{
 "schema_version": "0.2",
 "name": "[[53,13,6]]",
 "code_type": "CSS",
 "n": 53,
 "k": 13,
 "checks": {
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  ]
 },
 "distance": {
  "d": 6,
  "X": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
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    12,
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    33,
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    52
   ],
   "witness_provenance": {
    "found_by": [
     "@MathysRennela"
    ],
    "date": "2026-11-07",
    "found_at_samples": 300,
    "survived_samples": 300,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     42
    ]
   }
  },
  "Z": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
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    46,
    48,
    50
   ],
   "witness_provenance": {
    "found_by": [
     "@MathysRennela"
    ],
    "date": "2026-11-07",
    "found_at_samples": 300,
    "survived_samples": 300,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     43
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "code-calculus v0.1 E-PEEL of a CSS parent",
  "origin": "submission",
  "date": "2026-11-07",
  "model": "Beam 1.0"
 },
 "family": "other",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 3,
    "confidence": "upper_bound",
    "witness": [
     2764,
     2765,
     3525
    ]
   },
   "X": {
    "value": 3,
    "confidence": "upper_bound",
    "witness": [
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     12113,
     12147
    ]
   }
  },
  "rounds": 6,
  "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 (9 X + 9 Z CX layers per round, coloring candidate 1); 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)"
 }
}