Spectral Simplicity as the Origin of Time

This paper establishes a global simplicity theorem for the universal quartic variational equation underlying the Ψ–Γ framework. By analysing the full, unreduced Euler–Lagrange structure, I prove that any nontrivial solution necessarily corresponds to a simple emergent eigenvalue. No degenerate eigenspaces are compatible with the quartic constraints or with the internal coherence of the variational system. This result implies the nondegeneracy of the Hessian, the uniqueness (up to phase) of the static minimizer, and the absence of internal zero–modes. More importantly, spectral simplicity forces the emergence of a unique temporal scale. The theory yields the identity 1 Hz=3 α7/2, showing that time and frequency arise as mathematically necessary consequences of the quartic structure, without external postulates, free parameters, or empirical input. The result provides a fully self–contained route from a purely variational principle to the existence of temporal units, placing the origin of time within the internal logic of the functional itself.