What question did this study set out to answer?

The research aims to derive flat galactic rotation curves and isothermal halos within the framework of R-layer Mode Theory (RLMT).

June 27, 2026Open Access

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

Puntos clave

The research aims to derive flat galactic rotation curves and isothermal halos within the framework of R-layer Mode Theory (RLMT).
Developed a complete derivation of R-layer dynamics using Einstein–tension equations.
Analyzed AUP-dominant outer R-layers with scale-invariant tension gradients.
Explored the relationship between isothermal halos and the AUP/MUP/CUP hierarchy.
Demonstrated an isothermal density profile ρ(r) ∝ r⁻² leading to flat rotation curves v(r) ≈ const.
Identified that ultra-light AUP modes create density granularity consistent with gravitational-lensing anomalies.
Showed that the R-layer hierarchy supports the emergence of chemically primitive galaxies.

Resumen

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.

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