  We establish Anderson localization for Schr\"odinger operators with even
analytic potentials on the first supercritical stratum for Liouville
frequencies in the sharp regime $\{E: L(\omega,E)>\beta(\omega)>0,
\kappa(\omega,E)=1\}$, with $\kappa(\omega,E)$ being Avila's acceleration. This
paper builds on the large deviation measure estimate and complexity bound
scheme, originally developed for Diophantine frequencies by Bourgain, Goldstein
and Schlag \cites{BG,BGS1,BGS2}, and the improved complexity bounds in
\cite{HS1}. Additionally, it strengthens the large deviation estimates for weak
Liouville frequencies in \cite{HZ}. We also introduce new ideas to handle
Liouville frequencies in a sharp way.
