R-layer Mode Theory (RLMT) XLII‑B: AUP-dominant Outer R-layers, Isothermal Halos, and Flat Galactic Rotation Curves in RLMT

Volume XLII‑B develops a complete R-layer derivation of flat galactic rotation curves within R-layer Mode Theory (RLMT).Starting from the Einstein–tension equations, the volume derives the R-layer Newtonian limit and shows that an AUP-dominant outer R-layer with a scale-invariant tension gradient naturally produces an isothermal density profile ρ(r) ∝ r⁻² and a flat rotation curve v(r) ≈ const.The analysis connects the isothermal halo to the AUP/MUP/CUP hierarchy, mode imbalance, R-waves, and the R-layer renormalization-group fixed point.Ultra-light AUP modes generate wavelike density granularity consistent with gravitational-lensing anomalies, and the layer hierarchy supports the early emergence of chemically primitive galaxies.