A complete derivation of gravitational lensing and gravitational slingshot phe- nomena is constructed exclusively from the internal variational structure of a closed quartic Ψ/Γ functional without introducing fundamental spacetime curvature, grav- itational fields, geodesic postulates, externally imposed metrics, or Einstein equa- tions. Starting from the exact quartic variational object, the work derives the com- plete Hessian geometry, coherent spectral structure, admissible propagating sector
