  Particle acceleration mechanisms in supermassive black hole jets, such as
shock acceleration, magnetic reconnection, and turbulence, are expected to have
observable signatures in the multi-wavelength polarization properties of
blazars. The recent launch of the Imaging X-ray Polarimetry Explorer (IXPE)
enables us, for the first time, to use polarization in the X-ray band (2-8 keV)
to probe the properties of the jet synchrotron emission in
high-frequency-peaked BL Lac objects (HSPs). We report the discovery of X-ray
linear polarization (degree $\Pi_{\rm x}=15\pm$2\% and electric-vector position
angle $\Psi_{\rm x}=35^\circ\pm4^\circ$) from the jet of the HSP Mrk~421 in an
average X-ray flux state. At the same time, the degree of polarization at
optical, infrared, and millimeter wavelengths was found to be lower by at least
a factor of 3. During the IXPE pointing, the X-ray flux of the source increased
by a factor of 2.2, while the polarization behavior was consistent with no
variability. The higher level of $\Pi_{\rm x}$ compared to longer wavelengths,
and the absence of significant polarization variability, suggest a shock as the
most likely X-ray emission site in the jet of Mrk 421 during the observation.
The multiwavelength polarization properties are consistent with an
energy-stratified electron population, where the particles emitting at longer
wavelengths are located farther from the acceleration site, where they
experience a more disordered magnetic field.
