Hopkins's chromatic splitting conjecture

Work $p$-locally. For each $n\geq 1$, consider the chromatic fracture square and the map $L_{n-1}X\to L_{n-1}L_{K(n)}X$. If $X$ is the $p$-completion of a finite spectrum, let $\gamma_n$ denote a prospective splitting of this map.

Chromatic splitting conjecture. If $X$ is the $p$-completion of a finite spectrum, then a splitting $\gamma_n$ exists for all $n$.

The conjecture describes how the chromatic localizations $L_nS^0$ assemble through the chromatic tower and is motivated by computations of Morava stabilizer group cohomology and the homotopy groups of $L_{K(n)}S^0$. Its resolution is not given in the supplied source.