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[[103,71,2]] d ≤
n
103
k
71
d
2
kd²/n
2.75728
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)
[43, 59]
d_Z 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[1, 76, 95]
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 1.864) · H_Z 1–3 (mean 1.864)
trapping sets H_X (1,1)×37 (2,0)×50 (3,0)×272 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 37 (1,2): 43 (1,3): 23 (2,0): 50 (2,1): 221 (2,2): 356 (2,3): 277 (2,4): 78 (3,0): 272 (3,1): 1448 (3,2): 3440 (3,3): 3987 (3,4): 2554 (3,5): 908 (3,6): 220 (3,7): 26
trapping sets H_Z (1,1)×30 (2,0)×50 (3,0)×192 (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): 57 (1,3): 16 (2,0): 50 (2,1): 234 (2,2): 416 (2,3): 240 (2,4): 45 (3,0): 192 (3,1): 1672 (3,2): 3942 (3,3): 3811 (3,4): 2068 (3,5): 706 (3,6): 139 (3,7): 15

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

[[103,71,2]] greedy 3 from 107-61-2

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/107-61-2.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/107-61-2.json, apply E-PUNCTURE on the target sector, and repeat greedily with Pareto ranking and staged deep-verify.

Parity checks

X-checks 16 (max weight 12) · Z-checks 16 (max weight 12)
H_X (16 checks, sparse supports)
[3, 14, 16, 27, 34, 44, 53, 60, 71, 84, 85, 96] [4, 15, 17, 25, 35, 45, 51, 61, 72, 82, 86, 94] [7, 13, 20, 28, 38, 47, 54, 63, 75, 79, 89, 97] [5, 11, 21, 29, 39, 46, 55, 62, 73, 80, 90, 98] [0, 9, 22, 33, 40, 49, 58, 65, 68, 78, 91, 102] [1, 10, 23, 31, 41, 50, 57, 66, 69, 76, 92, 100] [0, 12, 23, 25, 36, 43, 53, 61, 68, 80, 93, 94] [1, 13, 24, 26, 34, 44, 51, 59, 69, 81, 91, 95] [3, 14, 20, 28, 39, 46, 56, 63, 71, 83, 90, 97] [6, 9, 17, 31, 42, 48, 58, 66, 74, 77, 87, 100] [7, 10, 18, 32, 40, 49, 57, 64, 75, 78, 85, 101] [0, 10, 21, 33, 35, 43, 52, 59, 67, 78, 90, 100] [1, 8, 19, 31, 36, 44, 53, 60, 68, 76, 88, 101] [2, 12, 23, 29, 37, 47, 54, 63, 72, 80, 92, 99] [3, 13, 24, 30, 38, 46, 55, 62, 70, 81, 93, 97] [5, 14, 17, 26, 40, 50, 57, 66, 75, 83, 86, 96]
H_Z (16 checks, sparse supports)
[0, 9, 16, 32, 42, 45, 58, 61, 67, 77, 85, 102] [1, 10, 17, 33, 40, 43, 57, 59, 68, 78, 86, 100] [3, 12, 19, 29, 36, 47, 53, 63, 70, 80, 88, 99] [4, 13, 20, 30, 34, 46, 51, 62, 71, 81, 89, 97] [6, 14, 22, 26, 39, 50, 56, 66, 73, 83, 91, 96] [7, 15, 23, 27, 37, 48, 54, 64, 74, 84, 92, 94] [1, 9, 17, 25, 41, 50, 58, 66, 69, 76, 86, 94] [4, 12, 20, 28, 38, 45, 56, 61, 72, 79, 89, 97] [2, 13, 21, 29, 39, 43, 54, 59, 70, 80, 90, 98] [3, 11, 19, 30, 37, 44, 55, 60, 71, 81, 88, 99] [7, 14, 23, 31, 35, 47, 53, 63, 75, 82, 92, 100] [5, 15, 24, 32, 36, 46, 51, 62, 73, 83, 93, 101] [7, 10, 17, 26, 34, 49, 51, 66, 75, 78, 85, 95] [5, 8, 18, 27, 35, 50, 52, 64, 73, 76, 86, 96] [6, 9, 16, 25, 36, 48, 53, 65, 74, 77, 87, 94] [4, 15, 23, 32, 40, 44, 57, 61, 72, 84, 91, 101]
Code ID 103-71-2 · download JSON · raw on GitHub