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Description
The X-ray pulsar Her X-1 has a number of well-known periodicities, including a $\sim 35$-day superorbital cycle due to precession of a tilted twisted accretion disk around a magnetized neutron star. In addition to precession, the tilted accretion disk should experience tidal nutation (wobbling). We present results of analysis of dedicated SRG/ART-XC observations confirming the accrtetion disk wobbling. We have studied the long-term behavior of the 35-day cycle of Her X-1 using CGRO/BATSE,RXTE/ASM, Swift/BAT, Fermi/GBM, MAXI data and archival turn-on moments of the 35-day cycle spanning more than 50 years. We show that the turn-on moments of the source are distributed bimodally over the orbital phases with maxima near phases 0.2 and 0.7 as predicted in the model of the wobbling accretion disk. A sliding-window averaged Х-ray phase light curve and classical O--C diagram for individual 35-day turn-ons enabled us to reveal a long-term parabolic trends on the O--C diagram suggesting a secular decrease in the 35-d precession period with $\dot P_{pr} \sim$ a few $\times10^{-5} \,\mathrm{~s\,s}^{-1}$. This long-term 35-day period decay can be due to the accretion disk precessional period change directly related to the accretion-induced decrease in the neutron star free precession period.