The Imprinted Curvature Hypothesis: A Geometric Framework for Dark Matter, Dark Energy, and Cosmological Tensions

Version 2.0 — Major revision This version introduces a refined formulation of the Imprinted Curvature Hypothesis (ICH). Updates include:• clearer geometric formulation within general relativity• explicit curvature-imprint parameterization• expanded testable predictions• clarified observational implications --- This paper introduces the Imprinted Curvature Hypothesis (ICH), a geometric framework in which long-lived curvature imprints originating in the early universe influence the large-scale structure of spacetime. Within this framework, dark matter– and dark energy–like phenomena may arise as effective manifestations of persistent curvature structures embedded in the initial spatial geometry, without modifying the Einstein field equations or introducing new particle species. The hypothesis is formulated within standard general relativity and produces a set of observational predictions that can be tested using large-scale cosmological surveys such as Euclid, the Vera C. Rubin Observatory, and JWST. If supported by observations, the framework may provide a geometric interpretation of several outstanding cosmological anomalies while remaining consistent with the established foundations of gravitational physics.