{
  "family_id": "116",
  "title": "Uniform black-box noncommutative identity testing across characteristics",
  "discipline": "Theoretical computer science",
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "papers": [
    {
      "title": "Uniform Matrix Hitting Points in Every Positive Characteristic",
      "path": "preprints/Uniform-Matrix-Hitting-Points-in-Every-Positive-Characteristic-October-4-2026/uniform-matrix-hitting-points-positive-characteristic.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-Matrix-Hitting-Points-in-Every-Positive-Characteristic-October-4-2026/uniform-matrix-hitting-points-positive-characteristic.pdf",
      "readme_path": "preprints/Uniform-Matrix-Hitting-Points-in-Every-Positive-Characteristic-October-4-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "One Rational Matrix Hitting Point for Noncommutative Formulas",
      "path": "preprints/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026.pdf",
      "readme_path": "preprints/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Polynomial Hitting Lists for Noncommutative Rational Formulas",
      "path": "preprints/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026.pdf",
      "readme_path": "preprints/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    }
  ],
  "lean_scope_path": "lean/docs/116.md",
  "lean_scope_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/116.md",
  "verification_status": "scope_document_available_not_independently_verified",
  "review_status": "inventory_complete_deep_review_pending"
}