The coefficient inequality conjecture for rational cuspidal plane curves

Let $(C,p_i)_{i=1}^\nu$ be a collection of locally irreducible local plane curve singularities satisfying

$$2\delta=(d-1)(d-2)$$

for some integer $d$. Let $c_l$ be the coefficients associated with the polynomial $R(t)$ defined in the surrounding discussion. Coefficient inequality conjecture. If these singularities can be realized as the local singularities of a degree-$d$ projective plane curve, then

$$c_l\leq \frac{(l+1)(l+2)}{2}\qquad\text{for all }l=0,\ldots,d-3.$$

The source presents these inequalities as necessary conditions motivated by examples of rational cuspidal curves; it does not give a proof or resolution.