Conjecture that inflation-NPA convergence yields commutator bilocality

Let $\vec{Q}=\{q(abc|xyz)\}$ be a distribution in the bilocal scenario. Say that $\vec{Q}$ passes the bilocal inflation-NPA hierarchy when it satisfies the hierarchy of compatible inflation-NPA moment-matrix tests. Inflation-NPA factorisation conjecture. If $\vec{Q}$ passes the bilocal inflation-NPA hierarchy, then it passes the factorisation bilocal hierarchy and is therefore a commutator bilocal distribution. This conjecture concerns the asymptotic factorisation of inflation moment matrices and the resulting convergence of the inflation-NPA hierarchy; a formal proof is not given.