The Thermodynamic Bridge—A Zero-Parameter Local Extension of GERT and the Emergent Origin of Dark Matter Phenomenology

Background: Papers I–V of the Gibbs Energy Redistribution Theory (GERT) established a thermodynamic description of cosmic evolution and its observational calibration, but explicitly left open the local-scale regime of bound systems. In particular, the framework had not yet been tested against galaxy rotation curves, the Radial Acceleration Relation (RAR), the baryonic Tully–Fisher relation (BTFR), or cluster mass discrepancies. Methods: We derive a local bridge equation directly from the Paper I thermodynamic fractions and from the measured Hubble scale (H0 = 72.5 km/s/Mpc), without introducing any new fields, particles, or fitted constants. The resulting correction is controlled by the same entropic function fL(x) already fixed at cosmological level, with a deterministic suppression in high-density regimes and enhancement in dilute halos. We then test this single equation across four independent local observables. Results: (i) Solar-System consistency is recovered through strong suppression (corrections below 1e-12 at planetary densities). (ii) Six SPARC galaxies are reproduced with improved outer-halo behavior in all cases (6/6), and the RAR scatter is reduced by 37.5%. (iii) In the asymptotic limit, the model analytically yields BTFR slope = 4 and predicts an amplitude within 11% of the observed McGaugh normalization. (iv) Six galaxy clusters are matched with zero free parameters, including Coma within 5% of weak-lensing estimates, with predicted baryonic-to-total mass enhancement in the observed range. Conclusions: The phenomenology commonly attributed to dark matter emerges here as a thermodynamic retention effect of entropic work generated in cosmic history. The Milgrom acceleration scale is not postulated as a new constant, but derived from the same global calibration that governs background expansion. This provides a single, falsifiable bridge linking cosmological and local gravitational anomalies within one parameter-closed framework.