{
  "family_id": "243",
  "title": "Separating choiceless counting from polynomial time and witnessed choice",
  "discipline": "Mathematical logic",
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "papers": [
    {
      "title": "Choiceless polynomial time with counting does not capture polynomial time",
      "path": "preprints/Choiceless-polynomial-time-with-counting-does-not-capture-polynomial-time-September-23-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Choiceless-polynomial-time-with-counting-does-not-capture-polynomial-time-September-23-2026/paper.pdf",
      "readme_path": "preprints/Choiceless-polynomial-time-with-counting-does-not-capture-polynomial-time-September-23-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Witnessed symmetric choice is strictly stronger than choiceless polynomial time with counting",
      "path": "preprints/Witnessed-symmetric-choice-is-strictly-stronger-than-choiceless-polynomial-time-with-counting-September-24-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Witnessed-symmetric-choice-is-strictly-stronger-than-choiceless-polynomial-time-with-counting-September-24-2026/paper.pdf",
      "readme_path": "preprints/Witnessed-symmetric-choice-is-strictly-stronger-than-choiceless-polynomial-time-with-counting-September-24-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    }
  ],
  "lean_scope_path": "lean/docs/243.md",
  "lean_scope_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/243.md",
  "verification_status": "scope_document_available_not_independently_verified",
  "review_status": "inventory_complete_deep_review_pending"
}