Quég​uiner-Mathieu–Semenov–Zainoulline conjecture on the J-invariant after generic splitting

Let $(A,\sigma)$ be a central simple algebra with orthogonal involution and trivial discriminant, and let $G=\operatorname{PGO}^+(A,\sigma)$ be the connected component of its automorphism group, an adjoint group of type $D_n$. Write

$$J(G)=(j_1,\ldots,j_r).$$

Let $F_A$ be the function field of the Severi–Brauer variety of $A$, a generic splitting field of $A$, and denote by $(j_i)_{F_A}$ the $i$-th component of the $J$-invariant after extension to $F_A$. Quég​uiner-Mathieu–Semenov–Zainoulline conjecture. The remaining components do not change after generic splitting of $A$:

$$j_i=(j_i)_{F_A}\qquad\text{for }i=2,\ldots,r.$$

The first component is known to vanish after splitting $A$; the conjecture asserts that all the other components are already unchanged by this generic splitting. The source gives no resolution, so the conjecture is recorded as open.