Christol's conjecture on diagonals of rational functions

Let $A(t)=\sum_{n\ge 0} a_n t^n\in\mathbb Z[[t]]$, suppose that $|a_n|<c^n$ for all $n\in\mathbb N$ and some $c>0$, and suppose that $A$ is D-finite. Christol's conjecture. Then $A$ is a diagonal. This conjecture asserts that exponential coefficient growth is the only obstruction to a D-finite integer power series being a diagonal; the paper uses it as context for cogrowth series, but does not give a resolution.