The Short Leash: Why the Weak Force Is Short-Ranged and the Yang-Mills Mass Gap Is 1/3

One axiom. One operation. Zero free parameters. The weak force’s defining feature is its short range, not feebleness; and confining gauge theories must have a positive mass gap (the Yang–Mills problem). This paper forces both, and they are the same 1/3. A mediator’s reach is how far the field carries its mass-part before running out. A massless mediator pays nothing and reaches unbounded (electromagnetism, gravity). A massive mediator of mass-part 1/3 reaches exactly 2 — a finite leash equal to period(1/3). The weak force is leashed, not feeble: its carrier is massive (1/3). And that 1/3 is the Yang–Mills mass gap: the Mirror of the strong coupling 2/3, forming a closed period-2 orbit (fold(1/3)=2/3) that sums to the One. The gap is forced positive because a zero is forbidden — no massless soft mode can exist. 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