Arithmetic signed count conjecture for 2-torsion points on principally polarized abelian varieties

Let $A$ be an abelian variety of dimension $g$ over a field $k$ with $\operatorname{char}(k)\neq 2$, and let $\lambda\colon A\to A^\vee$ be a principal polarization. For each $a\in A_2$, let $\operatorname{id}_{\kappa(a)}$ denote the base change of $\operatorname{id}\colon A\to A$ to $\kappa(a)$. Arithmetic signed count conjecture. One has

$$\sum_{a\in A_2}\operatorname{Tr}_{\kappa(a)/k}\bigl(\deg_{a}^{{\mathbb A}^1}(\operatorname{id}_{\kappa(a)},\lambda(a))\bigr)=2^{g-1}\cdot\bigl((2^g+1)\cdot\langle1\rangle+(2^g-1)\cdot\langle-1\rangle\bigr).$$

This conjecture proposes an arithmetic refinement of the signed count of the 2-torsion points of a principally polarized abelian variety, with the local degrees valued in the Grothendieck–Witt group. The supplied text gives no resolution status or further evidence, so its status remains open.