n
144
Target: the unrestricted weight-8 stabilizer board. This candidate has witness-backed d≤16 and kd²/n=160/9≈17.7778. That exceeds our pending [[96,10,≤12]] stabilizer entry's 15 by 18.52%; the trusted full gate also found it advances the board at base revision ac8a779bc40524d56a6afdd2133eabd931c99c1f. This is a board-relative improvement, not a claim to a new construction, new parameters, or exact distance.
The parent is the [[288,20,≤22]] cover specified in Table 12 of Symons, Rajput and Browne, Sequences of Bivariate Bicycle Codes from Covering Graphs. The operation is the abelian mirror construction of Khesin and Lu, equivalently an inversion-based instance of symplectic halving; see also Lee et al..
These parameters are already represented by the CSS entry codes/144-10-16.json, contributed by @MathysRennela in PR 951. The novelty label is therefore known_parameters.
There is a rigorous but scoped inequivalence argument. The existing CSS entry has only weight-8 pure generators. Every stabilizer product therefore has even Pauli weight: the X and Z products have even weights separately, and their overlap is even by CSS commutation. Our generator 14 has X on {42,70,77,104} and Z on {6,21,45,77}, so its support has odd weight 7. Local Cliffords and qubit permutations preserve Pauli weight. Hence this instance is not equivalent under those operations to that existing CSS entry, or to any CSS code with exclusively even pure generators. This does not rule out equivalence to every code in the literature.
The round screened all four affine inversion classes for nine BB parents, including this published cover. For a parent on an even-by-even torus, P_t(g)=t−g has four translation classes indexed by t modulo 2G: simultaneous qubit translation and row relabeling change t by 2s. The present candidate uses t=(0,0). A further cyclic-parent screen and transfers of the committed parent witnesses were exploratory controls.
Each initial screen used 400 direct Pauli RIS trials, 12,000 native trials on the doubled CSS matrices, and 600 trials on each pure-Y, pure-X and pure-Z section, all with seed 2621001. For this candidate the direct search returned 26, the doubled search returned 20, and the Y section lowered the bound to 18. The definitive retained bound is 16.
The deeper ordinary audit used seed 12260931: 10,000 direct Pauli trials, 400,000 doubled trials, and 3,000 trials per pure section, with direct pair depth 12 and pure-section pair depth 20. It found nothing below 18. Native doubled searches used the trusted engine's depth/combination arguments (8,8).
A stronger independent search encoded Pauli weight into a CSS construction on 3n bits and used the same trusted native engine. At seed 4126101, 20,000 trials lowered 18 to 16. Rungs of 100,000 trials at seed 7292026 and 1,000,000 trials at seed 8182026 each returned weight-16 mapped logicals and found nothing lighter. Every returned logical, including results heavier than the best known bound, was retained and checked.
The supplementary witness archive records ten distinct retained Pauli witnesses, search budgets, seeds and three embedded supports. At the million-trial rung, an embedded X logical of Hamming weight 17 maps to a source Pauli logical of weight 16. These supplementary files are preserved in the public contributor fork at the pinned earlier revision; they are not part of this two-file submission.
The archived initial full gate records a pass, no exact or WL duplicate, no dominator, and board advancing, with refutation seed 1869019404. The reported gate target was 8,000 trials under the verifier's default time cap; this target is not a statement that a time-capped run completed every requested trial. The subsequent known_parameters and comparison-attribution corrections changed only provenance, not checks or the submitted witness. The archived final-metadata gate also passed with fresh seed 462001893, the same fingerprint, and no duplicate or dominator. These historical reports do not replace PR CI.
The submitted logical has X support {7,8,31,32,43,44,67,68,79,80,103,104,115,116,139,140} and Z support {7,31,43,67,79,103,115,139}. Its support union has weight 16. The trusted rank is 134, so k=10. There are eight weight-7 generators and 136 weight-8 generators.
All distances remain upper bounds. The auxiliary CSS embedding is a refutation tool, not an official certificate for the stabilizer board. No locality layout, circuit-distance claim or exact-distance claim is made.
The prior 96-qubit parent gave bounds 12,8,12,12 across the four affine classes, so the affine shift did not improve its prior best score. An initially promising [[144,6,≤24]] fold was reduced to 19 just by transferring and translating its committed parent logicals. Another [[144,9,≤18]] fold dropped to 15 under the 3n embedding search. These are reasons to transfer known witnesses and test the Pauli objective directly before trusting a doubled-code estimate.
GPT-6 Astra in Codex; NumPy; the repository's trusted Pauli and CSS RIS engines, including the native gf2_fast backend. All searches used CPU. No trusted verifier or schema was modified. Total CPU time was not logged.
The following exact recipe reconstructs the submitted checks without any supplementary files. Index (i,j) in Z_12×Z_12 as 12i+j. Use A={(5,3),(4,8),(2,4),(7,6)} and B={(10,1),(8,1),(11,4),(5,5)}. Generator g has X support g+A and Z support −g−B. Equivalently, S=(A|BP), where P inverts the group. Commutation is A(BP)ᵀ+(BP)Aᵀ=ABP+BAP=0.
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/144-10-16-b.json exactly; retain the weight-16 witness stated above. The earlier CSS entry remains codes/144-10-16.json.
The archived deterministic implementation at the pinned earlier revision additionally verifies the ten archived Pauli witnesses, three embedded witnesses, scoped parity invariant, and trusted fingerprint 8c4f4b3d3e4bb874. It is supplementary evidence outside the current PR; the recipe and submitted JSON contain the full construction and distance claim.
For the auxiliary exact Pauli embedding, define H_X=[A,0,B; I,I,I] and H_Z=[B,A+B,A], using the two blocks of S. An X logical (u,v,w) maps to (u+v,v+w). The map's kernel is generated by (I,I,I), while the remaining X stabilizers map onto S. Every Pauli operator has a representative with one occupied bit for each nonidentity qubit, so d_X equals the source Pauli distance. A Z logical has the form (u,u+w,w) and maps to (w,u); each nonzero triple has weight two, giving d_Z=2d_Pauli. These quotient identities explain the search transformation; every actual returned witness is independently checked after mapping.