The periodic efficient total girth coloring conjecture for cubic maps

Let $M(G)$ be a connected simple cubic map of girth $4$ embedded in a genus-realizing orientable surface, and suppose all its belts have lengths $\ell$ with $\ell\equiv 0\pmod 4$. Let a DETGC and an RETGC denote the two types of efficient total girth colorings used in the source, let a 3PFC denote an associated 3-permutation face coloring, and let $G\square K_2$ be the prism graph. Periodic efficient total girth coloring conjecture. Such a map contains DETGCs and RETGCs with associated 3PFCs from which the original colorings can be recovered, yielding unique induced EGCs in $G\square K_2$. This is the paper's broad correspondence claim; the supplied text does not state a resolution.