Cherednik–Danilenko–Philipp conjecture for motivic superpolynomials

Let $(C,0)$ be a planar curve singularity. Let $L(q,t,a)$ be its Hilbert $L$-function and let $\mathrm{H}^{\mathrm{mot}}(q,t,a)$ be its normalized motivic superpolynomial. Cherednik–Danilenko–Philipp conjecture.

$$L(q,t,a)=\mathrm{H}^{\mathrm{mot}}(q,t,a).$$

This equality connects the generating function of Hilbert schemes of points on the singularity with the motivic superpolynomial arising from double affine Hecke algebra representations. The source calls the displayed assertion an abridged version of the conjecture and does not report a general resolution.