  We relate moduli stabilization ($V'=0$) in the bulk of $AdS_D$ or $dS_D$ to
basic properties of the Wilsonian effective action in the holographic dual
theory on $dS_{D-1}$: the single-trace terms in the action have vanishing beta
functions, and higher-trace couplings are determined purely from lower-trace
ones. In the de Sitter case, this encodes the maximal symmetry of the bulk
spacetime in a quantity which is accessible within an observer patch. Along the
way, we clarify the role of counterterms, constraints, and operator redundancy
in the Wilsonian holographic RG prescription, reproducing the expected behavior
of the trace of the stress-energy tensor in the dual for both $AdS_D$ and
$dS_D$. We further show that metastability of the gravity-side potential energy
corresponds to a nonperturbatively small imaginary contribution to the
Wilsonian action of pure de Sitter, a result consistent with the need for
additional degrees of freedom in the holographic description of its ultimate
decay.
