  Context: Tracing unstable isotopes produced in supernova nucleosynthesis
provides a direct diagnostic of supernova explosion physics. Theoretical models
predict an extensive variety of scenarios, which can be constrained through
observations of the abundant isotopes $^{56}$Ni and $^{44}$Ti. Direct evidence
of the latter was previously found only in two core-collapse supernova events,
and appears to be absent in thermonuclear supernovae.Aims: We aim to to
constrain the supernova progenitor types of Cas A, SN 1987A, Vela Jr.,
G1.9+0.3, SN1572, and SN1604 through their $^{44}$Ti ejecta masses and
explosion kinematics. Methods: We analyzed INTEGRAL/SPI observations of the
candidate sources utilizing an empirically motivated high-precision background
model. We analyzed the three dominant spectroscopically resolved de-excitation
lines at 68, 78, and 1157\,keV emitted in the decay chain of $^{44}$Ti. The
fluxes allow the determination of the production yields of $^{44}$Ti. Remnant
kinematics were obtained from the Doppler characteristics of the lines.
Results: We find a significant signal for Cas A in all three lines with a
combined significance of 5.4$\sigma$. The fluxes are $(3.3 \pm 0.9) \times
10^{-5}$ ph cm$^{-2}$ s$^{-1}$, and $(4.2 \pm 1.0) \times 10^{-5}$ ph cm$^{-2}$
s$^{-1}$ for the $^{44}$Ti and $^{44}$Sc decay, respectively. We obtain higher
fluxes for $^{44}$Ti with our analysis of Cas A than were obtained in previous
analyses. We discuss potential differences. Conclusions: We obtain a high
$^{44}$Ti ejecta mass for Cas A that is in disagreement with ejecta yields from
symmetric 2D models. Upper limits for the other core-collapse supernovae are in
agreement with model predictions and previous studies. The upper limits we find
for the three thermonuclear supernovae consistently exclude the double
detonation and pure helium deflagration models as progenitors.
