Hasselblatt's stable–unstable slice dimension conjecture for hyperbolic sets

Let $f$ be a smooth diffeomorphism with a hyperbolic set $\Lambda$. For each $x\in\Lambda$, let the stable and unstable slices be the intersections of the local stable and unstable manifolds of $x$ with $\Lambda$. Hasselblatt's conjecture. The fractal dimension of a hyperbolic set is, at least generically or under mild hypotheses, the sum of the dimensions of its stable and unstable slices, where fractal dimension can mean either Hausdorff dimension or upper box dimension. This conjecture extends dimension-additivity results known for certain hyperbolic sets, such as the solenoid and surface basic sets, to higher-dimensional settings where stable and unstable holonomies are generally only Hölder continuous; the stated genericity or mild hypotheses remain to be specified and established in general.