{
 "schema_version": "0.2",
 "name": "[[12,5,2]]",
 "code_type": "CSS",
 "n": 12,
 "k": 5,
 "checks": {
  "X": [
   [
    0,
    1,
    7,
    9,
    11
   ],
   [
    2,
    3,
    6,
    8,
    10
   ],
   [
    4,
    5,
    6,
    8,
    10
   ]
  ],
  "Z": [
   [
    0,
    2,
    4,
    6,
    7
   ],
   [
    1,
    3,
    5,
    6,
    7
   ],
   [
    0,
    2,
    4,
    8,
    9
   ],
   [
    0,
    2,
    4,
    10,
    11
   ]
  ]
 },
 "distance": {
  "d": 2,
  "X": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    1,
    3
   ]
  },
  "Z": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    8,
    10
   ]
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "C-DELETE-CHECK a1 from codes/12-4-2-b.json (priced construction calculus)",
  "origin": "submission",
  "date": "2026-10-19",
  "model": "Beam 1.0"
 },
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     11,
     12
    ]
   },
   "X": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     0,
     2
    ]
   }
  },
  "rounds": 2,
  "stim_version": "1.16.0",
  "notes": "Generic sequential two-block extraction: one ancilla per check, X checks then Z checks each round with joint reset and measurement layers; CX layers are a proper edge coloring of each Tanner graph (5 X + 5 Z CX layers per round, coloring candidate 0); generated by qldpc submit (research/circuit_autogen.py, seed 0), the first of up to 6 candidates whose RIS screen at 2 rounds found nothing below d; witnesses from RIS on ker(H_dem) at twice the gate's trial budget, validated in GF(2)"
 }
}