the question is forced; the answer is open.
Haar convergence (geometry.md) requires sufficiently decorrelated inputs. the mediation chain provides decorrelation (channel_capacity.md: spectral decay). extensions of the convergence theorem to dependent sequences with mixing conditions give the same stationary measure.
whether the mediation chain’s specific decay rate satisfies the mixing conditions for the foam’s particular dynamics. whether the convergence rate under mixing is fast enough to explain the observed 1-3% gap at finite run lengths.