Generalized stringy Grothendieck standard conjecture

Let $X$ be a $d$-dimensional normal irreducible projective variety with at worst log-terminal singularities, and let $\phi$ be a family of bounded motivic invariants of type $(a,b)$. Write $\phi^{st}(X;u,v)$ for its stringy $\phi$-function. Generalized stringy Grothendieck standard conjecture. One should have

$$\phi^{st}(X;u,v)=(u^av^b)^d\phi^{st}(X;u^{-1},v^{-1}).$$

The formula extends the analogous duality known for Batyrev's stringy $E$-function and the corresponding stringy invariants $G^{st}$ and $F^{st}$. Its validity for arbitrary bounded motivic invariants remains open.