Local optimization of oxygen transport gives rise to Kleiber’s law

For nearly a century, the physical origin of metabolic scaling has remained unresolved: metabolism is proportional to body mass in small organisms but follows Kleiber’s three-quarter-power law in larger animals. We derive both regimes from the Metabolic Holon (MH), a locally optimized capillary–tissue oxygen-supply unit coupling convection, diffusion, and cellular oxygen consumption. Physical similarity predicts that the effective number N of repeated MHs is body-mass invariant within metabolic groups, while independent observations constrain its group-specific magnitude. Without calibration to metabolic-rate or heart-rate data, the theory predicts absolute metabolic rates across 18 orders of magnitude, regime transition, group-specific levels, and heart-rate scaling. One empirical lifetime-heartbeat constraint sets lifespan. Kleiber’s law is thus one asymptotic consequence of a general physical theory of organismal aerobic metabolism.