{
  "author": "Maclain Hunter",
  "title": "Tautological Sieve",
  "identifier": "formal-tautological-sieve",
  "sourceKind": "formal-theorem",
  "content": "Formal statement: {P ↔ Q, Q ↔ R} |= R → (Q ↔ P)\n\nProof: By biconditional transitivity: P ↔ Q ↔ R, therefore R → (Q ↔ P)",
  "formal": "{P ↔ Q, Q ↔ R} |= R → (Q ↔ P)",
  "structuredAuthoredProof": "By biconditional transitivity: P ↔ Q ↔ R, therefore R → (Q ↔ P)",
  "authoredSteps": null,
  "recordedAt": null,
  "originalAuthoredAt": null,
  "propositionMeaningBoundary": "Atomic identifiers retain their meanings in the exact source. No arbitrary truth assignment establishes an ontological or empirical premise; the formal witness checks the written inference."
}