Origin of mass v3

Origin of Mass v3: From Physical Mechanism to Mathematical Framework Version 3 of the Oasis Theory introduces the first phenomenological mathematical framework for describing the observed fermion mass hierarchy. Building upon the physical mechanism proposed in Version 2, the model represents particle masses as exponentially suppressed geometric states within a short-lived non-homogeneous phase of the early universe known as the Oasis. The framework employs an effective elliptical geometry characterized by two phenomenological suppression parameters and a set of discrete geometric states. Numerical results demonstrate that a simple geometric relation can reproduce the overall hierarchy of charged fermion masses across multiple orders of magnitude while using only a small number of free parameters. This version focuses on mathematical reproducibility, explicit state assignments, numerical comparisons with experimental masses, and a clear separation between electroweak and QCD contributions to mass generation. The work remains phenomenological and exploratory, serving as a foundation for future investigations into the physical origin of the geometric suppression mechanism and the role of boundary effects within the Oasis framework.