The \(\Phi^{-1}(p)\) Hypothesis: Geometric Resonance of Prime Numbers, Support for the Riemann Hypothesis, and Interdisciplinary Applications

We introduce the \Phi^{-1}(p) hypothesis — a geometric resonance model that maps the trajectory of prime numbers onto a spiral and reconstructs a real-valued counterpart to the imaginary parts of the non-trivial zeros of the Riemann zeta function. Spectral and quantum analyses confirm a remarkable correspondence between \Phi^{-1} and Riemann zeros. Applications span quantum mechanics, DNA resonance detection, and post-quantum cryptography