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[[44,25,2]] d ≤
n
44
k
25
d
2
kd²/n
2.273
w
8
X/Z
1
g
0.0538
r
3.6056
layers
1
swaps
17

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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)
[14, 15]
d_Z 2 · witness weight 2 (claimed upper_bound)
witness operator (support, 2 qubits)
[14, 15]
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 1.636) · H_Z 1–2 (mean 1.818)
trapping sets H_X (1,1)×16 (2,0)×82 (3,1)×240 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 16 (1,2): 28 (2,0): 82 (2,1): 32 (2,2): 96 (3,1): 240 (3,2): 684
trapping sets H_Z (1,1)×8 (2,0)×66 (3,1)×184 (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): 36 (2,0): 66 (2,1): 32 (2,2): 128 (3,1): 184 (3,2): 916
witness diameter X 1.0 · Z 1.0 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 3.606
X checkZ checkqubit site (44)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release
routing cost 17 nearest-neighbor SWAPs per round in total, at most 2 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction C-DELETE-CHECK
model Beam 1.0 (claimed, not verified)
date 2026-10-20
family other (a tag, not a ranking)
locality 2D-local single (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

[[44,25,2]] — C-DELETE-CHECK reduction

Direction & hypothesis

Targeted the frontier by deleting a check from a board entry, raising k while preserving d (inherited witnesses).

What was searched

Single C-DELETE-CHECK on parents in n=41–50, all rows, inherited-witness validation, full gate.

Evidence trail

  • Parent: a board entry with n=44.
  • Delete one check → n=44, k=25, d=2.
  • Distance is a witness-backed upper bound (both sides), gate passes.
  • board_advancing: true.

Dead ends

Many deletions collapsed d via new lower-weight logicals; only a few survived the gate.

Tools

Model: Beam 1.0. Calculus: the priced construction calculus, operation C-DELETE-CHECK.

Reproduction

Apply C-DELETE-CHECK with the row id in the candidate's provenance.

Parity checks

X-checks 9 (max weight 8) · Z-checks 10 (max weight 8)
H_X (9 checks, sparse supports)
[0, 1, 20, 21, 22, 23, 42, 43] [2, 3, 4, 5, 24, 25, 26, 27] [4, 5, 6, 7, 26, 27, 28, 29] [6, 7, 8, 9, 28, 29, 30, 31] [8, 9, 10, 11, 30, 31, 32, 33] [10, 11, 12, 13, 32, 33, 34, 35] [12, 13, 14, 15, 34, 35, 36, 37] [14, 15, 16, 17, 36, 37, 38, 39] [16, 17, 18, 19, 38, 39, 40, 41]
H_Z (10 checks, sparse supports)
[0, 1, 2, 3, 22, 23, 24, 25] [2, 3, 4, 5, 24, 25, 26, 27] [4, 5, 6, 7, 26, 27, 28, 29] [6, 7, 8, 9, 28, 29, 30, 31] [8, 9, 10, 11, 30, 31, 32, 33] [10, 11, 12, 13, 32, 33, 34, 35] [12, 13, 14, 15, 34, 35, 36, 37] [14, 15, 16, 17, 36, 37, 38, 39] [16, 17, 18, 19, 38, 39, 40, 41] [18, 19, 20, 21, 40, 41, 42, 43]
Code ID 44-25-2 · download JSON · raw on GitHub