All-time existence conjecture for odd-dimensional Ricci Yang-Mills flow

Let $(M^{2n+1},g)$ be a Riemannian manifold, let $L\to M$ be the total space of a $U(1)$-bundle with connection $A$, and let $F$ be the curvature of $A$ satisfying

$$[F^{\wedge n}]\neq 0.$$

Odd-dimensional all-time existence conjecture. The solution to the Ricci Yang-Mills flow exists for all time.

This is presented as an odd-dimensional analogue of the even-dimensional conjecture above. The paper gives no resolution of this general assertion, so its validity beyond the analyzed surface cases remains open.