The Irreducibility Theorem

We prove that physical determinism—the thesis that the future state of theuniverse is in principle computable from present conditions without simulating ev-ery intermediate step—is untenable. The proof proceeds from two independentlyverified facts: (1) computationally irreducible sequences exist and are mathe-matically proven to resist any predictive shortcut, and (2) such sequences arephysically instantiated in the universe. We show that irreducibility is observer-independent: no vantage point, internal or external, overcomes it. The onlyremaining refuge of determinism—an inaccessible “fixed future”—is shown tocarry no physical content and is discarded on empirical grounds. The resultis grounded simultaneously in rigorous mathematical proof and direct physicalobservation.