Energy Path Freedom and Gravitational Coupling: A Three-Regime State-Space Hypothesis for Free, Intermediate, and Confined Energy

This paper develops the earlier Tri-State Energy Representation into a sharper three-regime state-space hypothesis. Energy is organized into a free/null radiative reference, an intermediate sub-luminal or non-null regime, and a confined/bound regime. The central proposal is that the physically relevant ordering variable is not coordinate speed, but the effective freedom of admissible causal or energy-transport paths. A decrease in this freedom is hypothesized to correspond to non-decreasing confinement and stronger structural participation of the system's stress-energy in a self-consistent curved-spacetime configuration. The framework introduces a bounded path-accessibility coordinate P and an independently constructed confinement coordinate χ = f_C, with the principal hypothesis dχ/dP ≤ 0. Crucially, χ is not defined as 1 − P. Path freedom and confinement must be constructed independently and frozen before testing, preventing the proposed inverse relation from becoming a mathematical identity. The accompanying mathematical appendix develops operational constructions of P using accessible causal or transport channels, including escape-cone fractions, flux-channel fractions, and trajectory-ensemble measures. Minkowski spacetime provides the maximal-accessibility benchmark P = 1. A Schwarzschild escape-cone calculation supplies an analytic strong-field benchmark in which accessibility approaches unity at large radius and zero near the horizon. The analysis also identifies an important null result: for static spherical Schwarzschild configurations, the escape-cone estimator is an explicit function of compactness and therefore carries no independent information beyond that established relativistic quantity. Any genuinely new empirical test must consequently employ an accessibility estimator that retains information not algebraically reducible to mass, radius, compactness, or curvature alone. The framework preserves standard special and general relativity as required limiting descriptions. It does not claim that light fails to gravitate, that gravity switches on below the speed of light, or that the proposed three regimes constitute newly established fundamental states of nature. The remaining operational problem is the independent construction of the confinement weight χ. The framework therefore defines explicit falsification criteria and a research program in which the accessibility and confinement estimators must be pre-registered, tested against standard relativistic controls, and rejected or reduced to a taxonomy if they provide no independent physical information.