Generation conjecture for orthogonal semi-invariants of symmetric quivers

Let $(Q,\sigma)$ be a symmetric quiver whose underlying quiver $Q$ has no oriented cycles, and let $\beta$ be a symmetric dimension vector. Write $OSI(Q,\beta)$ for the ring of orthogonal semi-invariants, $Rep(Q)$ for the representations of $Q$, and let $\nabla$ and $\tau$ denote the duality and Auslander–Reiten translation used for symmetric quivers. For a representation $V$, let $c^V$ be its determinantal semi-invariant; when it is a square, write $pf^V:=\sqrt{c^V}$. Let $SpRep(Q)$ denote the symplectic representations of $Q$.

Generation conjecture for orthogonal semi-invariants. The ring $OSI(Q,\beta)$ is generated by the semi-invariants

$$c^V \quad\text{if } V\in Rep(Q)\text{ and }\langle\underline{\dim}\,V,\beta\rangle=0,$$

and

$$pf^V:=\sqrt{c^V} \quad\text{if } V\in Rep(Q),\ \langle\underline{\dim}\,V,\beta\rangle=0,\ V=\tau^-\nabla V,$$

where the almost split sequence $0\rightarrow\nabla V\rightarrow Z\rightarrow V\rightarrow 0$ has middle term $Z\in SpRep(Q)$.

This is the orthogonal analogue of the preceding generation claim, proposing determinantal and Pfaffian generators under the same acyclicity and Euler-pairing conditions. Its status is not resolved by the supplied text.