Temporal–Gravitational History Coupling Theory (TGHCT): An Operational Framework of Observer-Conditioned Diagnostics for Thermal Temporal Participation, Binding Accessibility, and Retained History

Temporal–Gravitational History Coupling Theory (TGHCT) is formulated as a falsifiable operational framework for studying observer-conditioned thermal temporal participation, gravitational binding accessibility, instability, and retained physical history while preserving standard general relativity. The central thermal diagnostic is the observer-conditioned mean inverse Lorentz factor, C_tau[u] = = , with E_u = -p_mu u^mu. For a classical relativistic Maxwell–Jüttner gas in the declared rest frame, this reduces to C_tau = K1(z)/K2(z), where z = mc^2/(k_B T). The framework explicitly distinguishes this diagnostic from proper time, from a new metric field, and from a rest-energy fraction. Gravitational organization is treated through established binding and Jeans diagnostics, while historical information is separated into individual history features, population-level information measures, and irreversible bookkeeping. The main empirical hypothesis is deliberately residual: after a rich operationally measured present-state description has been conditioned upon, does independently established history improve held-out prediction of subsequent physical evolution? The framework distinguishes total history predictiveness from carrier-mediated path dependence. Published controlled simulations provide replicated Level-2 history dependence and prospective matched-history analogues, while other simulations and observational studies produce null, transient, erased, or model-dependent effects. The present evidence therefore favors a conservative interpretation in which historical effects may be mediated by identifiable physical carriers such as gas, black-hole, structural, or phase-space state. TGHCT does not modify Einstein’s equations, does not introduce a new gravitational force or fundamental clock field, and does not claim completed empirical confirmation. Its strict Level-3 carrier-adjusted matched-history test remains open and explicitly falsifiable.