QMU Gravitational Field Theory III: Closure Invariants, Horizon States, and the End of Interior Geometry

The first two papers of QMU Gravitational Field Theory established a closure-based description of gravitation and derived the corresponding ledger constants directly from Ledger One and the propagation-force ledger. The resulting theory recovers the Newtonian inverse-square field, the Schwarzschild radius, and first-order light deflection while replacing the point-mass ontology with finite closure-density distributions associated with the ligamen circulatus. The present paper investigates the strong-field limit of the closure system. Rather than extending the coordinate description into an assumed interior spacetime region, the analysis examines which quantities remain physically meaningful as the closure horizon condition is approached. The central result is the Closure Saturation Principle: geometric descriptions remain valid only while closure relations remain operationally measurable. When the dimensionless closure potential reaches the horizon condition \2|c| = 1, \ coordinate-dependent quantities such as radius, volume, density, and interior geometric structure cease to possess independent physical meaning. The surviving description consists instead of closure invariants, propagation invariants, and ledger identities. The gravitational singularity is therefore reinterpreted not as a point of infinite density but as a finite closure state characterized by saturated invariant quantities. The Schwarzschild radius becomes a closure-saturation boundary rather than the entrance to a physically defined interior geometry. This interpretation preserves exterior gravitational behavior while removing the requirement for infinite curvature, infinite density, or unobservable interior states. Strong-field gravitation is therefore described as the approach toward closure saturation rather than the formation of a geometric singularity. Key Results Introduces the Closure Saturation Principle as the operational criterion for the physical validity of geometric descriptions. Identifies the horizon condition\2|c| = 1 a closure invariant rather than a coordinate singularity. Classifies propagation invariants, closure invariants, and ledger invariants that remain well defined in the strong-field regime. Proposes the Closure Saturation Hypothesis\|c| 12, the Schwarzschild radius as a saturation boundary rather than the entrance to an interior geometric domain. Reinterprets gravitational singularities as finite invariant closure states characterized by saturated closure potential. Demonstrates compatibility between finite-source closure distributions (ligamen circulatus structures) and horizon formation. Preserves previously recovered weak-field predictions including Newtonian gravity, Schwarzschild closure radius, and first-order lightdeflection. Establishes the conceptual foundation for development of the rotational closure sector and future strong-field gravitational dynamics. Series Context This paper is the third installment of the QMU Gravitational Field Theory program. Paper I established propagation-density curvature and closure-flow dynamics. Paper II derived closure coupling constants, ledger closure constants, and strong-field structure. The present paper develops the strong-field interpretation of the scalar closure sector, replacing geometric singularities with finite closure-saturation states defined by invariant ledger relations.