  Motivated by the flavored Peccei-Quinn symmetry for unifying the flavor
physics and string theory, we construct an explicit model by introducing a
$U(1)$ symmetry such that the $U(1)_X$-$[gravity]^2$ anomaly-free condition
together with the standard model flavor structure demands additional sterile
neutrinos as well as no axionic domain-wall problem. Such additional sterile
neutrinos play the role of a realization of baryogenesis via a new Affleck-Dine
leptogenesis. We provide grounds for that the $U(1)_X$ symmetry could be
interpreted as a fundamental symmetry of nature. The model will resolve rather
recent, but fast-growing issues in astro-particle physics, including leptonic
mixings and CP violation in neutrino oscillation, high-energy neutrinos, QCD
axion, and axion cooling of stars. The QCD axion decay constant, through its
connection to the astrophysical constraints of stellar evolution and the SM
fermion masses, is shown to be fixed at $F_A=1.30^{+0.66}_{-0.54}\times10^{9}$
GeV (consequently, its mass is $m_a=4.34^{+3.37}_{-1.49}$ meV and axion-photon
coupling is $|g_{a\gamma\gamma}|=1.30^{+1.01}_{-0.45}\times10^{-12}\,{\rm
GeV}^{-1}$). Interestingly enough, we show that neutrino oscillations at low
energies could be connected to astronomical-scale baseline neutrino
oscillations. The model predicts non-observational neutrinoless double beta
($0\nu\beta\beta$) decay rate as well as a remarkable pattern between leptonic
Dirac CP phase ($\delta_{CP}$) and atmospheric mixing angle ($\theta_{23}$);
{\it e.g.} $\delta_{CP}\simeq220^{\circ}-240^{\circ}$,
$120^{\circ}-140^{\circ}$ for $\theta_{23}=42.3^{\circ}$ for normal mass
ordering, and $\delta_{CP}\simeq283^{\circ},250^{\circ},100^{\circ},70^{\circ}$
for $\theta_{23}=49.5^{\circ}$ for inverted one.
