Abstract Tumor growth has traditionally been described through empirical laws—exponential, logistic, or Gompertz curves that capture observed dynamics but do not explain their origin [4–5]. In this work, we instead derive tumor growth from first principles by treating it as a boundary-mediated transport process. We propose a geometric–transport framework in which growth is governed by flux across a reactive boundary, yielding the scaling law \frac{dM}{dt} = C M^\alpha, \quad \alpha = \frac{d-1+\beta}{d} where the exponent α is not assumed but emerges from two coupled physical factors: geometric boundary scaling and transport amplification [6–8]. The parameter β encodes the efficiency with which biological systems overcome geometric constraints on resource delivery. Within this framework, we show that biologically sustained tumor growth is confined to a restricted exponent spectrum \frac{2}{3} \leq \alpha \leq 1 with the upper bound representing a critical transition. When β exceeds unity, the system enters a superlinear regime characterized by finite-time divergence, signaling instability and breakdown of regulated growth. This formulation unifies diffusion-limited growth, vascularized tumor expansion, exponential growth, and pathological runaway dynamics within a single governing equation [9–14,22–26]. Importantly, it establishes a falsifiable structure: measurable biological variables map directly to the growth exponent, allowing the theory to be tested against empirical data. Tumor growth thus emerges not as a collection of empirical laws, but as a manifestation of a deeper physical principle—structure formation through boundary-mediated flux under geometric constraint.