Gravitational–Thermal Matter–Energy Confinement Hypothesis

Dark-matter haloes set the wells in which baryons collect. That role is gravitational. The gas occupying those wells has its own heat, pressure, radiative losses, bulk motion, turbulence, rotation, and feedback. Nothing in this framework requires dark-matter particles to absorb heat or to couple thermally to baryons. The Gravitational–Thermal Matter–Energy Confinement Hypothesis (GTMEC) asks a narrower and testable question: after the usual controls are applied, does the joint state of dark-matter confinement and baryonic cooling at time t carry reproducible information about later baryonic concentration that neither quantity supplies independently? The same question is extended to subsequent baryon–dark-matter structural segregation and to changes in the baryonic share of the local gravitational potential. The framework does not modify gravity; it organizes a temporal observational and numerical test. Two dimensionless measures form the core of the framework. A dark-matter confinement parameter compares the escape speed associated with the dark-matter potential with the gas temperature. A cooling-efficiency parameter compares the free-fall time with the radiative cooling time. Collisionless orbital measures and an operational gravitational-anchor audit are evaluated alongside this pair. Predictors are measured at time t, while outcomes are measured at later times. An additive null model is compared with a joint alternative using grouped cross-validation, bootstrap intervals, permutation tests, matched-potential controls, primitive-variable null tests, and decomposed backreaction analyses. An optional cosmic-web connectivity audit examines whether node degree and filamentary supply add predictive information after halo mass, accretion rate, and environment are controlled. If the proposed joint term does not survive these tests, GTMEC reduces to a quantitative organization of established gravitational, thermal, and dynamical physics.