A Simple Observation on the Dynamics of Logarithmic Slopes in Two-Power Scaling Laws

We consider observables composed of two power-law contributions y(δ) = Aδᵖ + Bδ^q, p < q. We show that the logarithmic slope α(δ) = d log y / d log δ admits an exact Möbius representation and satisfies an autonomous Riccati equation. Conversely, any positive function whose logarithmic slope satisfies this Riccati closure must be a two-mode power law. This establishes a complete equivalence between two-power mixtures, Möbius slope laws, and logistic/Riccati dynamics.