R-layer Mode Theory (RLMT) LXXIII: Late-time R-layer Geometry, Information Budget Saturation, and the 27→28 Transition

This volume develops the late-time completion of R-layer Mode Theory (RLMT). Building on the early-time dynamics established in previous volumes, it introduces the global information budget Itot as the maximal coarse-grained information capacity of the R-layer stack. The saturation of this budget governs the transition from layer 227 to a new layer 228, marking the onset of an asymptotic regime in which self-organization stabilizes and the R-layer geometry approaches a slowly varying configuration. By integrating out the R-direction, we derive an effective four-dimensional action containing a dark-energy component with an equation-of-state parameter weff(z)=−1+Δw(z). As the information budget saturates, Δw(z) tends to zero, producing an emergent de Sitter-like state without invoking a fundamental cosmological constant. The volume analyzes the asymptotic geometry, the conditions for terminating the hierarchy at 228, and the possibility of further layers, providing a unified information-geometric interpretation of late-time cosmic acceleration.