There Is No Nothing: How the No-Zero Axiom Forces a Universe That Cannot Be Empty

One axiom. One operation. Zero free parameters. Most of physics is built on the real line, which contains zero. The Smithian Fold is built on a domain that excludes it: every magnitude lives on (0,1], zero is forbidden. This paper draws out what that one axiom forces. Because there is no zero, there is a positive floor — a smallest realized magnitude — and so: the vacuum energy sits at the floor (cosmological constant 2⁻²⁰, positive, the 10¹²⁰ catastrophe dissolved); the lowest excitation of a confining sector sits at the floor (Yang-Mills mass gap 1/3, no massless soft mode); the matter residue after annihilation is forced positive (so matter exists); a fluid cascade cannot concentrate onto a sub-floor scale (Navier-Stokes does not blow up); the critical exponents classical theory sets to zero sit at the floor. The No-Zero axiom forces a universe that cannot be empty, cannot be silent, cannot collapse to a point. Existence is a theorem. 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