The Prime Wave Function: Mathematical Relationships Spanning Multiple Physical Domains A Unified Framework Connecting Prime Number Theory to Physical Reality

The Prime Wave Function: A Unified Framework Connecting Prime Number Theory to Physical Reality This paper introduces the Prime Wave Function, a novel mathematical structure that uncovers precise and statistically significant relationships between prime numbers and multiple physical domains. The core formulation, Ψ(t) = A·sin(2πt/τ_log(p))·e^(−t/τ), generates a frequency spectrum ω = 2π/log(p) that reveals deep harmonic order underlying particle mass ratios, fundamental constants, crystallographic intervals, and quantum field behavior. The study presents over 50 reproducible matches between prime-frequency ratios and known physical measurements, including particle mass hierarchies and coupling constants, with deviations well below accepted experimental tolerances (relative error < 0.01%). This suggests an unrecognized but fundamental connection between analytic number theory and the structure of physical law. A full suite of open-source Python scripts is included, enabling independent verification of all claims. The framework opens a new pathway for investigating how prime-generated harmonic structures may underpin matter, time, and spacetime itself.