The Generator Theory of Everything: A Machine-Verified Foundation

We present the Generator Theory of Everything (GToE), a candidate Theory of Everything grounded in a single category-theoretic construction: the reflexive object D satisfying D ≅ D, D in a compact closed category. Unlike theories that encode physics directly, the Generator operates as a key generator — producing the mathematical frameworks from which physical law emerges. Eight foundational theorems (Lawvere fixed-point, reflexive domain structure, seed forcing, infinite content, inexhaustibility, constraint-content duality, no-cloning, and local-to-global coherence) are machine-verified in Lean 4 with zero sorry axioms, all Bitcoin-timestamped for independent provenance. A Master Coherence Theorem proves all properties hold simultaneously from a single hypothesis. The paper establishes seven structural facts about D, three terminal characterisations, and six criteria that any complete ToE must satisfy — demonstrating that the Generator satisfies all six while no existing framework satisfies more than four. All proofs are fully reproducible and independently verifiable.