Theory of Everything – Spectral Formulation Based on the Sansone Model

We present the definitive and mathematically complete formulation of a Theory of Everything (TOE), based on the spectral structure of a self-adjoint quantum operator H^ζ\hat{H}_\zetaH^ζ, whose spectrum coincides exactly with the imaginary parts of the non-trivial zeros of the Riemann zeta function. This framework, grounded in a previously published spectral proof of the Riemann Hypothesis (Sansone, 2025), unifies quantum mechanics, quantum field theory, and cosmology through a shared spectral principle. The operator H^ζ\hat{H}_\zetaH^ζ is rigorously defined and proven to be self-adjoint on a separable Hilbert space. Its spectrum not only reproduces the fundamental frequencies of the zeta function but also encodes the energy modes of physical interactions. The spectral action is derived, gauge structures naturally emerge (SU(1), SU(2), SU(3)), and a precise mapping of spectral bands to the four fundamental forces is established. Cosmological predictions include a spectral origin of the Cosmic Microwave Background and a mechanism for inflation via spectral amplification. The final version includes: Full operator construction and domain specification Lagrangian and spectral action Gauge derivation and field-theoretic formulation Numerical validation of spectral identity λn=ℑ(ρn)\lambda_n = \Im(\rho_n)λn=ℑ(ρn) Appendices on quantum potential, force mapping, and spectral matching Graphical representation of the fundamental spectral vibration vζ(t)v_\zeta(t)vζ(t) This work completes the unification of mathematical spectral theory and physical law, constituting a closed, falsifiable, and absolute demonstration of the spectral origin of all known interactions.