General-position conjecture for all simple mechanical systems

For each manifold $M$ and each simple mechanical system with kinetic energy $T$ and potential energy $V$, let $\psi(M,T,V)$ be the homomorphism from the universal Lie algebra $L_{\mathfrak P}(A,B)$ onto the Lie algebra generated by the system. The grading by degree gives identities, and the common kernel records identities satisfied by every such system. General-position conjecture for simple mechanical systems. The only identities satisfied by all simple mechanical systems are those due to the grading by degree; equivalently,

$$\bigcap_{M,T,V}\ker\psi(M,T,V)=0.$$

This asks whether the class of all simple mechanical systems is in general position collectively. The supplied text gives no evidence that the conjecture has been resolved.