The classification conjecture for rational cuspidal plane curves with at least three cusps

Let $C$ be a rational cuspidal plane curve of degree $d\geq 6$ with at least three cusps. If $C$ is free, write $(d_1,d_2)$ for its exponents, with $d_1=mdr(f)$.

Main classification conjecture. The curve $C$ is free, and its exponents determine the infinite series to which it belongs as follows:

1. $C\in {\mathcal F}{\mathcal Z}_1(d,a)$ if and only if $d_1=2$, in which case $d_2=d-3$.
2. $C\in {\mathcal F}{\mathcal Z}_2(k)$ if and only if $d_1=(d-1)/2\geq 3$, in which case $d_2=d_1$.
3. $C\in {\mathcal F}{\mathcal F}(k)$ if and only if $d_1=(d+2)/3\geq 4$, in which case $d_2=(2d-5)/3$.

This conjecture combines the preceding family-specific freeness conjectures and predicts that all rational cuspidal plane curves of the stated degree and cusp number belong to one of the three listed families. No resolution is stated in the supplied text.