  In 2005 Dunfield, Gukov and Rasmussen conjectured an existence of the
spectral sequence from the reduced triply graded Khovanov-Rozansky homology of
a knot to its knot Floer homology defined by Ozsv\'ath and Szab\'o. The main
result of this paper is a proof of this conjecture. For this purpose, we
construct a bigraded spectral sequence from the $\mathfrak{gl}_0$ homology
constructed by the last two authors to the knot Floer homology. Using the fact
that the $\mathfrak{gl}_0$ homology comes equipped with a spectral sequence
from the reduced triply graded homology, we obtain our main result. The first
spectral sequence is of Bockstein type and comes from a subtle manipulation of
coefficients. The main tools are quantum traces of foams and of singular
Soergel bimodules and a $\mathbb Z$-valued cube of resolutions model for knot
Floer homology originally constructed by Ozsv\'ath and Szab\'o over the field
of two elements. As an application, we deduce that the $\mathfrak{gl}_0$
homology as well as the reduced triply graded Khovanov-Rozansky one detect the
unknot, the two trefoils, the figure eight knot and the cinquefoil.

Geometric Topology;Algebraic Topology