Let $f$ be a flip-invariant Hölder continuous functionon theunit tangent bundle $T^1 M$ of a closed negatively curved Riemannian manifold$M$. We show that conditionals on strong unstable manifoldsof the Gibbs equilibrium state defined by $f$can be realized as Hausdorff measures. Moreover,cohomology classes of flip invariant cocycles are inone-to-one correspondence to cross ratios on the space offour pairwise distinct pointsof the ideal boundary of the universal covering $\tilde M$ of $M$.