  The fraction of positronium (Ps) emitted from a surface of a germanium single
crystal at high temperature is usually assumed to approach unity at zero
positron implantation energy. In the experiment, however, the determination of
the absolute Ps fraction is not straight forward since recording a reference
spectrum with $100\,\%$ Ps formation remains demanding. We use GEANT4-simulated
detector responses to $2\gamma$ and $3\gamma$ radiation sources mimicking
positron and Ps annihilation inside the (coincidence) Doppler-broadening
spectrometer at NEPOMUC, FRM II, in order to derive a reliable value for the Ps
fraction reemitted from a Ge(100) target heated close to its melting point.
Analysis of the measured spectra by fitting the simulated spectra shows an
absolute value of $(72\,\pm{4})\,\%$ maximum Ps formation, contradicting the
$100\,\%$ assumption.
