n
52
Construct the plain-fold parameters reported in Section VII.4 of Jong Yeon Lee, Koki Okada, Nishad Maskara, Kenta Kasai and Hengyun Zhou, arXiv:2609.30069v1. The construction and parameters are published work; metadata records known_parameters. The published parent is [[104,30,8]], represented by codes/104-30-8.json on this board and credited there to Jong Yeon Lee's contribution to the Okada–Kasai CPM catalogue, arXiv:2607.14091.
This targets the weight-8, unrestricted stabilizer Pareto frontier at a small blocklength and high rate. Its witnessed score is 15*7²/52 = 14.134615. At main commit 0ad745c011ce7393c921a39cf35fe760090222c4, this exceeds every merged weight-8 stabilizer score except [[144,10,16]] and [[96,10,12]]. It trades lower distance for fewer physical qubits and more logical qubits. This is a literature reproduction, not a claim of new parameters or a category-wide maximum. Scores depend on the retained distance upper bound.
This was a targeted reconstruction, not a random code-family sweep. We used the exact parent exponent arrays recorded in the existing base entry. We enumerated the 105 perfect matchings of eight block columns, six block-row permutations and 13 possible first-row offsets, solving Proposition 4 with plain sign eta=+1. The explicit accepted map is given below.
The trusted stabilizer submission builder used 2,000 direct Pauli RIS trials, seed 31010052, and returned a weight-7 logical. An independent direct audit requested 20,000 trials with a 90-second cap, seed 31010152 and pair depth 20; it returned weight 7 after 35.02 seconds. The trial figure is the configured ceiling. A native search of the exact three-bit Pauli-to-CSS embedding used 200,000 trials per CSS side, seed 31010352, pair depth 20 and four threads, returning an X-side weight-7 logical mapping to source Pauli weight 7. Every returned logical was checked with the unchanged trusted Pauli predicate and retained.
The submission has 39 generators, stabilizer rank 37, n=52, k=15 and maximum Pauli check weight 8. The unchanged verifier accepts its structure and the weight-7 Pauli witness embedded in the JSON. The submitted distance remains upper_bound, d<=7. Agreement with the paper and the independent searches is evidence, not an exact-distance certificate.
For the three-bit audit, write the source checks as S=(A|B). We used HX=[A,0,B; I,I,I] and HZ=[B,A+B,A]. The X-side witness (u,v,w) maps to source Pauli (u+v,v+w), over GF(2). Both the embedded and source logicals were checked. The exact mapping preserves the minimum lift objective; heuristic search on that mapping does not certify the minimum.
The independent direct audit returned X support [5,20,28,38] and Z support [15,19,28,39]. The three-bit audit returned X support [12,32,35,36,44,48] and Z support [12,51]. Each has Pauli weight 7. The JSON preserves the builder's independently found witness in this same qubit ordering.
The unchanged full candidate gate passed against main commit 0ad745c011ce7393c921a39cf35fe760090222c4. It found no exact or WL duplicate, no dominator and no distance-only gain, and labelled the candidate board-advancing. Fresh refutation seed: 581601131. The receipt's 4,580-trial figure is a configured ceiling under the default 10-second cap, not an independently measured completed count. Fingerprint: f004e6b25cd148db. The gate was run before board promotion.
The same paper reports a reversing fold of the common parent with distance 6. This submission uses the plain fold with reported distance 7. No claim that arbitrary folds preserve distance is made. We did not use the native doubled-code Hamming weight as the source Pauli distance, because Y support is counted differently. No geometric layout or circuit performance is claimed.
Author: @mrvee-qC-bee. Model: GPT-6 Astra in Codex. Reconstruction used NumPy; all logical searches and validation used the challenge's unchanged trusted Pauli RIS, native RIS and GF(2) routines. The bounded confirmation took under a minute; the full board comparison adds several minutes. No trusted verifier, schema or workflow was modified.
Set P=13, with all exponent arithmetic modulo P:
E = [[0,0,0,0,0,0,0,0],
[0,7,11,5,2,12,6,3],
[0,2,7,9,1,5,4,8]]
D = [[0,4,12,3,3,12,4,0],
[0,1,3,4,1,4,0,3],
[0,5,6,11,0,5,6,11]]
sigma = [5,7,4,6,2,0,3,1]
rho = [2,0,1]
alpha = [10,2,3]
beta = [11,12,1,2,12,2,11,1]
Use parent qubit index q=13*ell+t, for ell=0,...,7 and t=0,...,12. For j=0,...,2 and s=0,...,12, in that order, the parent X-check row 13*j+s has support {13*ell+(s-E[j,ell] mod 13): ell=0,...,7}. Replace E by D for the parent Z checks. This is a stated reindexing of the catalogue's interleaved parent convention.
The identities D[j,ell]=E[rho[j],sigma[ell]]+alpha[j]+beta[ell] and beta[sigma[ell]]=-beta[ell] hold modulo 13. Thus pi(ell,t)=(sigma[ell],t+beta[ell] mod 13) is a fixed-point-free involution exchanging the CSS check spaces, as required by Proposition 4.
Enumerate the 52 pairs (q,pi(q)) with q<pi(q), in increasing q. For each parent X-check row, put an X on folded qubit i when that pair's first coordinate is in the row, and a Z when its second coordinate is in the row. An overlap is Y. Preserve parent row order and sort the two support lists within each row. These instructions recover the exact ordered submitted checks. The folding identity implies A B^T+B A^T=0; the rank is 37.
The JSON and this note are the only files required from this submission. In the challenge environment, independently recheck its structure and witness and run a fresh bounded refutation with:
uv run --frozen python verify/qldpc_verify.py codes/52-15-7.json