RGMEC — Mathematical Structure: Relative Gravitational Matter–Energy Confinement — A Structural Interpretation of Gravitational Time Dilation

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 organizes the physical variables into a constrained configuration space and develops associated fiber-bundle geometry, structural transport and curvature, sheaf-theoretic global organization, spectral geometry, persistent topology, variational principles, and observational correspondence. It carefully distinguishes established relativistic relations from exploratory structural descriptors and hypotheses. The work also includes contribution-specific material associated with the separate Słowik–Alhawarat investigation of extreme gravitational collapse and the post-neutron-star-stability boundary. The finite-core and microscopic-hierarchy hypothesis originates with Marcin Słowik; its subsequent mathematical and physical investigation with Ali Alhawarat constitutes their joint contribution. This does not alter the attribution of the parent RGMEC framework to Ali Alhawarat. Scientific status: RGMEC is presented as a zero-parameter structural interpretation, not as a modification of General Relativity. Exploratory quantities such as the Structural Coherence Index (SCI) and Structural Connectivity Index (SCN) remain candidates requiring independent operational definition and observational validation.