Structural Constraints on Entropy-Gradient Gravity from Cluster Merger Geometry: Falsification of Local Couplings and Predictive Tests of Non-Local Formulations

Galaxy cluster mergers provide one of the strongest geometric tests for gravitational theories beyond standard collisionless dark matter. We use the Bullet Cluster as a structural benchmark to evaluate entropy-gradient gravitational couplings within the Energy-Flow Cosmology (EFC) framework.We first demonstrate that purely local entropy-gradient formulations are geometrically incompatible with the observed lensing–gas separation, as the gradient operator acts as an edge-enhancer and displaces convergence peaks away from galaxy concentrations. This establishes a falsification of local EFC couplings at cluster-merger scales.We then introduce a minimal non-local, component-sensitive extension with a single global mixing parameter. This formulation reproduces the Bullet Cluster geometry without invoking dark matter particles, provided the coupling to collisionless baryonic components exceeds that of shock-heated plasma. Using parameters calibrated solely on the Bullet Cluster, we generate a priori predictions for MACS J0025 and Abell 520, both of which recover the observed peak geometry in synthetic reconstructions without additional tuning.All lensing maps used in this study are reconstructed from published parameters rather than raw shear catalogs. The results therefore constitute structural and theoretical constraints, along with falsifiable predictions, rather than a definitive observational validation. The provided pipeline is fully reproducible and designed for future testing against direct weak-lensing data products.