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[[108,60,2]] d ≤
n
108
k
60
d
2
kd²/n
2.22222
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 2, d_Z ≤ 2 · w_X = 8, w_Z = 8 (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)
[78, 79]
d_Z 2 · witness weight 2 (claimed upper_bound)
witness operator (support, 2 qubits)
[78, 79]
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 8 · H_Z 8
qubit degrees H_X 1–2 (mean 1.63) · H_Z 1–2 (mean 1.926)
trapping sets H_X (1,1)×40 (2,0)×70 (3,0)×168 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 40 (1,2): 68 (2,0): 70 (2,1): 208 (2,2): 304 (3,0): 168 (3,1): 1032 (3,2): 1840 (3,3): 352 (3,4): 288
trapping sets H_Z (1,1)×8 (2,0)×54 (3,1)×312 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 8 (1,2): 100 (2,0): 54 (2,1): 48 (2,2): 576 (3,1): 312 (3,2): 3912 (3,3): 96 (3,4): 736

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction code-calculus v0.2rc C-DELETE-CHECK
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

[[108,60,2]] greedy 3 from 108-56-2

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 C-DELETE-CHECK.

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/108-56-2.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/108-56-2.json, apply C-DELETE-CHECK on the target sector, and repeat greedily with Pareto ranking and staged deep-verify.

Parity checks

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