Horizons as Dimensional Interfaces: Curvature–Memory Coupling and Testable Deviations from Classical Gravity

This version presents a revised and refocused formulation of the Horizons-as-Dimensional-Interface Framework (HDIF). Compared to earlier versions, the manuscript adopts a more conservative and technically grounded presentation, emphasizing curvature–memory coupling as a covariant, non-Markovian extension of classical gravity rather than a broad unification claim. The framework introduces admissible geometric memory kernels that allow spacetime curvature to respond to accumulated interface-local dynamics. In the vanishing-memory limit, the formulation reduces exactly to Einstein’s field equations. Finite memory effects generate controlled, falsifiable deviations with experimentally accessible signatures. This update includes:– A revised title reflecting narrower technical positioning– Clarified limiting behavior and GR consistency statements– Improved discussion of falsifiability and experimental implications– Removal of speculative or overextended interpretive framing Future work will further develop the formal structure and empirical modeling.