  We show that the triply-graded Khovanov-Rozansky homology of the $(m,n)$
torus knot can be recovered from the finite-dimensional representation
$\mathrm{L}_{m/n}$ of the rational Cherednik algebra at slope $m/n$, endowed
with the Hodge filtration coming from the cuspidal character D-module. Our
approach involves expressing the associated graded of the cuspidal character
D-module in terms of a dg module closely related to the action of the shuffle
algebra on the equivariant K-theory of the Hilbert scheme of points on the
plane, thereby proving the rational master conjecture. As a corollary, we
identify the Hodge filtration with the inductive and algebraic filtrations on
$\mathrm{L}_{m/n}$.
