{
 "schema_version": "0.4",
 "name": "[[12,4,4]]",
 "code_type": "stabilizer",
 "n": 12,
 "k": 4,
 "checks": {
  "S": [
   {
    "X": [
     6,
     7,
     8,
     9,
     10,
     11
    ],
    "Z": []
   },
   {
    "X": [],
    "Z": [
     6,
     7,
     8,
     9,
     10,
     11
    ]
   },
   {
    "X": [
     0,
     3,
     4,
     7,
     11
    ],
    "Z": [
     4,
     5,
     8,
     10
    ]
   },
   {
    "X": [
     4,
     5,
     8,
     10
    ],
    "Z": [
     0,
     3,
     5,
     7,
     8,
     10,
     11
    ]
   },
   {
    "X": [
     1,
     3,
     5,
     7,
     10
    ],
    "Z": [
     4,
     5,
     9,
     11
    ]
   },
   {
    "X": [
     4,
     5,
     9,
     11
    ],
    "Z": [
     1,
     3,
     4,
     7,
     9,
     10,
     11
    ]
   },
   {
    "X": [
     2,
     3,
     4,
     5,
     8,
     9
    ],
    "Z": [
     10,
     11
    ]
   },
   {
    "X": [
     10,
     11
    ],
    "Z": [
     2,
     3,
     4,
     5,
     8,
     9,
     10,
     11
    ]
   }
  ]
 },
 "distance": {
  "d": 4,
  "P": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": {
    "X": [],
    "Z": [
     4,
     5,
     6,
     7
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "Grassl additive-table quantum code; quantum code over GF(2^2) as tabulated at codetables.de: stored stabilizer matrix for cell [[12,4]] (table bounds 4-4, https://codetables.de/QECC.php?q=4&n=12&k=4) read as binary symplectic rows [x | z]; rank(A|B) < rank(A) + rank(B), so the group has no pure-X/pure-Z basis and the entry is typed stabilizer; generators reduced here to the lightest independent subset ordered by Pauli weight, k = n - rank S, n/k/check weight recomputed from those rows; distance.P witness from this submission's own search.",
  "origin": "submission",
  "date": "2026-09-28",
  "model": "MiMo v2.6 Flash",
  "notes": "Not equivalent to any entry on the board: validate_candidate fingerprint and WL-signature dedup came back clean on 2026-09-27 against main@fc36aafe, and no committed entry is typed stabilizer to share the cell."
 },
 "locality": {
  "coordinates": [
   [
    1.0,
    0.0
   ],
   [
    2.0,
    3.0
   ],
   [
    0.0,
    0.0
   ],
   [
    0.0,
    1.0
   ],
   [
    0.0,
    3.0
   ],
   [
    1.0,
    1.0
   ],
   [
    2.0,
    0.0
   ],
   [
    2.0,
    2.0
   ],
   [
    1.0,
    2.0
   ],
   [
    1.0,
    3.0
   ],
   [
    2.0,
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   ],
   [
    0.0,
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   ]
  ],
  "layers": 1,
  "interaction_radius": 3.1623,
  "contributed_by": {
   "by": [
    "@dorakingx"
   ],
   "date": "2026-10-03",
   "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."
  }
 }
}