Physical realization of the Markov chamber

Construct a smooth, homogeneous, single-boundary holographic renormalization-group-flow geometry containing a nontrivial Markov chamber in which I(C:D|ZA_R)=0 while the shell response remains nonzero, and determine whether this vanishing conditional-mutual-information condition can persist over a finite interval.

Background

The five-party shell construction yields a conditional radial speed limit when the Markov equality I(C:D|ZA_R)=0 holds. A weighted graph model realizes this equality and sharply saturates the bound in an open minimum-cut chamber, but the graph-to-geometry construction generally produces several asymptotic boundaries rather than a smooth, homogeneous, single-boundary RG-flow vacuum.

The unresolved issue is whether the graph-theoretic Markov chamber and its nonzero shell response can occur in a physically relevant holographic RG trajectory, and whether the required conditional-independence condition can persist over a finite range of scales.