In a near-future world where AI breakthroughs have transformed mathematics and verification processes, you, a disillusioned former mathematician turned proof detective, are brought into a web of mystery surrounding the sudden success of a new AI system that generates formal proofs at lightning speed. As you unravel the secrets behind its capabilities, you discover a conspiracy involving experimental proofs, competing factions, and the ethical dilemmas of machine intelligence. Use your puzzle-solving skills to decipher complex scenarios, confront treacherous characters, and navigate philosophical quandaries that challenge your understanding of truth, integrity, and what it means to be human in an algorithm-driven world.