Skorobogatov's conjecture for algebraic K3 surfaces

Let $X$ be an algebraic K3 surface over a number field. The Hasse principle asks whether a rational point exists when points exist over every completion of the number field. The Brauer–Manin obstruction is the obstruction arising from the Brauer–Manin set $X(\mathbb{A})^{\operatorname{Br}}$.

Skorobogatov's conjecture. The Brauer–Manin obstruction is the only obstruction to the Hasse principle for algebraic K3 surfaces over number fields.

This is the algebraic K3-surface formulation used to discuss the implications of the paper's Brauer-group computations. The source supplies no evidence of a resolution.