RGMEC — Mathematical Structure: Zero-Parameter Structural Interpretation of Gravitational Time Dilation

Relative Gravitational Matter–Energy Confinement (RGMEC) is presented as a zero-parameter structural interpretation of gravitational time dilation, mathematically identical to the Schwarzschild limit of General Relativity. Gravitational compactness, C = GM/(Rc²), determines the relative temporal evolution factor Θ = √(1 − 2C) for static observers in the applicable exterior geometry. The framework introduces no new gravitational field, force, adjustable parameter, or modification of Einstein's equations. This ten-chapter mathematical monograph organizes the underlying physical quantities into a constrained configuration space and develops fiber-bundle representations, structural transport and connections, sheaf-theoretic organization, spectral geometry, persistent topology, and variational formulations. It distinguishes established relativistic identities from exploratory structural descriptors, including the Structural Coherence Index (SCI) and Structural Connectivity Index (SCN). Supplementary developments examine dynamical confinement and trapped-regime boundaries, a conditional quantum-localization bridge, candidate SCI closures with numerical benchmarks and null tests, and operational causal accessibility. These constructions are explicitly presented within their stated assumptions and limitations, without treating mathematical consistency as independent experimental confirmation. The monograph provides an organized mathematical foundation for further investigation while preserving the distinction between established General Relativity, structural interpretation, and hypotheses requiring operational definition and independent validation.