n
96
Target: the unrestricted weight-8 stabilizer board. At base revision ac8a779bc40524d56a6afdd2133eabd931c99c1f, its largest reported kd²/n was 700/75 = 9.33333 for [[75,7,10]]. This candidate has kd²/n = 15 using its witnessed d≤12, a 60.714% increase in that headline figure. The historical candidate gate found no duplicate or dominator. This is a board-relative advance, not a global record or a claim to new parameters.
The construction applies standard symplectic halving to the [[192,20,≤16]] BB cover in Table 12 of Symons, Rajput and Browne, Sequences of Bivariate Bicycle Codes from Covering Graphs, also recorded in codes/192-20-16.json. The reconstruction matches that parent's two check matrices bit for bit. Halving is not a new operation; see also Lee et al..
The parameters [[96,10,12]] already occur in CSS codes: Section 6.2 and Table 10 of the cover-code paper list an example and credit earlier instances to Lin and Pryadko. Therefore provenance.novelty is known_parameters.
There is a scoped inequivalence proof. The Table 10 CSS example has even-weight pure generators, so every stabilizer product has even Pauli weight: the X and Z products have even weight separately, and their overlap is even by CSS commutation. Our stored generator 20 has X support {2,36,44,59} and Z support {47,48,59,87}, whose union has weight 7. Local Cliffords and qubit permutations preserve Pauli weight, so our code cannot be equivalent under those operations to that published even-generator CSS example. This does not settle equivalence to every published code or establish new parameters.
Nine group-inversion folds of selected on-board BB parents were screened. Five standard weight-6 parents used 150 direct Pauli RIS trials and 1,000 native trials on the doubled CSS matrices. Four weight-8 cover parents used 2,500 Pauli trials and 50,000 native trials. The retained candidate is the fold of [[192,20,≤16]], over Z_24 × Z_4.
The final code was searched at independent seeds 61721 and 424242, each with 20,000 direct Pauli RIS trials and 400,000 native doubled-code trials, pair depth 8. Both reached weight 12. A separate pure-Pauli section audit used seed 198176, 3,000 trials per section and pair depth 20, finding pure-Y, pure-X and pure-Z witnesses of weights 12, 28 and 28 respectively. It used the repository's CSS RIS engine on the restricted sections and checked the mapped witnesses with the trusted general Pauli predicate.
The submission carries a checked weight-12 logical: X on {14,21,36,45,62,69,84,93}, Z on {14,21,38,47,62,69,86,95}. Its Pauli support is the union, counting each Y once. The supplementary witness archive retains the independent deep-search and section witnesses. All five archived witnesses were checked against the submitted stabilizer. This archive is in the public contributor fork at the pinned earlier revision; it is not part of this two-file submission.
The archived full candidate gate on the stated base returned passed: true, board_advancing: true, no exact or WL duplicate, and no dominator. Refutation seed 1420900430 found nothing lighter under the gate's reported target of 6,340 trials and its default time cap. This is historical evidence, not a substitute for PR CI. The author binding and literature metadata were subsequently corrected; checks, distance and submitted witness are unchanged. Their hashes and the trusted fingerprint tie the archived run to this artifact.
A fresh trusted verifier run on the final submission also passed, with refutation seed 1557006449 and a reported target of 6,340 trials under the default time cap. Its complete report is preserved in the pinned supplementary verification record.
The claim remains d≤12, witness-backed upper bound. The searches do not prove d=12. Separate bounded SAT attempts via a Pauli-to-CSS reduction timed out on the relevant distance queries, so they did not close this gap. No locality layout, circuit distance or exact certification is claimed. General stabilizer codes currently have no circuit tier in this repository.
The [[144,12,12]] gross-code fold screened as [[72,6,≤9]] but the trusted gate found an all-Y logical on {5,13,27,41,49,63}, lowering its bound to 6. The [[144,14,14]] weight-8 parent folded to a candidate first estimated at [[72,7,≤10]]; the pure-Y audit and gate lowered that bound to 8. These collapses motivated the additional section audit.
The doubled-code accelerator scores a Y twice in its Hamming objective. Its valid proposals can tighten a Pauli bound after rescoring, but a large native budget alone can miss light all-Y operators.
GPT-6 Astra in Codex; NumPy; the repository's Pauli RIS implementation, optional native gf2_fast backend and trusted validation stack. All searches were CPU-only. Budgets and seeds are given above; total CPU time was not logged. No file under the trusted verifier or schema was changed.
The following exact recipe is sufficient to reconstruct the submitted checks without supplementary files. Index (i,j) in Z_24 × Z_4 as 4i+j. Let
A monomial x^a y^b has its row (i,j) supported on column (i+a,j+b), with modular arithmetic. Submit S=(A|BP): generator g acts as X on g+supp(A) and Z on −g−supp(B). Isotropy follows from A(BP)ᵀ+(BP)Aᵀ = ABP+BAP = 0. The trusted rank is 86, giving k=10. There are eight weight-7 generators and 88 weight-8 generators.
Enumerate generators in lexicographic order of (i,j), sorting each X and Z support in increasing qubit-index order. This reproduces the checks.S array in codes/96-10-12.json exactly; retain the weight-12 witness stated above. For a CSS parent reconstruction, use H_X=[A|B] and H_Z=[Bᵀ|Aᵀ].
The archived deterministic implementation at that pinned earlier revision additionally checks the parent matrices, all archived witnesses and the trusted fingerprint fb542f66ab7f22b0. It is supplementary evidence outside the current PR; the recipe above and the submitted JSON contain the full construction and distance claim.