{
 "schema_version": "0.2",
 "name": "[[35,18,3]] reduction of [[41,18,3]]",
 "code_type": "CSS",
 "n": 35,
 "k": 18,
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 "distance": {
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  "X": {
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   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
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    "date": "2026-10-02",
    "found_at_samples": 20000,
    "survived_samples": 20000000,
    "tool": "gf2_fast RIS ladder (verify/gf2_fast.cpp), both sides searched jointly",
    "seeds": [
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    "date": "2026-10-02",
    "found_at_samples": 4000,
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    "tool": "gf2_fast RIS in the packaging search; the ladder searched both sides jointly",
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 "provenance": {
  "authors": [
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  "construction": "Reduction of the board's codes/41-18-3.json ([[41,18,3]]) by 6 qubits at unchanged k, unchanged check-weight class and unchanged locality class, by one move applied to a fixpoint: graft a qubit away using a low-weight element of the stabilizer ROW SPACE. Let S be an element of the row space of H_X with support T and let a be in T. Replace one generator of the subset summing to S by S itself -- the span is unchanged, that generator being S plus the rest of the subset -- and add S into every other X row meeting a, so that a survives only in S. Then apply the CNOT fan-out from a to T\\{a}, which acts on the check matrices as H_X[:, b] ^= H_X[:, a] and H_Z[:, a] ^= H_Z[:, b] for each b in T\\{a}. Only S still meets a, so the first substitution turns S into the weight-1 stabilizer X_a and leaves every other X row alone; the second zeroes column a of H_Z, because commutation forces every Z row to meet T an even number of times. Qubit a is then 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. The weight of S separates three regimes, and the difference is entirely in the clearing step R ^= S. |S| = 1: nothing is added anywhere, so the weights, the radius AND THE DISTANCE are all preserved exactly, and no distance search is 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), which the implementation in research/local2d/boundary_engine.py applies only to literal weight-1 generator ROWS. |S| = 2: R loses a and toggles one other index, so its weight changes by 0 or -2 and can never rise. |S| >= 3: R can grow, so every touched row is checked against the code's weight class and its locality radius, measured in the source's own layout. This generalises the capped merge-graft I introduced with [[454,8,17]], which only ever built S from the generators a single qubit happens to lie in. Here the accepted grafts were . Low-weight row-space elements are enumerated as sums of at most three checks with a connected overlap pattern. Every graft with |S| >= 2 was accepted only if k was unchanged and a bit-packed RIS search found nothing lighter than 3, screened once and confirmed twice with independent seeds; those in-loop rungs are a filter, not the evidence. QUBIT POSITIONS ARE THE SOURCE'S: every surviving qubit keeps the coordinate it has in codes/41-18-3.json, so the layout is inherited rather than re-derived, and the reduction only deletes. The surviving qubits' indices into the source numbering are [0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12]... (full list implied by the coordinates in this file).",
  "references": [
   "arXiv:2504.08887"
  ],
  "date": "2026-10-02",
  "notes": "Derived from codes/41-18-3.json, not an independent construction; the source's authors are @vprusso and the reduction is mine. The gate reports no exact duplicate and no WL-equivalent entry. It dominates [[35,17,3]], [[41,17,3]], [[41,18,3]] on (n, k, d, w), which therefore leave the frontier of every cell they share with it. Distance is a witness-backed upper bound: the deepest null result is 20000000 fresh-seed RIS trials. Literature novelty is unverified.",
  "model": "Claude Opus 5 (Claude Code)",
  "origin": "submission",
  "novelty": "unknown"
 },
 "family": "check-deletion"
}