{
  "family_id": "029",
  "title": "Primitive roots for every admissible integer base",
  "discipline": "Number theory",
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "papers": [
    {
      "title": "Primitive roots for every admissible integer base",
      "path": "preprints/Primitive-roots-for-every-admissible-integer-base-October-4-2026/primitive-roots-all-integer-bases.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Primitive-roots-for-every-admissible-integer-base-October-4-2026/primitive-roots-all-integer-bases.pdf",
      "readme_path": "preprints/Primitive-roots-for-every-admissible-integer-base-October-4-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Simultaneous primitive roots: a conditional lower bound for prime bases",
      "path": "preprints/Simultaneous-primitive-roots-a-conditional-lower-bound-for-prime-bases-October-4-2026/simultaneous-primitive-roots-conditional-lower-bound-prime-bases.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Simultaneous-primitive-roots-a-conditional-lower-bound-for-prime-bases-October-4-2026/simultaneous-primitive-roots-conditional-lower-bound-prime-bases.pdf",
      "readme_path": "preprints/Simultaneous-primitive-roots-a-conditional-lower-bound-for-prime-bases-October-4-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    }
  ],
  "lean_scope_path": null,
  "lean_scope_url": null,
  "verification_status": "no_family_scope_document",
  "review_status": "inventory_complete_deep_review_pending"
}