{
  "family_id": "229",
  "title": "Exact three- and four-state reconstruction thresholds and four-state tree capacity",
  "discipline": "Probability and statistical mechanics",
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      "title": "The Reconstruction Threshold for the Ferromagnetic Four-State Potts Model",
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    {
      "title": "A Capacity Criterion for Four-State Potts Reconstruction on Trees",
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    },
    {
      "title": "The exact reconstruction threshold for the three-state symmetric channel",
      "path": "preprints/The-exact-reconstruction-threshold-for-the-three-state-symmetric-channel-September-25-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-exact-reconstruction-threshold-for-the-three-state-symmetric-channel-September-25-2026/paper.pdf",
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