An Inhomogeneous, Non-linear, and Ghost-Free Formulation of Dynamic Scalar Field Theory (DSFT): Resolving Singularities, the Great Attractor, and the Phantom Divide

We present the comprehensive, mathematically complete, and rigorous formulation of

Dynamic Scalar Field Theory (DSFT) under a fully inhomogeneous and non-linear regime.

By completely abandoning the idealized assumptions of spatial homogeneity and linear

perturbations, we establish a robust mathematical framework capable of describing deep

non-linear gravitational systems. We present step-by-step analytical proofs for three critical

cosmological and astrophysical frontiers: (1) the precise, non-linear kinematic tracking of

galaxy peculiar velocities (650–950 km/s) aligned with the Great Attractor, governed by

a conserved cosmic charge Q and localized kinetic screening; (2) the exact mathematical

elimination of black hole spacetime singularities, replacing them with expanding, non-singular

Euclidean cores that resolve the information paradox via cubic volume growth; and (3) a

dynamic dark energy equation of state that crosses the phantom divide (wDE < −1) while

remaining strictly immune to ghost or tachyonic instabilities. Rather than presenting raw

code scripts, the advanced numerical results from Python multi-physics PDE solvers are

fully translated into exact phenomenological predictions, structural formulas, and statistical

bounds, providing a self-contained and unassailable scientific defense of DSFT.