{
  "id": "proof-theory",
  "domain": "foundations-logic",
  "type": "Concept",
  "title": "Proof Theory",
  "slug": "proof-theory",
  "url": "/mathematics/foundations-logic/proof-theory/",
  "summary": "Studies mathematical proofs as formal objects. Founded by Hilbert 1920s; transformed by Gödel 1931. Key tools: cut elimination (Gentzen 1934), ordinal analysis, reverse mathematics, proof complexity.",
  "added_to_codex": "2026-07-09",
  "last_verified": "2026-07-09",
  "sources": [
    {
      "tier": 1,
      "citation": "Gentzen, G. (1935). Mathematische Zeitschrift, 39, 176-210."
    },
    {
      "tier": 1,
      "citation": "Simpson, S.G. (2009). Subsystems of Second Order Arithmetic. 2nd ed."
    },
    {
      "tier": 2,
      "citation": "Buss, S.R. (ed.) (1998). Handbook of Proof Theory."
    },
    {
      "tier": 3,
      "citation": "Negri, S. and von Plato, J. (2001). Structural Proof Theory."
    }
  ],
  "entry_status": "live",
  "reading_levels_available": [
    "curious",
    "exploring",
    "deep_dive"
  ],
  "completeness": 1.0,
  "codex_version": "2.5"
}