  J191213.72-441045.1 is a binary system composed of a white dwarf and an
M-dwarf in a 4.03-hour orbit. It shows emission in radio, optical, and X-ray,
all modulated at the white dwarf spin period of 5.3 min, as well as various
orbital sideband frequencies. Like in the prototype of the class of
radio-pulsing white dwarfs, AR Scorpii, the observed pulsed emission seems to
be driven by the binary interaction. In this work, we present an analysis of
far-ultraviolet spectra obtained with the Cosmic Origins Spectrograph at the
Hubble Space Telescope, in which we directly detect the white dwarf in
J191213.72-441045.1. We find that the white dwarf has an effective temperature
of 11485+/-90 K and mass of 0.59+/-0.05 solar masses. We place a tentative
upper limit on the magnetic field of ~50 MG. If the white dwarf is in thermal
equilibrium, its physical parameters would imply that crystallisation has not
started in the core of the white dwarf. Alternatively, the effective
temperature could have been affected by compressional heating, indicating a
past phase of accretion. The relatively low upper limit to the magnetic field
and potential lack of crystallisation that could generate a strong field pose
challenges to pulsar-like models for the system and give preference to
propeller models with a low magnetic field. We also develop a geometric model
of the binary interaction which explains many salient features of the system.
