Burns–Climenhaga–Todd conjectures on Lyapunov exponent level sets

Let $(T^1M,f^t)$ be the geodesic flow on a compact rank $1$ surface of nonpositive curvature. For $\alpha\geq 0$, let $L(\alpha)$ be the level set of Lyapunov exponents, and write $h(Z,T)=\underline{h}(Z,T)=\overline{h}(Z,T)$ when the lower and upper entropies agree. Burns–Climenhaga–Todd conjectures. When $\alpha>0$,

$$\dim_H(L(\alpha))=\dim_P(L(\alpha))=1+2\frac{h(L(\alpha),T)}{\alpha}.$$

When $\alpha=0$,

$$\dim_H(L(0))=\dim_P(L(0))=3.$$

These conjectures concern the Hausdorff and packing dimensions of Lyapunov exponent level sets for geodesic flows on compact rank $1$ surfaces of nonpositive curvature. The surrounding discussion presents point-to-set principles as a way to study such noncompact or dynamically nonuniform level sets, without requiring compactness, invariance, or an invariant measure; the supplied text does not state whether these conjectures have been resolved.