  We demonstrate efficient sub-thermal cooling of the modified cyclotron mode
of a single trapped antiproton and reach particle temperatures
$T_+=E_+/k_\text{B}$ below $200\,$mK in preparation times shorter than
$500\,$s. This corresponds to the fastest resistive single-particle cyclotron
cooling to sub-thermal temperatures ever demonstrated. By cooling trapped
particles to such low energies, we demonstrate the detection of antiproton spin
transitions with an error-rate $<0.000025$, more than three orders of magnitude
better than in previous best experiments. This method will have enormous impact
on multi-Penning-trap experiments that measure magnetic moments with single
nuclear spins for tests of matter/antimatter symmetry, high-precision
mass-spectrometry, and measurements of electron $g$-factors bound to
highly-charged ions that test quantum electrodynamics.
