[[142,84,2]] · QEC Challenge

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[[142,84,2]] d ≤

142

kd²/n

2.3662

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, 56]

d_Z 3 · witness weight 3 (claimed upper_bound)

witness operator (support, 3 qubits)

[74, 89, 104]

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 2.451) · H_Z 1–3 (mean 2.451)

trapping sets H_X (1,1)×11 (2,0)×6 (3,0)×30 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_X

(1,1): 11 (1,2): 56 (1,3): 75 (2,0): 6 (2,1): 95 (2,2): 346 (2,3): 705 (2,4): 619 (3,0): 30 (3,1): 433 (3,2): 2560 (3,3): 7082 (3,4): 10815 (3,5): 7869 (3,6): 1501 (3,7): 816

trapping sets H_Z (1,1)×7 (2,0)×8 (3,0)×30 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_Z

(1,1): 7 (1,2): 64 (1,3): 71 (2,0): 8 (2,1): 94 (2,2): 377 (2,3): 699 (2,4): 596 (3,0): 30 (3,1): 440 (3,2): 2686 (3,3): 7277 (3,4): 10752 (3,5): 7626 (3,6): 1391 (3,7): 840

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

[[142,84,2]] greedy 0 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 0 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 29 (max weight 12) · Z-checks 29 (max weight 12)

H_X (29 checks, sparse supports)

[3, 20, 24, 34, 49, 59, 73, 85, 99, 114, 119, 130] [4, 21, 25, 35, 46, 60, 70, 82, 100, 115, 120, 131] [5, 18, 22, 36, 47, 61, 71, 83, 101, 116, 121, 132] [6, 19, 23, 37, 48, 58, 72, 84, 98, 117, 118, 133] [7, 17, 29, 39, 50, 64, 74, 86, 104, 111, 124, 135] [8, 14, 26, 40, 51, 65, 75, 87, 105, 112, 125, 136] [9, 15, 27, 41, 52, 62, 76, 88, 102, 113, 122, 137] [0, 12, 32, 42, 57, 67, 81, 93, 95, 106, 127, 138] [1, 13, 33, 43, 54, 68, 78, 90, 96, 107, 128, 139] [2, 11, 31, 45, 56, 66, 80, 92, 94, 109, 126, 141] [1, 14, 32, 36, 46, 61, 70, 85, 97, 111, 126, 131] [2, 16, 30, 34, 48, 59, 72, 83, 95, 113, 128, 133] [0, 17, 31, 35, 49, 60, 73, 84, 96, 110, 129, 130] [4, 18, 28, 40, 50, 65, 74, 89, 101, 115, 122, 135] [5, 19, 29, 41, 51, 62, 75, 86, 98, 116, 123, 136] [6, 20, 26, 38, 52, 63, 76, 87, 99, 117, 124, 137] [3, 21, 27, 39, 53, 64, 77, 88, 100, 114, 125, 134] [7, 10, 24, 44, 54, 69, 78, 93, 105, 107, 118, 139] [8, 11, 25, 45, 55, 66, 79, 90, 102, 108, 119, 140] [9, 12, 22, 42, 56, 67, 80, 91, 103, 109, 120, 141] [2, 11, 26, 44, 48, 58, 71, 82, 97, 109, 123, 138] [0, 12, 27, 45, 49, 59, 72, 83, 94, 106, 124, 139] [1, 13, 28, 42, 46, 60, 73, 84, 95, 107, 125, 140] [6, 15, 30, 40, 52, 62, 75, 86, 101, 113, 127, 134] [3, 16, 31, 41, 53, 63, 76, 87, 98, 110, 128, 135] [4, 17, 32, 38, 50, 64, 77, 88, 99, 111, 129, 136] [5, 14, 33, 39, 51, 65, 74, 89, 100, 112, 126, 137] [9, 19, 22, 36, 56, 66, 79, 90, 105, 117, 119, 130] [7, 21, 24, 34, 54, 68, 81, 92, 103, 115, 121, 132]

H_Z (29 checks, sparse supports)

[1, 10, 25, 42, 57, 59, 78, 85, 95, 106, 120, 140] [2, 12, 23, 44, 55, 61, 80, 83, 97, 108, 118, 138] [0, 13, 24, 45, 56, 58, 81, 84, 94, 109, 119, 139] [4, 14, 29, 38, 49, 63, 70, 89, 99, 110, 124, 136] [5, 15, 26, 39, 46, 64, 71, 86, 100, 111, 125, 137] [6, 16, 27, 40, 47, 65, 72, 87, 101, 112, 122, 134] [3, 17, 28, 41, 48, 62, 73, 88, 98, 113, 123, 135] [7, 18, 33, 34, 53, 67, 74, 93, 103, 114, 128, 132] [8, 19, 30, 35, 50, 68, 75, 90, 104, 115, 129, 133] [9, 20, 31, 36, 51, 69, 76, 91, 105, 116, 126, 130] [1, 11, 22, 37, 54, 69, 80, 90, 97, 107, 118, 132] [2, 13, 24, 35, 56, 67, 78, 92, 95, 109, 120, 130] [0, 10, 25, 36, 57, 68, 79, 93, 96, 106, 121, 131] [4, 15, 26, 41, 50, 61, 76, 82, 101, 111, 122, 136] [5, 16, 27, 38, 51, 58, 77, 83, 98, 112, 123, 137] [6, 17, 28, 39, 52, 59, 74, 84, 99, 113, 124, 134] [3, 14, 29, 40, 53, 60, 75, 85, 100, 110, 125, 135] [7, 19, 30, 45, 46, 65, 72, 86, 105, 115, 126, 140] [8, 20, 31, 42, 47, 62, 73, 87, 102, 116, 127, 141] [9, 21, 32, 43, 48, 63, 70, 88, 103, 117, 128, 138] [9, 11, 23, 34, 49, 66, 72, 92, 102, 109, 119, 130] [7, 13, 25, 36, 47, 68, 70, 90, 104, 107, 121, 132] [8, 10, 22, 37, 48, 69, 71, 91, 105, 108, 118, 133] [2, 15, 27, 38, 53, 62, 76, 88, 94, 113, 123, 134] [0, 16, 28, 39, 50, 63, 77, 89, 95, 110, 124, 135] [1, 17, 29, 40, 51, 64, 74, 86, 96, 111, 125, 136] [6, 19, 31, 42, 57, 58, 80, 84, 98, 117, 127, 138] [3, 20, 32, 43, 54, 59, 81, 85, 99, 114, 128, 139] [4, 21, 33, 44, 55, 60, 78, 82, 100, 115, 129, 140]

Code ID 142-84-2 · download JSON · raw on GitHub