Kohn's conjecture on finite generation of the trivial multiplier

Let $\Omega\subset\mathbb{C}^n$ be a bounded pseudoconvex domain with smooth boundary of finite type. A $q$-multiplier is a germ of a smooth function whose product with a $(0,q)$-form satisfies a subelliptic estimate; the trivial multiplier is $f=1$. Kohn's conjecture. The trivial multiplier $f=1$ can be generated by a finite sequence of Kohn's procedures. This extends Kohn's finite-generation result from real-analytic boundaries to smooth boundaries and remains open in the stated generality.