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CTCV J2056–3014 is a nearby cataclysmic variable with an orbital period of approximately 1.76 h 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 ⊙ ). 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 ⊙ and a maximum mass of around 1.38 M ⊙ . 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 ⊙ ), which is on the order of 7 × 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.