Poisson torus-action linearization conjecture

For $n\geq 1$, let $P_n=\mathbb{K}[z_1,\ldots,z_{2n}]$ be the commutative Poisson algebra with bracket

$$\lbrace z_i,z_j\rbrace=\delta_{i,n+j}-\delta_{i+n,j}.$$

An action is effective if its kernel is trivial, and regular if it is algebraic. Poisson torus-action linearization conjecture. Every effective regular action of $\mathbb{T}_n$ on $P_n$ by Poisson algebra automorphisms is linearizable. This is posed as a symplectic analogue of the Białynicki-Birula linearization results, and the supplied text does not state a resolution.