The $p$-parity conjecture for self-dual Artin twists

Let $A$ be an abelian variety over a number field $K$, let $F/K$ be a Galois extension, let $p$ be a prime, and let $\tau$ be a self-dual representation of $\operatorname{Gal}(F/K)$. Write $\mathcal X_p(A/F)$ for the corresponding $p$-Selmer vector space and let $w(A/K,\tau)$ denote the global root number of the twist of $A$ by $\tau$. $p$-parity conjecture for twists.

$$(-1)^{\langle\tau,\mathcal X_p(A/F)\rangle}=w(A/K,\tau).$$

This is the representation-theoretic analogue of the parity conjecture for $A/K$, relating the multiplicity of a self-dual Artin representation in the Selmer space over $F$ to the twisted root number. The source frames it as an expected parity statement and supplies no general resolution.