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 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
     "@MathysRennela"
    ],
    "date": "2026-10-10",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
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    ]
   }
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
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   "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 color code of arXiv:2610.03682 (L=1 family): finite quotient |G|=384 of the triangle group with corner-rotation orders [6, 6, 6], realized as the transitive generating tuple of involutions in S_8 [0, 1, 2, 3, 5, 4, 7, 6], [0, 1, 4, 6, 2, 7, 3, 5], [4, 6, 3, 2, 0, 5, 1, 7]; a qubit per tile (group element), stabilizers on tiling vertices (X and Z on every vertex), max check weight 12. 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"
}