] d ≤
n
139
k
94
d
2
kd²/n
2.70504
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, 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 12 · H_Z 12
qubit degrees H_X 1–3 (mean 1.986) · H_Z 1–3 (mean 1.899)
trapping sets H_X (1,1)×35 (2,0)×36 (3,0)×208 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 35 (1,2): 71 (1,3): 33 (2,0): 36 (2,1): 244 (2,2): 530 (2,3): 492 (2,4): 134 (3,0): 208 (3,1): 1709 (3,2): 4787 (3,3): 6755 (3,4): 4890 (3,5): 1863 (3,6): 525 (3,7): 84
trapping sets H_Z (1,1)×42 (2,0)×57 (3,0)×262 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 42 (1,2): 69 (1,3): 28 (2,0): 57 (2,1): 292 (2,2): 505 (2,3): 412 (2,4): 108 (3,0): 262 (3,1): 1955 (3,2): 4827 (3,3): 5966 (3,4): 3953 (3,5): 1453 (3,6): 424 (3,7): 58

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

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