Finite-partition conjugacy gives no density-contraction theorem

The normalized-gamma construction and finite-partition posterior update state no topology on $\mathcal{P}(\mathsf{X})$ and specify no density model. They therefore establish neither a weak-support theorem nor density-posterior consistency or contraction. A weak-support claim requires a specified topology and an argument that the prior assigns positive mass to each neighborhood in question. A density-posterior consistency or contraction claim additionally requires a specified sampling model and truth class, plus its own proof under the relevant model-specific hypotheses. For example, the finite-dimensional prior-mass bound in Ghosal--van der Vaart is one ingredient in a separate mixture analysis, not a consequence of the conjugate update alone.