The Arrow of Time: Why the Future Differs from the Past, Forced by the Non-Invertible Fold

One axiom. One operation. Zero free parameters. Time has a direction — eggs break but never unbreak — yet the microscopic laws are time-symmetric. Where does the arrow come from? This paper forces it. The fold is two-to-one and non-invertible: forward, each state has one definite successor; backward, every state has two preimages and the fold has erased which one it came from. So the dynamics is deterministic and unique going forward but ambiguous going backward — the definition of an arrow. The rate of this irreversibility is the fold’s Kolmogorov-Sinai entropy, which is positive (equal to one): information is produced every step, never reversibly destroyed. The universe begins at the One (the unique fold fixed point) and unfolds forward because it cannot unfold backward — a zero is forbidden, so the discarded bit cannot be recovered. The arrow of time is the non-invertibility of the fundamental map — the same non-invertibility behind quantum unpredictability and the introspective blind spot. Machine-checked; reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory