The symplectic product fibering conjecture for closed oriented 3-manifolds

Let $M$ be a closed oriented $3$-manifold, and let $S^1\times M$ denote its product with the circle. Suppose that $S^1\times M$ admits a symplectic structure. The symplectic product fibering conjecture. Then $M$ fibers over $S^1$. The paper presents this as the converse to the fact that a fibration of a closed oriented $3$-manifold over $S^1$ induces a symplectic structure on $S^1\times M$; the supplied context says that the paper gives an affirmative proof, so the conjecture is solved.