RGMEC — Mathematical Structure: Zero-Parameter Structural Interpretation

Relative Gravitational Matter–Energy Confinement (RGMEC) provides a complementary structural interpretation of gravitational time dilation while remaining mathematically identical to the Schwarzschild limit of General Relativity. Compactness C = GM/(Rc²) is identified as the primary descriptor of gravitational confinement, with the relative temporal evolution factor Θ = √(1 − 2C). No new field, force, free parameter, or modification of Einstein’s equations is introduced. This monograph develops the mathematical organization of RGMEC through constrained configuration spaces, fiber-bundle geometry, structural transport and curvature, sheaf-theoretic global organization, spectral geometry, persistent topology, variational principles, and observational correspondence. It maintains a strict distinction between established relativistic quantities, derived confinement quantities, and exploratory structural descriptors such as the structural correlation length ξ, Structural Coherence Index SCI = ξ/R, and Structural Connectivity Index SCN = N_eff/N_total. The work also examines extensions toward dynamical gravitational confinement, candidate structural-coherence closures, conditional quantum-localization correspondences, and operational causal accessibility, while preserving the parent RGMEC equations and explicitly separating established results from hypotheses and open tests. The central methodological principle throughout the work is that physical meaning precedes mathematical representation.