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    85,
    95,
    172,
    210,
    287
   ]
  ]
 },
 "distance": {
  "d": 3,
  "X": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    29,
    73,
    143
   ]
  },
  "Z": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    32,
    104,
    247
   ]
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Regular {6,6} hyperbolic surface code on a closed orientable surface. Quotient Q = Delta_6/Gamma_PBC with Q = PSL(2,11); the face-vertex swap is a projective involution J in PGL(2,11) imposing y = J x J^-1, with ord(x) = ord(y) = 6 and ord(xy) = 2. Data qubits on edges = left cosets of the order-2 subgroup <xy>; Z checks on face boundaries = left cosets of <x>; X checks on vertex stars = left cosets of <y>; checks commute because each face boundary meets each vertex an even number of times. n = |Q|/2 = 330 and k/n = (6-4)/6 + 2/n by Euler, giving k = 112. Regenerated from the algebra of arXiv:2610.10948 Sec. II by research/hyperbolic_psl.py (class 0 of the check-support-signature enumeration, 330 classes at (p,q)=(6,11)); the matrices are recomputed, not copied, since that paper publishes its matrices on request only.",
  "origin": "submission",
  "date": "2026-10-15",
  "model": "MiMo-V2.6-Flash",
  "notes": "Distance is a homological systole: a shortest cycle in the primal graph outside the GF(2) span of the face boundaries is a genuine logical. Both sides carry explicit weight-3 witnesses, so d<=3 is witness-backed, not certified exact; thirty generator classes measured the same, the other 300 were not measured.",
  "search_budget": {
   "candidates_screened": 7,
   "ris_trials_per_side": 400000
  }
 },
 "family": "topological"
}
