{
  "family_id": "009",
  "title": "Function-field reconstruction from Milnor K-theory and Galois data",
  "discipline": "Number theory",
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "papers": [
    {
      "title": "Reconstruction of Function Fields from Mod-ℓ Milnor K-Theory",
      "path": "preprints/Reconstruction-of-Function-Fields-from-Mod-ell-Milnor-K-Theory-October-5-2026/mod-ell-bogomolov-pop.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Reconstruction-of-Function-Fields-from-Mod-ell-Milnor-K-Theory-October-5-2026/mod-ell-bogomolov-pop.pdf",
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    },
    {
      "title": "Reconstruction from Milnor K-theory modulo the characteristic",
      "path": "preprints/Reconstruction-from-Milnor-K-theory-modulo-the-characteristic-October-5-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Reconstruction-from-Milnor-K-theory-modulo-the-characteristic-October-5-2026/paper.pdf",
      "readme_path": "preprints/Reconstruction-from-Milnor-K-theory-modulo-the-characteristic-October-5-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "The Bogomolov-Pop reconstruction theorem",
      "path": "preprints/The-Bogomolov-Pop-reconstruction-theorem-September-23-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Bogomolov-Pop-reconstruction-theorem-September-23-2026/paper.pdf",
      "readme_path": "preprints/The-Bogomolov-Pop-reconstruction-theorem-September-23-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    }
  ],
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  "lean_scope_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/009.md",
  "verification_status": "scope_document_available_not_independently_verified",
  "review_status": "inventory_complete_deep_review_pending"
}