Sharp o-minimal complexity conjecture for self-dual flux vacua

Let the self-dual flux-vacuum locus be the locus of flux vacua satisfying the self-duality conditions, and let $(F,D)$ denote its sharp o-minimal format and degree. Sharp o-minimal complexity conjecture. The self-dual flux-vacuum locus is definable in a sharply o-minimal structure, with

$$D=\operatorname{poly}(L),\qquad F=\mathcal{O}(h^{3,1}),$$

where $L$ is the tadpole bound and $h^{3,1}$ is the number of moduli. Such a definability result would provide complexity-controlled bounds for counting self-dual flux vacua. The source does not state a resolution, so the conjecture remains open.