The Valdivia compacta ccc dichotomy conjecture

Let $K$ be a nonempty Valdivia compact space satisfying the countable chain condition (ccc). Valdivia compacta ccc dichotomy conjecture. Either $K$ has a $G_\delta$ point or $K$ admits a nontrivial convergent sequence in the complement of a dense $\Sigma$-subset. The paper presents a counterexample to this conjecture under $\diamondsuit$, so the asserted dichotomy is not valid in general.