The NFM exact-recovery impossibility conjecture under Dirichlet noise

Let $G$ be a graph generated according to the node-feature model (NFM), with the simplex distribution chosen to be the Dirichlet distribution with constant parameter. Exact recovery of the true clusters in $G$ by any algorithm should have probability converging to $0$ as $n\to\infty$.

NFM exact-recovery impossibility conjecture. No algorithm can exactly recover the true clusters in $G$ with probability not converging to $0$ as $n\to\infty$.

The conjecture asserts that constant-parameter Dirichlet noise makes exact recovery asymptotically impossible, despite the deterministic sufficient condition established earlier for the optimization program. Its resolution would characterize a fundamental information-theoretic limitation of clustering under this noise model.