Photonic synthesis of radio frequency waveforms revived the quest for unrivalled microwave purity by its seducing ability to convey the benefits of the optics to the microwave world. In this contribution, we will present a high-fidelity transfer of frequency stability between an optical reference and a microwave signal via a low-noise fiber-based frequency comb and cutting-edge photo-detection techniques. We will show the generation of the purest microwave signal with a fractional frequency stability below 6.5 x 10(-16) at 1 s and a timing noise floor below 41 zs Hz(-1/2) (phase noise below-173 dBc Hz(-1) for a 12 GHz carrier). This outclasses existing sources and promises a new era for state-of-the-art microwave generation. The characterization is achieved through a heterodyne cross-correlation scheme with lowermost detection noise. This unprecedented level of purity can impact domains such as radar systems, telecommunications and time-frequency metrology. The measurements methods developed here can benefit the characterization of a broad range of signals.