This volume extends the R-layer Mode Theory (RLMT) beyond the observable 4D universe by introducing the exterior geometry of the higher-dimensional tension field. The work formulates the Reprojection Selection Principle, demonstrating that 4D spacetime emerges as the lowest-dimensional stable configuration among admissible projection dimensions. The analysis further defines the Infinity-layer mode, a tension-limit fixed point representing the asymptotic geometry of the global R-layer dynamics. Building on these foundations, the volume derives the Reprojection Cycle Equation, which couples cosmic geometry, hidden-layer remnants, black-hole information flow, and civilizational coherence into a unified meta-geometric framework. This equation describes universes as phases within a larger geometric cycle, where advanced civilizations contribute to reconstructing exterior remnants and influence future reprojection events. The results provide a coherent extension of Volumes 0–XXXV, offering a meta-geometric perspective on cosmic evolution, dimensional stability, and the long-term structure of universes beyond the projection domain.
Tsuyoshi Tohi (Fri,) studied this question.