  CTCV J2056--3014 is a nearby cataclysmic variable with an orbital period of
approximately $1.76$ hours at a distance of about $853$ light-years from the
Earth. Its recently reported X-ray properties suggest that J2056-3014 is an
unusual accretion-powered intermediate polar that harbors a fast-spinning white
dwarf (WD) with a spin period of $29.6$ s. The low X-ray luminosity and the
relatively modest accretion rate per unit area suggest that the shock is not
occurring near the WD surface. It has been argued that, under these conditions,
the maximum temperature of the shock cannot be directly used to determine the
mass of the WD (which, under the abovementioned assumptions, would be around
$0.46$ $M_\odot$). Here, we explore the stability of this rapidly rotating WD
using a modern equation of state (EoS) that accounts for electron--ion,
electron--electron, and ion--ion interactions. For this EoS, we determine the
mass density thresholds for the onset of pycnonuclear fusion reactions and
study the impact of microscopic stability and rapid rotation on the structure
and stability of WDs, considering them with helium, carbon, oxygen, and neon.
From this analysis, we obtain a minimum mass for CTCV J2056--3014 of
$0.56~M_\odot$ and a maximum mass of around $1.38~M_\odot$. If the mass of CTCV
J2056--3014 is close to the lower mass limit, its equatorial radius would be on
the order of $10^4$~km due to rapid rotation. Such a radius is significantly
larger than that of a nonrotating WD of average mass ($0.6\, M_\odot$), which
is on the order of $7\times 10^3$~km. The effects on the minimum mass of
J2056-3014 due to changes in the temperature and composition of the stellar
matter were found to be negligibly small.
