Prime Harmonic Modulation and the Riemann Zeta Function: Quantum States on the Critical Line

We investigate the mathematical structure of the Prime Harmonic
Modulation (PHM) wavefunction and establish that its amplitude
coefficients A_p = 1/sqrt(p) are the Dirichlet series coefficients
of the Riemann zeta function evaluated on the critical line Re(s) = 1/2.
We prove the PHM wavefunction's normalizability boundary is exactly the
critical line, state the PHM-GUE conjecture, and provide numerical
evidence from N=500 and N=2000 prime spectra. IBM Quantum hardware
experiments validate PHM circuit properties. Patent PCT/US25/39370.