n
196
codes/201-15-11.json (#996) was my reduction of @vprusso's codes/216-15-11.json (that entry has since been removed from the board as disconnected legacy in 14095599; the original file is pinned at github.com/unitaryfoundation/qldpc-challenge @ f55706ac, codes/216-15-11.json), made with a move set framed around a single qubit: remove a qubit lying in exactly one stabilizer of a type, or merge the two or three it lies in until it lies in one. The framing, not the code, was the limit. Five more qubits come out under the general form of the same move, and **every one of them needed a stabilizer that no single qubit selects**.
Let S be any element of the row space of H_X — an element of the stabilizer group, not necessarily a published generator — with support T, and let a ∈ T.
1. Replace one generator of the subset summing to S by S itself; the span is unchanged, since that generator equals S plus the rest of the subset. 2. Add S into every other X row meeting a, so a survives only in S. 3. Apply the CNOT fan-out from a to T \ {a}: H_X[:, b] ^= H_X[:, a] and H_Z[:, a] ^= H_Z[:, b].
Only S still meets a, so step 3 turns it into the weight-1 stabilizer X_a and leaves every other X row alone; and column a of H_Z becomes the XOR of its entries over T, which commutation forces to be 0. Qubit a is disentangled and is deleted: n → n-1, k unchanged, and the Z rows only lose an index, so their weights and support diameters cannot rise.
|S| selects the regime, entirely through the clearing step R ^= S:
|S| = 1 — nothing is added anywhere: weight, radius and distance exactlypreserved, no search needed. This is the row-space form of the weight-1 stabilizer cleanup of Liang, Eberhardt and Chen (arXiv:2504.08887 Sec. III D step 4); research/local2d/boundary_engine.py fires only on a literal weight-1 generator ROW.
|S| = 2 — the row loses a and toggles one other index, so its weight changes by0 or −2 and cannot rise.
|S| ≥ 3 — the row can grow, so each touched row is checked against the code'sweight class and its locality radius, measured in the source's own layout.
Accepted on this code: |S| = 2 once, |S| = 3 once, |S| = 4 twice, |S| = 6 once. Low-weight row-space elements are enumerated as sums of at most three checks with a connected overlap pattern.
Fresh-seed RIS ladder: 11 at 20k → 200k → 1M → 5M → 20M trials per rung, independent seeds, both sides searched jointly. Nothing lighter than 11 appeared. Each graft was also screened and confirmed twice in the loop with independent seeds; those rungs are a filter, not the evidence. The distance is an upper bound — on this project a [[682,10,38]] candidate survived three fresh seeds to five million trials and then fell at twenty million, so a flat ladder is not a proof.
verify/validate_candidate.py passes: board_advancing: true, dominated_by: [], no duplicate and no WL-equivalent entry, cell weight-8 × local-2d-bilayer.
Max check weight 8 throughout. Interaction radius 5.3852 → 6.0828, inside the bilayer cap of 7.0; layers unchanged at 2. Unlike the |S| ≤ 2 grafts, an |S| ≥ 3 graft can widen a check, and it is capped by the locality class rather than by the source's own radius, so the reduced code is less local while staying in the same cell. Qubit positions are the source's — every surviving qubit keeps the coordinate it has in codes/201-15-11.json, and the reduction only deletes. kd²/n 9.030 → 9.260.
It dominates three current board entries on (n, k, d, w): 201-15-11 (mine), 216-15-11 and 214-15-11 (@vprusso's).
The construction is @vprusso's [[216,15,11]] (original file pinned as described above); codes/201-15-11.json is my earlier reduction of it and this goes five qubits further. @mathysrennela established on this board that a reduction is a contribution in its own right, with [[240,12,12]] (since re-filed as codes/239-12-12-graft.json in #1066).