  On the pre-main-sequence, the rotation rates of Sun-like stars are dictated
by the interplay between the protostellar disk and the star's contraction. At
ages exceeding 100 million years (Myr), magnetic spin-down erases the initial
stellar spin rate and enables rotation-based age dating (gyrochronology). The
exact time at which the transition between these two regimes occurs depends on
stellar mass, and has been challenging to empirically resolve due to a lack of
viable calibration clusters. The $\alpha$ Persei open cluster ($t\approx80$
Myr, $d\approx170$ pc) may provide the needed calibrator, but recent analyses
of the Gaia data have provided wildly varying views of its age and spatial
extent. As such, we analyze a combination of TESS, Gaia, and LAMOST data to
calibrate gyrochronology at the age of $\alpha$ Per and to uncover the
cluster's true morphology. By assembling a list of rotationally-confirmed
$\alpha$ Per members, we provide strong evidence that $\alpha$ Per is part of a
larger complex of similarly-aged stars. Through kinematic back-integration, we
show that the most diffuse components of $\alpha$ Per were five times closer
together 50 Myr ago. Finally, we use our stellar rotation periods to derive a
relative gyrochronology age for $\alpha$ Per of 67 $\pm$ 12% the age of the
Pleiades, which yields 86 $\pm$ 16 Myr given current knowledge. We show that by
this age, stars more massive than $\approx$0.8 M$_{\odot}$ have converged to
form a well-defined slow sequence.
