  This letter explores a transition in the type of von Neumann algebra for
asymptotically AdS spacetimes from the implementations of the different
gravitational constraints. We denote it as the \emph{centaur-algebra} of
observables. In the first part of the letter, we employ a class of flow
geometries interpolating between AdS$_2$ and dS$_2$ spaces, the centaur
geometries. We study the type II$_\infty$ crossed product algebra describing
the semiclassical gravitational theory, and we explore the algebra of bounded
sub-regions in the bulk theory following $T\overline{T}$ deformations of the
geometry and study the gravitational constraints with respect to the
quasi-local Brown-York energy of the system at a finite cutoff. In the second
part, we study arbitrary asymptotically AdS spacetimes, where we implement the
boundary protocol of an infalling observer modeled as a probe black hole
proposed by arXiv:2211.16512 to study modifications in the algebra. In both
situations, we show how incorporating the constraints requires a type II$_1$
description.
