The ellipsoidal superpotential nonvanishing conjecture for plane curves

Let $p,q,d in \mathbb{Z}_{\geq 1}$ satisfy

$$p+q=3d,\qquad \gcd(p,q)=1,\qquad (p-1)(q-1)\leq(d-1)(d-2),$$

and let $[L]\in H_2(\mathbb{CP}^2)$ be the line class. The ellipsoidal superpotential nonvanishing conjecture. One has $\mathbf{T}_{\mathbb{CP}^2,d[L]}^{(q,p)}\neq 0$. This would provide the expected stabilized symplectic embedding obstruction for the corresponding plane-curve data; the source presents it among concrete questions that remain out of reach.