R-layer Mode Theory III: Generative Equations of the Universe — From Small-AUP/MUP to a Matter-Dominated Cosmos

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.