{
 "schema_version": "0.3",
 "name": "[[72,10,10]]",
 "code_type": "CSS",
 "n": 72,
 "k": 10,
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 "distance": {
  "d": 10,
  "X": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": [
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  "Z": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": [
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 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "2BGA (two-block group algebra) code on group ab(9,2,2) (|G|=36); H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] with a = [0, 4, 25, 31], b = [0, 13, 20, 34] as element indices of the Cayley table (identity = 0; table convention in the note)",
  "origin": "submission",
  "date": "2026-10-17",
  "model": "Claude Fable 5.1",
  "notes": "WL-signature match with 72-10-9 (Lin-Pryadko SmallGroup(36,2) row) is a collision, not an equivalence: a SAT search with verify/sat_certify.py (selector encoding, 600 s per solve) returned UNSAT for logicals of weight <= 9 on both the X and the Z side of this code, so no weight-9 logical exists here, while 72-10-9 carries a verified weight-9 witness; a permutation-equivalent code would share it. Group here is the abelian Z_9 x Z_2 x Z_2 with 4+4 supports. Distance is nevertheless filed as upper_bound; a 3 x 20M fresh-seed gf2_fast ladder found nothing below 10.",
  "search_budget": {
   "candidates_screened": 3044305,
   "ris_trials_per_side": 60000000,
   "cpu_hours": 3,
   "tool": "research/kit/search.py-style sweep + gf2_fast on Brev n2d-highcpu-64"
  }
 },
 "family": "bivariate-bicycle",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 5,
    "confidence": "upper_bound",
    "witness": [
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     26935,
     27256,
     27963,
     28195
    ]
   },
   "X": {
    "value": 5,
    "confidence": "upper_bound",
    "witness": [
     25399,
     25409,
     27320,
     27328,
     27728
    ]
   }
  },
  "rounds": 10,
  "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 (10 X + 9 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)"
 }
}