n
85
Reproduce the non-CSS mirror code of Andrey Boris Khesin and Jonathan Z. Lu, arXiv:2603.05496v1, Section 5. This fills a literature gap in the unrestricted weight-6 stabilizer board. At base ac8a779, the merged maximum of kd²/n is 6.0; this code's witnessed score is 648/85 = 7.623529, a 27.06% increase. This is a category-specific comparison, not an overall rank or a new-parameters claim.
This PR contains the code JSON and this note. Supplementary search artifacts are preserved separately in the author's public fork at commit b22ad301f3661436a9f24cd2b3dc72d970852a10; the links below point to that pinned snapshot, not to additional files in this PR.
Seven explicitly specified non-CSS rows from the paper's table were reconstructed. The screen used 2,000 direct Pauli RIS trials and 20,000 native doubled-code trials, seed 26100111. Each pure-X, pure-Y and pure-Z section also received 1,000 trusted RIS trials, pair depth 20, seed 26100211. The construction recipes, all seven initial witnesses and all 21 axis witnesses are retained in evidence. The search script reproduces the screen using the repository's existing stabilizer submission builder.
The submitted matrices have 85 generators of maximum Pauli weight 6, stabilizer rank 77 and k=8. The initial screen found a weight-9 nontrivial Pauli logical. Two independent deeper runs, seeds 27100119 and 77100141, each completed 20,000 direct Pauli RIS trials plus a requested 400,000 native doubled-code trials, without a wall-clock cap; each returned weight 9. These are recorded in the same evidence file and can be repeated with the deep audit script. A separate 400,000-trial native search of the exact three-bit Pauli-to-CSS embedding, seed 9510017, pair depth 8, also returned source weight 9. Its full embedded and mapped witnesses are retained; the embedding audit verifies both.
The unchanged full gate receipt reports passed=true, no exact or WL duplicate, no dominator, and an advance on axes beyond distance alone. Its independent refutation seed is 1194327455; the reported 5,900 trials are a configured ceiling under the default 10-second cap, not a measured completed count.
The submitted distance remains upper_bound. The paper reports distance 9, but neither that statement nor these heuristic searches is an official challenge certificate. No circuit or physical-noise performance is claimed. A separate local SAT attempt on the exact three-bit Pauli-to-CSS embedding timed out on the relevant X side at weight bound 8 and a requested 120-second solve budget. Its derived Z-side UNSAT result only gives the weaker source lower bound d>=5. It did not certify d=9; the attempt receipt is retained. The deterministic reproducer reconstructs the matrices exactly and checks all 31 archived logical witnesses with the trusted Pauli predicate, including the unsuccessful rows.
The paper's larger weight-7 upper bounds are loose for several reconstructed instances. Our retained witnesses give [[99,4,<=15]], [[99,6,<=9]], [[93,5,<=11]] and [[75,4,<=10]], versus table upper bounds 23, 19, 21 and 17. The weight-6 [[91,4]] row has a weight-7 pure-Y logical. These findings tighten upper bounds; they do not contradict the paper's upper-bound labels. The published [[60,4,10]] row also reproduced, but this submission focuses on the higher category efficiency of [[85,8,9]].
GPT-6 Astra, coordinated by @mrvee-qC-bee, performed the literature audit, reconstruction and validation. The original construction and parameter set are due to Khesin and Lu; metadata records known_parameters. All distance searches used the repository's Pauli RIS or native doubled-code engine. The pure-Pauli audits reduce to the trusted CSS RIS engine and check each mapped witness with the general Pauli predicate. The trusted verifier, schema and workflows are unchanged. This bounded screen and confirmation ladder took several minutes of wall time on a local workstation.
Use G=Z5 × Z17, A={(0,0),(0,1),(1,9)} and B={(0,0),(0,4),(1,2)}. Qubit (i,j) has index 17i+j. Generator g has Z on A+g and X on B−g; an overlap carries Y. Addition is componentwise modulo (5,17). Commutation follows from pairing the overlaps of A+g with B−h and A+h with B−g in an abelian group.
Enumerate generators in increasing g=(i,j), with i=0,...,4 and j=0,...,16. Sort each generator's X and Z support indices in ascending order. This gives the exact ordered checks in the submitted JSON, which also retains the weight-9 Pauli witness. The pinned supplementary reproducer implements this recipe and checks all archived witnesses; those research files are not part of this PR.
For a fresh structure, submitted-witness and refutation check from the challenge repository root, run:
uv run --frozen python verify/qldpc_verify.py codes/85-8-9.json