Covariant Source Structure of the Reaction-based Model of Gravity (RMB)

This work presents Paper II of the Reaction-based Model of Gravity (RMB) and establishes the fully covariant source structure of the framework. It formalizes the dual-source architecture introduced in the RMB core paper and fixes the ontological and tensorial foundations required for all subsequent developments. RMB is not a modification of General Relativity and not a phenomenological extension. Instead, it defines a distinct ontological framework in which gravity emerges as the reaction of physical space to two co-primary sources: conventional matter stress–energy and the local kinematic state of matter-anchored motion. Rotation and vorticity are elevated to fundamental gravitational sources, rather than secondary effects. In this paper, the kinematic source sector is formulated fully covariantly using the irreducible 1+3 decomposition of the four-velocity field. Expansion, shear, and vorticity are incorporated into a symmetric, matter-weighted kinematic stress–energy contribution. Matter density acts as an activation and anchoring mechanism, ensuring that pure vacuum motion does not generate gravitational sources. The work further introduces the effective space reaction functional Phi_RMB, defined as a non-propagating, matter-activated state functional. Phi_RMB is not an independent dynamical field and does not introduce additional degrees of freedom. Memory and nonlocal effects are confined strictly to the reaction sector and remain dependent on matter and kinematic history, avoiding scalar–tensor or curvature-based reformulations. Key reduction limits are established, demonstrating the consistent recovery of: classical General Relativity, the Newtonian weak-field regime, and a galactic rotation regime in which flat rotation curves arise naturally from sustained, coherent vorticity rather than phenomenological interpolation. The framework is intentionally pre-Lagrangian. The focus of this paper is ontological clarity, covariant source hierarchy, and consistency conditions prior to any dynamical closure. By fixing the covariant source structure and reduction limits, this work prevents ambiguity in later action-based or phenomenological extensions. This paper serves as the formal foundation and reference point for all future RMB developments, including covariant action principles, quantitative tests, and applications to galactic dynamics and cosmology.