Finite abelian descent VSA conjecture for the thrice-punctured projective line

Let $k$ be a number field and let $\poneminusthreepoints_k$ denote the thrice-punctured projective line over $k$. VSA for $(\fab,f,k)$ is the finite abelian descent property used in the paper, and $A(\fab,f,k)$ is the associated obstruction property. Finite abelian descent conjecture for the thrice-punctured projective line. The variety $\poneminusthreepoints_k$ is VSA for $(\fab,f,k)$, and consequently $A(\fab,f,k)$ holds for any number field $k$. The preceding proposition establishes that its rational points are closed in the finite adelic points; the conjecture would provide the corresponding VSA statement over every number field.