  A numerical detection of the $\tau$-driven transition of galaxy spins is
presented, where $\tau$ is the degree of misalignment between the initial tidal
field and protogalaxy inertia tensors. Analyzing the data from the IllustrisTNG
300-1 simulations, we first measure the values of $\tau$ at the protogalactic
sites found by tracing the constituents of the galactic halos in the mass range
of $10.5\le \log \left[M_{h}/(h^{-1}M_{\odot})\right] \le 13$ back to the
initial stage, $z_{i}=127$. The probability density functions of $\tau$ are
shown to be well modeled by the $\Gamma$-distributions, whose shape and scale
parameters turn out to have universal values on a certain critical scale. Then,
we investigate how the strength and tendency of the galaxy spin alignments with
the principal axes of the local tidal fields depend on the initial condition,
$\tau$. It is found that on the scale lower than the critical one, the galaxy
spin transition occurs at two different thresholds from the major to
intermediate and from the intermediate to minor principal axes of the local
tidal fields, respectively. Noting that the $\tau$-dependent spin transition
supersedes in strength the previously found mass-dependent,
morphology-dependent, and radius-dependent counterparts, we suggest that $\tau$
should be the key driver of all types of the galaxy spin transition and that
the present galaxy spins are indeed excellent fossil records of the initial
condition.
