A Unified Scalar–Vector Modified Gravity Framework. A Causal Field Interpretation of the Four Fundamental Interactions

We introduce the foundational framework of the Wave–Universe Theory (TUO), a causal unification approach in which spacetime geometry, matter structure, and the four fundamental interactions emerge from a single physical substrate: a dynamical vacuum–tension field $T_v$. TUO addresses a persistent conceptual limitation of modern physics, namely the dual ontology that treats spacetime geometry as fundamental but physically empty in General Relativity, and particles as point-like excitations without intrinsic structure in quantum field theory. In contrast, TUO adopts a single-field description endowed with tension, gradients, and oscillatory degrees of freedom. In the macroscopic, long-wavelength regime, coherent variations of $T_v$ reproduce gravitational phenomena and recover General Relativity as a homogeneous limit. At smaller scales, stable and self-coherent solitonic configurations of $T_v$ provide a physical basis for particle structure, while electromagnetic and nuclear interactions arise as distinct scale–topology regimes of the same underlying field. This joint publication establishes the conceptual foundations of TUO (Part A) and introduces the corresponding scale–topology mapping of the four interactions (Part B). Together, these two components define a clean and minimal foundational layer, upon which subsequent quantitative developments, effective models, and observational tests can be consistently constructed.