The Quarter-Power Law of Life: Kleiber's Metabolic Scaling as the Fold's Four-Fork Branching Ratio

One axiom. One operation. Zero free parameters. From a bacterium to a blue whale, metabolic rate scales as body-mass to the three-quarter power (Kleiber’s law), and a family of biological rates follows in quarter-power steps. Why 3/4, not the naive 2/3? This paper forces it. The 3/4 is the fold’s four-fork branching ratio (m−1)/m at m=4 — the branching share of a supply network that fills three spatial dimensions plus one, the same form that gives one-half at a two-fork and two-thirds at a three-fork (the strong coupling, the turbulent exponent). The body’s branching distribution network is a four-fork covering, and its scaling share is exactly 3/4, which folds to the balance point one-half. From it the quarter-power family follows: lifespan as mass^(1/4), heart rate as mass^(−1/4), so every mammal gets a comparable number of heartbeats in a life. The law of life is one of the fold’s branching ratios. 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