Renormalization as a Symptom, Not a Principle Why Four-Dimensional Physics Requires It — and Five-Dimensional Geometry Does Not

Renormalization is traditionally regarded as a fundamental ingredient of quantum fieldtheories formulated in four dimensions. This paper defends a more precise and restricted thesis:renormalization is an effective necessity specific to a point-like four-dimensional description ofphysics, rather than a fundamental principle of nature. We show, rigorously and by explicitcounter-examples, that this necessity arises because the underlying geometric structure of physicaldegrees of freedom is not correctly captured in a strictly four-dimensional formulation. Whena geometrically extended framework in five dimensions is adopted, ultraviolet divergences maydisappear by construction, without the need for any infinite renormalization procedure at thefundamental level. Renormalization should therefore be understood as an effective languageassociated with a four-dimensional projection, not as an ontological requirement of physical laws.