Geometric Model of Prime Numbers (GMP): Angular Dynamics and Geometric Structure of Prime Gaps

This work presents a geometric formulation of the distribution of prime numbers through the Geometric Model of Prime Numbers (GMP), in which primes are interpreted as structural closure points arising from the interaction between a continuous ordinal axis ℝ and a discrete-value axis ℕ(ℙ). Within this framework, each prime defines a geometric state characterized by an associated angle, and the evolution of the sequence is described in terms of discrete angular dynamics, including velocity and acceleration. Building on this structure, the Basso Method is introduced not as a search procedure, but as an intrinsic geometric operator of the GMP. By exploiting local angular information extracted from consecutive primes, the method projects the geometric state associated with the next ordinal index and produces a continuous value corresponding to the expected location of the next prime closure. This projected value does not impose primality, reflecting the non-invertible nature of the geometric construction, but consistently lies in close proximity to the true prime across different scales. As a result, prime gaps are interpreted as the discrete realization of an underlying continuous geometric process. The formulation is further shown to be generalizable to arbitrary discrete sequences, indicating that the geometric framework is not restricted to primes but applies broadly to systems governed by ordered progression and discrete closure events. Prime numbers thus emerge as a particular instance of a more general geometric structure.