We demonstrate successful dry refrigeration of quantum fluids down to $T=0.16$,mK by using copper nuclear demagnetization stage that is pre-cooled by a pulse-tube-based dilution refrigerator. This type of refrigeration delivers a flexible and simple sub-mK solution to a variety of needs including experiments with superfluid $^3$He. Our central design principle was to eliminate relative vibrations between the high-field magnet and the nuclear refrigeration stage, which resulted in the minimum heat leak of $Q=4.4$,nW obtained in field of 35,mT. For thermometry, we employed a quartz tuning fork immersed into liquid $^3$He. We show that the fork oscillator can be considered as self-calibrating in superfluid $^3$He at the crossover point from hydrodynamic into ballistic quasiparticle regime.
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