Freeness conjecture for the paper's rational cuspidal curve families

Let $C$ be any of the rational cuspidal curves described in Proposition 2(i), Proposition 3, or Proposition 4, with degree $d$. Freeness conjecture. If $d\geq 5$, then $C$ is a free divisor.

The conjecture is suggested by the families checked in the paper, including the examples in degrees up to the ranges explicitly computed there; the general assertion remains unresolved in the source.