Prime-Locked Dynamical Signatures in Loschmidt Echo: Ensemble PSD Analysis of Mozga-Type Operators

We propose a new theoretical framework (TUF-M) in which the spacetime metric is not a fundamental entity but an emergent state of a complex scalar field Ψ. By introducing a non-local
constitutive relation between the field’s stress-energy tensor and the metric perturbation, we recover the classical Newtonian limit in the solar system scale. Furthermore, we demonstrate that on
galactic scales, the self-interaction of the scalar condensate naturally generates a halo-like structure
with a ρ ∼ r
−2
effective density profile. This leads to flat rotation curves for spiral galaxies without
the need for particulate Dark Matter. The theory preserves the Weak Energy Condition and offers
a consistent cosmological background.