The hyperbolic rational homology 3-sphere deformation conjecture

Let $Y$ be a hyperbolic rational homology $3$-sphere, and let $H^{1,-}_0(Y\times\mathbb R)$ denote the relevant space of bounded solutions on the cylindrical anti-self-dual space $Y\times\mathbb R$. The hyperbolic deformation conjecture.

$$H^{1,-}_0(Y\times\mathbb R)=\mathbb R.$$

The preceding calculations establish that the $t$-invariant part is one-dimensional, as predicted by the rigidity of hyperbolic structures, but do not rule out periodic solutions. Thus the full assertion remains open in the source.