Extension of the Lyapunov-map theorem to heterodimensional cycles

Let $\Lambda$ be a heterodimensional cycle linking saddles $P$ and $Q$. Let $I$ contain $0$, $d$, and the indices of dominated splittings on $\Lambda$, and let $\mu$ and $\sigma$ be the Lyapunov maps of the Dirac measures at $P$ and $Q$. For $0\leq\lambda\leq 1$, set

$$\tau_\lambda=\lambda\mu+(1-\lambda)\sigma.$$

A convex Lyapunov map $\tau$ is admissible when $\tau\geq\tau_\lambda$ and agrees with $\tau_\lambda$ at every index in $I$.

Heterodimensional-cycle extension conjecture. Theorem on possible limit Lyapunov maps for a homoclinic tangency still works if one replaces the homoclinic tangency by a heterodimensional cycle.

The claim predicts that the characterization and generic realization of limit Lyapunov maps proved for homoclinic tangencies extends to heterodimensional cycles. The source gives no resolution.