  We attempt to identify a phenomenologically viable solution to the strong
$CP$ problem in which the axion is composed entirely out of Standard Model
fermion species. The axion consists predominantly of the $\eta'$ meson with a
minuscule admixture of a pseudoscalar bilinear composite of neutrinos,
$\eta_{\nu}$. The Peccei-Quinn symmetry is an axial symmetry that acts on the
up quark and the neutrino species and is spontaneously broken by the QCD
condensate of quarks as well as the condensate of neutrinos triggered by chiral
gravitational anomaly. The up-quark mass is spontaneously generated by the
neutrino condensate which plays the role of an additional composite Higgs
doublet with the compositeness scale of the order of the neutrino masses. Such
a scenario is highly economical: it solves the strong $CP$ problem, generates
the up-quark and neutrino masses from fermion condensates and simultaneously
protects the axion shift symmetry against gravitational anomaly. The
phenomenology is different from the standard hidden axion case. One of the
experimental signatures is the existence of a gravity-competing
isotope-dependent attractive force among nucleons at (sub)micron distances.
