Scale-Dependent Radius Stability Law: On the Variation of a in r = a ×10^n(m)

This paper introduces the Probabilistic Radius Law, a new formulation within Closed Surface Quantum Geometry.It proposes that the probabilistic nature of quantum phenomena does not originate from uncertainty in spatial position, but rather from the fluctuation of the closed-surface radius itself.At microscopic scales, the relative fluctuation ratio Δr/r becomes large, producing a broad statistical distribution of possible radii; at macroscopic or astronomical scales, the ratio approaches zero, yielding deterministic geometry.Thus, quantum probability emerges as a geometric property of small closed surfaces, not as an intrinsic randomness of nature.This framework provides a continuous and physically interpretable transition between the probabilistic (quantum) and deterministic (classical) regimes.