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  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    184,
    187,
    265,
    270
   ],
   "witness_provenance": {
    "found_by": [
     "@MathysRennela"
    ],
    "date": "2026-10-10",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     0
    ]
   }
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    36,
    39,
    240,
    243
   ],
   "witness_provenance": {
    "found_by": [
     "@MathysRennela"
    ],
    "date": "2026-10-10",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "hyperbolic surface code of arXiv:2610.03682 (L=1 family): finite quotient |G|=360 of the quadrilateral group with corner-rotation orders [3, 4, 3, 4], realized as the transitive generating tuple of involutions in S_6 [0, 1, 3, 2, 5, 4], [0, 2, 1, 3, 5, 4], [1, 0, 3, 2, 4, 5], [1, 0, 2, 4, 3, 5]; a qubit per tile (group element), stabilizers on tiling vertices (X on red, Z on blue vertices of the bipartite tiling), max check weight 8. Enumerated by an exhaustive/sampled search over generating tuples with exact corner-rotation orders (the smooth-surface condition); n, k and the witnesses are recomputed and refutation-tested by the board's verifier.",
  "references": [
   "arXiv:2610.03682"
  ],
  "date": "2026-10-10",
  "notes": "",
  "model": "MiMo-V2.6-Flash",
  "origin": "submission",
  "search_budget": {
   "ris_trials_per_side": 1000000
  }
 },
 "family": "topological"
}