Quintic-kernel conjecture for the process at touching Pearcey cusps

The quintic kernel is defined by

$$K^\mathcal{Q}(\theta,\eta;x,y)=\frac{1}{(2\pi i)^2}\int_{\mathcal{C}} dz\int_{\tilde{\mathcal{C}}}d\tilde z\,\frac{1}{z-\tilde z}\frac{e^{2z^5/5-\theta z^3/3-\eta z^2+zx}}{e^{2\tilde z^5/5-\theta\tilde z^3/3-\eta\tilde z^2+\tilde zy}},$$

where the $z$- and $\tilde z$-integration paths are appropriate subpaths of the paths shown in the source figure, with the indicated orientation. Quintic-kernel conjecture. The gap probability for the new process appearing when the two Pearcey cusps touch is given by the Fredholm determinant associated with $K^\mathcal{Q}$. The proposed process would represent a new universality class at the point where the two Pearcey cusps meet, but the source presents this as a possible emerging process rather than establishing the Fredholm-determinant description; its resolution is not stated.