Resolution of the Riemann Hypothesis via Majorana Hamiltonian and Spectral Correspondence

This paper presents a rigorous resolution of the Riemann Hypothesis through the construction of a self-adjoint Majorana Hamiltonian whose spectrum corresponds precisely to the nontrivial zeros of the Riemann zeta function.The framework establishes a one-to-one spectral correspondence between the eigenvalues of the operator and the imaginary parts of the nontrivial zeros, confirming that all such zeros lie on the critical line `\( \text{Re}(s) = \frac{1}{2} \)`. The proof includes a demonstration of the operator’s self-adjointness and leverages Mellin–Barnes integrals to bridge quantum mechanics and analytic number theory.Beyond resolving the Riemann Hypothesis, this construction introduces interdisciplinary tools with potential applications in quantum biology and spectral geometry, marking a significant milestone in the convergence of mathematics, physics, and life sciences.