{
 "schema_version": "0.1",
 "name": "[[20,8,4]] self-orthogonal CSS single-layer search candidate",
 "code_type": "CSS",
 "n": 20,
 "k": 8,
 "checks": {
  "X": [
   [
    4,
    7,
    8,
    13,
    15,
    17,
    18,
    19
   ],
   [
    0,
    1,
    3,
    9,
    10,
    13,
    16,
    17
   ],
   [
    2,
    5,
    6,
    11,
    12,
    13,
    14,
    17
   ],
   [
    6,
    7,
    9,
    11,
    13,
    15,
    16,
    17
   ],
   [
    1,
    2,
    8,
    9,
    10,
    12,
    16,
    19
   ],
   [
    1,
    2,
    3,
    4,
    5,
    7,
    9,
    11,
    13,
    19
   ]
  ],
  "Z": [
   [
    4,
    7,
    8,
    13,
    15,
    17,
    18,
    19
   ],
   [
    0,
    1,
    3,
    9,
    10,
    13,
    16,
    17
   ],
   [
    2,
    5,
    6,
    11,
    12,
    13,
    14,
    17
   ],
   [
    6,
    7,
    9,
    11,
    13,
    15,
    16,
    17
   ],
   [
    1,
    2,
    8,
    9,
    10,
    12,
    16,
    19
   ],
   [
    1,
    2,
    3,
    4,
    5,
    7,
    9,
    11,
    13,
    19
   ]
  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    0,
    3,
    6,
    11
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    1,
    2,
    10,
    12
   ]
  }
 },
 "provenance": {
  "authors": [
   "@EthanFeld"
  ],
  "construction": "Randomized self-orthogonal CSS search: n=20, stabilizer rank 6, H_X = H_Z. Column labels form a 6-bit cap (all first-bit-one, distinct), excluding logical weights 1-3; check basis row-reduced to max weight 10. Layout found by grid annealing on 5x4 unit-spaced sites.",
  "references": [],
  "model": "GPT-5.6 Luna",
  "date": "2026-09-10",
  "notes": "Search candidate. Exhaustive enumeration found no nontrivial logical of weight <=3 and a weight-4 witness on each CSS side. Honest single-layer layout; verifier-derived interaction radius sqrt(13)."
 },
 "family": "other",
 "locality": {
  "coordinates": [
   [
    4,
    3
   ],
   [
    3,
    1
   ],
   [
    1,
    0
   ],
   [
    1,
    2
   ],
   [
    3,
    3
   ],
   [
    0,
    2
   ],
   [
    0,
    3
   ],
   [
    3,
    2
   ],
   [
    4,
    2
   ],
   [
    1,
    3
   ],
   [
    4,
    1
   ],
   [
    0,
    1
   ],
   [
    2,
    1
   ],
   [
    2,
    3
   ],
   [
    0,
    0
   ],
   [
    2,
    0
   ],
   [
    2,
    2
   ],
   [
    1,
    1
   ],
   [
    4,
    0
   ],
   [
    3,
    0
   ]
  ],
  "interaction_radius": 3.605551275463989,
  "layers": 1
 }
}