  Following the work of [2008.03319], we define a generally covariant
max-entanglement wedge of a boundary region $B$, which we conjecture to be the
bulk region reconstructible from $B$. We similarly define a covariant
min-entanglement wedge, which we conjecture to be the bulk region that can
influence the state on $B$. We prove that the min- and max-entanglement wedges
obey various properties necessary for this conjecture, such as nesting,
inclusion of the causal wedge, and a reduction to the usual quantum extremal
surface prescription in the appropriate special cases. These proofs rely on
one-shot versions of the (restricted) quantum focusing conjecture (QFC) that we
conjecture to hold. We argue that these QFCs imply a one-shot generalized
second law (GSL) and quantum Bousso bound. Moreover, in a particular
semiclassical limit we prove this one-shot GSL directly using algebraic
techniques. Finally, in order to derive our results, we extend both the
frameworks of one-shot quantum Shannon theory and state-specific reconstruction
to finite-dimensional von Neumann algebras, allowing nontrivial centers.
