  We study the statistical capacity of the classical binary perceptrons with
general thresholds $\kappa$. After recognizing the connection between the
capacity and the bilinearly indexed (bli) random processes, we utilize a recent
progress in studying such processes to characterize the capacity. In
particular, we rely on \emph{fully lifted} random duality theory (fl RDT)
established in \cite{Stojnicflrdt23} to create a general framework for studying
the perceptrons' capacities. Successful underlying numerical evaluations are
required for the framework (and ultimately the entire fl RDT machinery) to
become fully practically operational. We present results obtained in that
directions and uncover that the capacity characterizations are achieved on the
second (first non-trivial) level of \emph{stationarized} full lifting. The
obtained results \emph{exactly} match the replica symmetry breaking predictions
obtained through statistical physics replica methods in \cite{KraMez89}. Most
notably, for the famous zero-threshold scenario, $\kappa=0$, we uncover the
well known $\alpha\approx0.8330786$ scaled capacity.
