Meylan–Mir–Zaitsev convergence conjecture for real analytic targets

Let $M\subset\mathbb C^N$ be a real analytic generic submanifold and let $p\in M$ be a point of finite type. Let $M'\subset\mathbb C^{N'}$ be a real analytic set containing no nontrivial holomorphic varieties, let $p'\in M'$, and let $F:(\mathbb C^N,p)\to(\mathbb C^{N'},p')$ be a formal mapping sending $M$ into $M'$. Meylan–Mir–Zaitsev convergence conjecture. The formal mapping $F$ is convergent. This removes the algebraicity assumption from the known convergence theorem; the conjecture remains open even for embeddings into strictly pseudoconvex hypersurfaces, although a special result is known for mappings between such hypersurfaces.