This Volume III develops the generative equations of the universe within the R-layer Mode Theory (RLMT). The framework begins with Small-AUP and Small-MUP, minimal existence modes that precede spacetime and form the substrate of the higher-dimensional pre-universe. Density fluctuations of these minimal modes generate a higher-dimensional tension field, whose structure seeds the formation of layered geometry. The first stable composite mode, the CUP (Common Unified Particle), emerges through torsion alignment, phase synchronization, and tension-field minimization. When the higher-dimensional tension exceeds a critical threshold, the CUP becomes unstable and undergoes a mode bifurcation, producing AUP and MUP as the fundamental constituents of the four-dimensional universe. Matter–antimatter asymmetry arises from two intrinsic mechanisms: (1) the non-zero purity parameter of the CUP, and (2) thermal mode transitions converting OAP into AUP. Annihilation is reinterpreted as mode de-escalation into Small-AUP/MUP, ensuring information preservation and providing a stable substrate for regeneration. We derive the generative equations governing higher-dimensional layer formation, collapse, and reprojection into 4D spacetime. Layered geometric structures arise as tension-field isosurfaces, whose dynamics determine uplift, collapse, and the emergence of a matter-dominated cosmos. This volume establishes the hierarchical origin of the universe in RLMT and completes the generative foundation for the global synthesis developed in later volumes.
Tsuyoshi Tohi (Thu,) studied this question.