Strong-subsolution conjecture for solutions of the Z-critical equation

Let $E$ be an object carrying a $Z$-critical equation, and let $h$ be a metric on $E$. A strong subsolution is a metric satisfying the positivity conditions on all formal matrix derivatives of the central charge, namely

$$\operatorname{Im}\bigl(e^{-i\varphi(E)}\widetilde Z^{(p)}(h)\bigr)>0$$

as an $\operatorname{End}E$-valued $(n-p,n-p)$-form for every $p=1,\dots,n$. Strong-subsolution conjecture. A solution to the $Z$-critical equation is a strong subsolution.

This is singled out as the principal analytical conjecture concerning subsolutions, within a proposed diagram relating solutions, strong subsolutions, ordinary subsolutions, and corresponding stability notions. Its resolution is not specified in the source.