Spectral Simplicity as the Origin of Time

This work establishes the Global Simplicity Theorem for the universal quartic variational equation governing the Ψ–Γ framework. Starting from the full, unreduced static equation—without imposing any spectral, perturbative, or geometric assumptions—we prove that the emergent eigenvalue γ associated with any nontrivial solution Ψ* is necessarily simple. This result is obtained by analysing the angular structure of the global quartic contraction and showing that no second, linearly independent solution inside the same eigenspace can satisfy the full Euler–Lagrange equation. The simplicity of γ has two fundamental consequences.First, the Hessian at Ψ* is nondegenerate modulo global phase, ensuring the uniqueness and stability of the minimizer.Second, and most importantly, spectral simplicity forces the emergence of a unique temporal unit within the framework. By combining the global variational structure with the nonlinear eigenvalue condition, we recover the identity 1 Hz=3 α7/2,1 demonstrating that the time scale is not an external postulate but a mathematically necessary consequence of the quartic structure.This provides the first fully internal route to the emergence of time, frequency, and physical units from a closed variational principle, without tuning, free parameters, or external assumptions.