R-layer Mode Theory Volume II: Higher-layer Geometry and Curvature Dynamics

This Volume II develops the geometric foundation of the higher-layer manifold RHL within the R-layer Mode Theory (RLMT). Building on the projection framework established in Volume I, this work introduces the layered geometry of the higher-dimensional manifold, including its metric structure, curvature, torsion, and inter-layer transition maps. The higher-layer manifold is modeled as a stratified structure with layer-dependent curvature, torsion, and geometric flow. We analyze how these geometric features determine the stability of projection modes, the behavior of MUP and AUP modes, and the effective physical properties observed in four-dimensional spacetime. Projection is formulated as a differential map whose Jacobian encodes geometric distortion and asymmetry. A fiber-bundle interpretation is developed, providing a geometric basis for nonlocality, entanglement, and effective transport across layers. Layer transitions—uplift, reprojection, and horizontal transport—are described through geometric flow equations, offering a mechanism for effective nonlocal motion in 4D. Higher-layer curvature is shown to influence effective mass, vacuum energy, and cosmological behavior. Torsion acts as a geometric amplifier for asymmetry, while curvature gradients determine projection stability and uplift dynamics. Cosmological implications include alternatives to inflation, curvature-induced coherence, and higher-layer contributions to early-universe structure. Together with Volumes 0 and I, this work establishes the geometric and dynamical core of RLMT and prepares the ground for the global synthesis presented in Volume ∞.