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   ],
   [
    242,
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    264,
    279,
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   ],
   [
    243,
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    265,
    280,
    327
   ],
   [
    244,
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    266,
    281,
    325
   ],
   [
    245,
    260,
    267,
    282,
    323
   ],
   [
    246,
    261,
    268,
    283,
    321
   ],
   [
    247,
    262,
    269,
    284,
    319
   ],
   [
    248,
    263,
    270,
    285,
    328
   ],
   [
    249,
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    271,
    275,
    326
   ],
   [
    250,
    254,
    272,
    276,
    324
   ],
   [
    251,
    255,
    273,
    277,
    322
   ],
   [
    252,
    256,
    274,
    278,
    320
   ]
  ]
 },
 "distance": {
  "d": 6,
  "X": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    11,
    78,
    94,
    158,
    201,
    289
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-10",
    "found_at_samples": 4000,
    "survived_samples": 4000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1
    ]
   }
  },
  "Z": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    109,
    137,
    156,
    164,
    253,
    265
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-10",
    "found_at_samples": 4000,
    "survived_samples": 4000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     2
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Regular {5,5} hyperbolic surface code on a closed orientable surface. Quotient Q = Delta_5/Gamma 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) = 5 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 and k/n = (5-4)/5 + 2/n by Euler, giving k=68 at n=330. Regenerated from the algebra of arXiv:2610.10948 Sec. II by research/hyperbolic_psl.py; the matrices are recomputed, not copied, since that paper publishes its matrices on request only.",
  "references": [
   "arXiv:2610.10948"
  ],
  "date": "2026-10-10",
  "notes": "Distance is a homological systole on each side, carried as explicit weight-6 witnesses, so d<=6 is witness-backed rather than certified exact.",
  "model": "human",
  "origin": "submission",
  "search_budget": {
   "candidates_screened": 660,
   "ris_trials_per_side": 1000000
  }
 },
 "family": "topological"
}