4 problems

Real Floer realization conjecture. There is an isomorphism of bigraded groups

Nontriviality conjecture. If $K$ admits a strong inversion, then there is a strong inversion on $K$ with nontrivial real knot Floer group.

Auxiliary-data invariance conjecture. The auxiliary data $\fra$ does not affect the real knot Floer groups.

Coverage conjecture. The bigraded group $\widehat{\operatorname{HFK}}(K)$ can be covered from