Bloom's conjecture on type, contact and order of vanishing

Let $M\subset \mathbb{C}^n$ be a pseudoconvex real hypersurface with $n\geq 3$. For $1\leq s\leq n-2$ and $p\in M$, write $t^{(s)}(M,p)$, $c^{(s)}(M,p)$ and $a^{(s)}(M,p)$ for the corresponding type, contact and order-of-vanishing invariants. Bloom's conjecture. One has

$$t^{(s)}(M,p)=c^{(s)}(M,p)=a^{(s)}(M,p).$$

Bloom proved the equality $a^{(1)}(M,p)=c^{(1)}(M,p)$ in complex dimension three under pseudoconvexity; the stated higher-dimensional and higher-$s$ equality is presented as the conjecture.