Continuity conjecture for Lyapunov exponents of volume-preserving Anosov diffeomorphisms on the three-torus

Let $f$ range over the $\mathcal{C}^2$ volume-preserving Anosov diffeomorphisms on $\mathbb T^3$, and let its Lyapunov exponents be computed with respect to the preserved volume.

Continuity conjecture. The Lyapunov exponents vary continuously as functions of $f$ in the space of $\mathcal{C}^2$ volume-preserving Anosov diffeomorphisms on $\mathbb T^3$.

The conjecture asserts continuity of the Lyapunov spectrum in this space, extending the conditional continuity results established earlier in the paper. The general continuity question remains open in the supplied source.