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[[102,19,2]] d ≤
n
102
k
19
d
2
kd²/n
0.745098
w
4
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 2, d_Z ≤ 2 · w_X = 4, w_Z = 4 (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 found by @mathysrennela · gf2_fast · found at 2000 trials · 2026-11-13
witness operator (support, 2 qubits)
[10, 14]
d_Z 2 · witness weight 2 (claimed upper_bound)
witness operator (support, 2 qubits)
[2, 5]
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 8 · H_Z 8 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 2–4 (mean 3.512) · H_Z 2–4 (mean 3.405)
qubit degrees H_X 1–2 (mean 1.412) · H_Z 1–2 (mean 1.402)
trapping sets H_X (1,1)×60 (2,0)×22 (3,0)×82 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 60 (1,2): 42 (2,0): 22 (2,1): 114 (2,2): 58 (3,0): 82 (3,1): 157 (3,2): 109 (3,3): 70 (3,4): 14
trapping sets H_Z (1,1)×61 (2,0)×21 (3,0)×77 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 61 (1,2): 41 (2,0): 21 (2,1): 110 (2,2): 55 (3,0): 77 (3,1): 145 (3,2): 103 (3,3): 67 (3,4): 12

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 ≤ 4 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[102,19,2]] greedy 3 from 106-15-2

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/106-15-2.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/106-15-2.json, apply E-PUNCTURE on the target sector, and repeat greedily with Pareto ranking and staged deep-verify.

Parity checks

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