Beloshapka's maximum conjecture for totally nondegenerate CR models

Let $M\subset\mathbb C^{n+k}$ be a totally nondegenerate CR model of length $\rho\geq 3$, with graded infinitesimal CR automorphism algebra

$$\frak{aut}_{CR}(M)=\underbrace{\frak g_{-\rho}\oplus\cdots\oplus\frak g_{-1}}_{\frak g_-}\oplus\frak g_0\oplus\underbrace{\frak g_1\oplus\cdots\oplus\frak g_\mu}_{\frak g_+}.$$

Here, rigidity means that the positive subalgebra $\frak g_+$ is trivial. Beloshapka's maximum conjecture. Every totally nondegenerate CR model $M$ of length $\rho\geq 3$ is rigid; equivalently, $\frak g_+=0$ in the displayed gradation of $\frak{aut}_{CR}(M)$. The conjecture asserts that the maximum positive grading index is absent for these models; determining the maximum index $\mu$ is otherwise an open question.