n
12
The stabilizer leaderboard was empty when this sweep ran: every entry in codes/ was typed CSS, so a general (X/Z-mixed) stabilizer code had no board to compete on and no bar to clear other than its own weight class. Grassl's additive [[n,k,d]] tables at codetables.de store the *generator matrix* behind most cells, not just the parameters, which makes them a ready-made source of such codes: fetch the matrix, keep what the verifier's caps allow, and an empty weight class is open by construction.
What made this cell worth packaging rather than any other: it has the best efficiency of the weight-8 class in the sweep (k d^2/n = 5.33) and a tight table bound (4-4).
A mirror of the table (all 33152 cells with n <= 256, of which 18141 carry a stored construction) was filtered to cells that have a stored matrix at n <= 80, plus exact-bound cells up to n = 126 — 3686 detail pages, fetched once and cached. 3607 of them rebuilt into a valid code (79 failed the isotropy / length / k checks): 664 CSS, 2943 non-CSS.
Screening ran cheapest-first, so no search budget was spent on what the gate would reject anyway:
n <= 700, check weight <= 32 -> 1252 survivors (119 CSS, 1133 stabilizer);direct sum, not one code — dropped 673 more (251 two-block, 150 three-block, ...) -> 443 stabilizer survivors;
verify/validate_candidate.py refutes with:ris-pauli at 1500 python trials plus the doubled accelerated search at 300000 trials, seed 0.
211 of the 443 lie on the frontier over (n, k, d, w); the weight-4/6/8 cells took one or two representatives each and weight-9plus took the two best by k d^2/n.
| step | budget | reading | |---|---|---| | codetables.de table, cell [[12,4]] | — | lower bound 4, upper bound 4 | | screen (RIS + accelerated, seed 0) | 1500 python + 300000 accelerated trials | d = 4, verdict *corroborated* | | packaging (./qldpc submit) | 20000 python + 2000000 accelerated trials | d = 4, distance.P.witness embedded | | validate_candidate refute pass | gate budget, random seed | passed, not refuted | | verify/validate_candidate.py from the CLI | fresh random seed | passed, not refuted |
The claim is a witness-backed upper bound: a weight-4 Pauli logical is in the file, so d <= 4, and the table's own lower bound says d >= 4. It is not marked exact: nothing here proved that no lighter logical exists.
check weight above the verifier's cap of 32 (high-rate d = 2 codes stored as a couple of very dense generators), 87 split into two or more blocks, and 2 were already on the board. One CSS code survived all of that and advanced; the rest of the track produced nothing.
Y, so the"CSS up to a local Hadamard" shortcut applied to 0 of 3607 cells.
cap: 673 stabilizer records, many of them a good code plus idle qubits.
n = 126 nothing was fetched in this run, so the claim of what livesthere is untested rather than negative.
Model: MiMo v2.6 Flash (opencode). Harness: the repo's own stack — the RIS searches in verify/heuristic_distance.py and research/kit/surrogate.py, the gf2_fast accelerator, and verify/validate_candidate.py as the only judge. The mirror/fetch/screen scripts were run locally and are not committed; the two sections above are the method in full. ~18 CPU-minutes for the mirror plus the 3686-page fetch, ~15 minutes to screen the 443 survivors four-way parallel.
The generators ship in this PR: codes/12-4-4.json, checks.S, one {"X": [...], "Z": [...]} per row. To rebuild from the source instead: fetch https://codetables.de/QECC.php?q=4&n=12&k=4, parse the stored matrix rows as binary symplectic rows [x | z] of length 2n, order them lightest-first by Pauli weight (a Y in both halves counts once) and keep an independent subset — the subset can only lower the max weight — then k = n - rank S. Distance: ris_min_pauli_logical in verify/heuristic_distance.py at the budgets above, seed 0.