Universal properties of the high- and low-{\alpha} disk: small intrinsic
  abundance scatter and migrating stars
  The detailed age-chemical abundance relations of stars measures
time-dependent chemical evolution.These trends offer strong empirical
constraints on nucleosynthetic processes, as well as the homogeneityof
star-forming gas. Characterizing chemical abundances of stars across the Milky
Way over time has been made possible very recently, thanks to surveys like
Gaia, APOGEE and Kepler. Studies of the low-${\alpha}$ disk have shown that
individual elements have unique age-abundance trends and the intrinsic
dispersion around these relations is small. In this study, we examine and
compare the age distribution of stars across both the high and low-${\alpha}$
disk and quantify the intrinsic dispersion of 16 elements around their
age-abundance relations at [Fe/H] = 0 using APOGEE DR16. We find the
high-${\alpha}$ disk has shallower age-abundance relations compared to the
low-${\alpha}$ disk, but similar median intrinsic dispersions of ~ 0.04 dex,
suggesting universal element production mechanisms for the high and
low-${\alpha}$ disks, despite differences in formation history. We visualize
the temporal and spatial distribution of disk stars in small chemical cells,
revealing signatures of upside-down and inside-out formation. Further,the
metallicity skew and the [Fe/H]-age relations - across radius indicates
different initial metallicity gradients and evidence for radial migration. Our
study is accompanied by an age catalogue for 64,317 stars in APOGEE derived
usingThe Cannon with ~ 1.9 Gyr uncertainty across all ages (APO-CAN stars) as
well as a red clump catalogue of 22,031 stars with a contamination rate of
2.7%.
