R-layer Mode Theory (RLMT) LXVII: Early Universe, Black Holes, and Quantum Geometry of 220–227 Layers

This volume extends R-layer Mode Theory (RLMT) to early-universe cosmology, black hole mechanics, and the quantum geometry of the full 220–227 layer hierarchy.By embedding the layer structure into an FRW background, it derives R-layer Friedmann equations, identifies the role of the 223 “dark skeleton” layer, and analyzes R-wave-induced primordial fluctuations.The volume formulates R-layer black hole mechanics, including first and second laws, and derives the quantum capacity Q(R) from the R-layer entanglement spectrum.It further connects AUP/MUP/CUP mode imbalance to a linear tension profile σ(R)=σ₀+σ′R, yielding a 1/r² density profile and providing the theoretical foundation for isothermal halos and flat rotation curves.The resulting wave-like granularity is compared with ultra-light dark matter phenomenology, suggesting a unified geometric origin for dark-matter-like behavior in RLMT.