Koh–Rogers–Lee–Toh conjecture on graceful variable windmills

Let $C_n$ be a cycle of length $n\geq 3$, and let $C_n^t$ be the graph obtained from the union of $t$ copies of $C_n$ with one vertex in common, called the central vertex. A graph is graceful if it has an injective vertex labelling with labels in $\{0,1,\ldots,m\}$, where $m$ is the number of edges, such that the induced edge labels are exactly $\{1,2,\ldots,m\}$. Koh–Rogers–Lee–Toh conjecture. The graph $C_n^t$ is graceful if and only if

$$nt\equiv 0,3\pmod 4.$$

This conjecture characterizes exactly which variable windmills are expected to admit graceful labellings; the supplied text gives no resolution or partial status, so it remains open.