Mishchenko–Fomenko conjecture for infinitely dimensional analytic integrals

Let $M$ be a real-analytic symplectic manifold of dimension $2n$, and consider a Hamiltonian system

$$\dot x=X_h(x).$$

Assume that the system is completely integrable by an infinitely dimensional non-commutative algebra $\mathcal F$ of real-analytic integrals. Mishchenko–Fomenko conjecture. The system possesses $n$ commuting real-analytic integrals. This is presented as the remaining general conjecture after the finite-dimensional analytic Lie-algebra cases were proved. The source gives no resolution for this infinitely dimensional case.