Density of typical Hodge loci at the expected dimension

Let $\mathbb V$ be as in Theorem mainqsimple, and let $(\mathbf M,D_M)\subsetneq(\mathbf G,D)$ be a strict Hodge sub-datum satisfying

$$\dim \Phi(S^\mathrm{an})+\dim D_M=\dim D.$$

The expected-dimension typical-point conjecture. In every neighbourhood $B\subset S^\mathrm{an}$, one has the strict containment

$$\mathrm{HL}(S,\mathbb V^\otimes,\mathbf M)_\mathrm{atyp}\cap B\subsetneq\mathrm{HL}(S,\mathbb V^\otimes,\mathbf M)\cap B.$$

This is described as the missing consequence of the Zilber–Pink conjecture needed to obtain a full characterization of density of typical Hodge loci.