Undecidability Does Not Kill Simulation: Provability, Execution, and the Missing Premise in Anti-Simulation Arguments

Abstract

Arguments based on Gödel incompleteness and undecidable questions in physics are sometimes presented as proofs that the universe cannot be simulated. This paper reconstructs that argument in its strongest form and identifies a missing premise. Generating a process one step at a time, predicting selected outcomes, deciding every global property, and certifying every semantic truth are different tasks. A system can generate finite histories even when no universal procedure decides everything those histories will eventually do. The paper distinguishes limits on classification and asymptotic prediction from exact continuum noncomputability and idealized relativistic hypercomputation. It states what would be needed to support a genuine anti-simulation result: a noncomputable physical transition or output, an observer-usable hypercomputational protocol, or a separately defended requirement that simulation include semantic omniscience. A fixed-commit Lean project by Jon Slotkin was independently reproduced and audited. It machine-checks a generator-versus-decider separation under theorem-stream definitions, while the paper explains why that formal result does not by itself settle physical simulation. The release includes thirteen numbered equations, three explanatory figures, twenty-three references, source and chronology ledgers, the fixed formal source, and a complete validation record. This is a preprint and has not undergone peer review.