The Floer-summand conjecture for Reebless foliations

Let $M$ be an irreducible rational homology sphere, and let $HM_*(M)$ have a direct $\mathbb{F}$-summand, where $\mathbb{F}=\mathbb{Z}/2\mathbb{Z}$. The Floer-summand conjecture. The manifold $M$ carries a Reebless $\mathcal{C}^0$-foliation.

This statement is presented as a consequence of the preceding contact-pair conjectures together with a positive answer to the paper's contact-realization question. It is therefore open in the source.