{
 "schema_version": "0.2",
 "name": "[[12,3,3]]",
 "code_type": "CSS",
 "n": 12,
 "k": 3,
 "checks": {
  "X": [
   [
    0,
    2,
    3,
    4,
    5,
    7
   ],
   [
    0,
    2,
    3,
    7,
    9,
    10
   ],
   [
    3,
    6,
    7,
    11
   ],
   [
    1,
    4,
    5,
    6,
    8,
    11
   ],
   [
    0,
    1,
    3,
    4,
    10,
    11
   ]
  ],
  "Z": [
   [
    2,
    7,
    8,
    9,
    10,
    11
   ],
   [
    0,
    3,
    5,
    7,
    8,
    9
   ],
   [
    0,
    2,
    4,
    6,
    7,
    9
   ],
   [
    0,
    1,
    3,
    6,
    9,
    10
   ]
  ]
 },
 "distance": {
  "d": 3,
  "X": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    0,
    9,
    11
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    6,
    9,
    10,
    11
   ]
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "model": "Claude Opus 5",
  "novelty": "known_parameters",
  "origin": "submission",
  "date": "2026-09-21",
  "construction": "Check deletion from the board entry [[12,2,4]] (codes/12-2-4.json): row 1 of H_Z removed. Dropping one stabiliser generator frees one logical qubit and cannot raise the distance.",
  "notes": "Found by sweeping every single-row deletion of every small board entry and keeping those that land undominated. The parent's remaining checks are unchanged."
 },
 "family": "check-deletion",
 "locality": {
  "coordinates": [
   [
    2.0,
    1.0
   ],
   [
    0.0,
    0.0
   ],
   [
    2.0,
    3.0
   ],
   [
    1.0,
    2.0
   ],
   [
    1.0,
    0.0
   ],
   [
    0.0,
    3.0
   ],
   [
    2.0,
    2.0
   ],
   [
    1.0,
    1.0
   ],
   [
    0.0,
    2.0
   ],
   [
    1.0,
    3.0
   ],
   [
    2.0,
    0.0
   ],
   [
    0.0,
    1.0
   ]
  ],
  "layers": 1,
  "interaction_radius": 3.1623,
  "contributed_by": {
   "by": [
    "@dorakingx"
   ],
   "date": "2026-09-26",
   "method": "Simulated annealing over site assignments on an integer grid with the repo's own research/local2d/fold_layout.search_layout (max-diameter objective, several bounding boxes and seeds); single layer at radius 4 tried first, then two layers at 7. Radius and per-site occupancy re-measured with the verifier's rule."
  }
 }
}