Three of Everything: Why There Are Exactly Three Generations of Matter, Forced from the Tripling Fold

One axiom. One operation. Zero free parameters. Matter comes in three generations and the Standard Model has never said why — Rabi’s ‘who ordered that?’ This paper derives the number. The generations are the fibre of the tripling fold — the preimages of 2/3 under x ↦ 3x mod the One — which has exactly three elements (2/9, 5/9, 8/9), because the tripling fold is three-to-one. The count is cross-checked by period(1/7) = 3 and equals the measured three (Z-boson invisible width 2.984). There is no fourth generation: the tripling map has no fourth preimage. The same three is the colour count and the number of spatial dimensions. 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