This work presents the current formulation of Alternate Covariant Field Theory (ACFT), a synchronization-based framework in which spacetime geometry, localized matter states, and propagating interaction fields emerge from the dynamics of a correlation matrix defined on an underlying network. The theory begins from a Lyapunov-type correlation flow and develops a hierarchy of emergent structures including Lorentzian signature selection, curvature saturation, localized defect-cell formation, cavity-like internal oscillation modes, long-range interaction channels, and radiative emission. The central organizing principle is that physical observables arise from spectral organization within the correlation flow rather than from independently postulated spacetime and matter fields. Extensive numerical investigations indicate the existence of topology-independent invariants relating curvature, dimensional collapse, particle capacity, internal resonance frequencies, field-energy storage, and radiation efficiency. The framework is currently compressed into two primary open mathematical problems: (i) proving unique Lorentzian signature selection (N^- = 1), and (ii) deriving the asymptotic spectral density \rho_\infty(\lambda) of the nonlinear correlation operator. These unresolved problems define the future mathematical development of the theory.