A Cosmology-Linked Low-Acceleration Scale from Galaxy Dynamics, Weak Lensing, and an Information-Theoretic Interpretation

This preprint studies a cosmology-linked low-acceleration scale in galaxy dynamics and weak lensing. The central hypothesis is that the characteristic transition scale is set by the cosmological background through a\*(z)=εcH(z)Ωϕ(z)a_\*(z)=\varepsilon c H(z)\sqrt{\Omega_\phi(z)}a\*(z)=εcH(z)Ωϕ(z).

The manuscript develops the idea in four layers:

• an empirical low-acceleration law
• a cosmological derivation of the transition scale
•  a candidate effective relativistic completion
•  and a deeper information-theoretic interpretation

The current formal core is the empirical law plus the cosmological origin of the scale; the relativistic completion is not yet lensing-complete, and the information-theoretic layer is presented as a candidate deeper interpretation rather than a finished microscopic derivation.