COREX-GC v6.4: A Covariant Vector–Scalar Theory of Gravity with Galaxy and Cluster Lensing Closure

COREX-GC v6.4 is a relativistic scalar–vector–tensor gravity framework that reproduces galaxy rotation curves, relativistic lensing, and large-scale structure without invoking particle dark matter or per-system tuning. The theory is defined by a covariant Einstein–Hilbert action augmented by a DBI-type scalar field and a unit-timelike vector field with fixed coupling. All free functions are eliminated; the only constants are fixed by stability and cosmological background evolution. Intrinsic stability (no ghosts, no gradient instabilities, subluminal propagation) is proven analytically. In the non-relativistic weak-field limit, the theory reduces to a MOND-like AQUAL equation with a derived acceleration scalea0=2Ky02πcH0a_0 = \frac{\sqrt{2 K y_0}}{2\pi} c H_0a0=2π2Ky0cH0,obtained from first principles rather than phenomenological insertion. COREX-GC v6.4 passes disk-galaxy tests under a strict no-knobs policy (fixed mass-to-light ratios, fixed geometry) and reproduces observed rotation curves across dwarfs and spirals. Automatic screening ensures recovery of General Relativity in high-acceleration regimes, satisfying Solar System and binary-pulsar constraints well below observational bounds. A relativistic transfer test is presented for the Bullet Cluster (1E0657-56), demonstrating that lensing convergence peaks follow the collisionless galaxy distribution rather than the shocked X-ray gas, without dark matter halos or tuning. This work positions COREX-GC as a viable, falsifiable alternative to dark-matter–based cosmology, unifying galactic dynamics, relativistic lensing, and cosmological acceleration within a single, closed theoretical framework.