Paper8_Gravity under B framework

This manuscript provides a mathematically operational formulation of gravity within the alpha-beta-phi framework. It establishes a clear separation of roles for the three fundamental symbols: Alpha (α): The deep sector, contributing via filtered effective potential. Phi (ϕ): The geometric channel, governing the coupling to curvature. Beta (β): The structural channel, organizing branches and mixing thresholds. Technical Contributions: Modified Field Equations: Explicit derivation of the modified Einstein and Friedmann systems from a single covariant visible action. Einstein Limit: Identification of the Einstein limit as an exact frozen branch of the theory. Phenomenology: Analysis of weak-field departures and the generation of finite-range Yukawa-type corrections through the geometric channel. Stability: Definition of the local mixing structure and normal-mode masses via the mixed visible Hessian.