Nominal Frequency-Phase Mathematics: Topology of an Everted Multidimensional Torus as a Framework for Infinite Wave Computations

This paper introduces the paradigm of Nominal Frequency-Phase Mathematics, which fundamentally obsoletes classical static numbers and positional numeral systems. Any macro-scale value is treated as a dynamic property of a wave packet confined within a bounded physical medium, governed by the upper quantum limit of the Planck frequency. The author delivers a novel topological solution to the fundamental challenge of phase-coalescence (ambiguity of identical phase values) when mapping an infinite number series onto a cyclic 2-pi circle. This is achieved by introducing the framework of a dynamically everting multidimensional Torus. Within this system, each complete phase cycle continuously shifts the wave vector onto a distinct, isolated layer of a spiral helicoid, preserving the absolute unique identity of ultra-large numbers. Furthermore, the paper provides a complete, robust algorithmic kernel for frequency-based arithmetic, wave interference geometry, transcendental functions, and an absolute primality criterion implemented as a transparent Python simulation model. This methodology offers new horizons for quantum processor architectures and analog wave computing environments by entirely eliminating accumulated machine noise and memory overflow errors.