The "Duality" Hidden in Numbers: Numbers are both "Quantity" and "Wave"

This paper proposes a fundamental redefinition of integers, shifting the paradigm from discrete units to the emergent results of continuous wave interference. By conceptualizing each prime p as a fundamental frequency (a "prime wave"), we elucidate the mechanism by which their superposition generates "chemically resonant compounding peaks" at composite numbers and "atomic prime valleys" at prime coordinates. Through this lens, non-integer regions are interpreted as "transition states" where energy disperses into the imaginary dimension. This framework provides a physical necessity for the emergence of primes and suggests that the distribution of numbers is an observable manifestation of phase-locked singularities within a complex manifold.