  Axions as dark matter is an increasingly important subject in astrophysics
and cosmology. Experimental and observational searches are mounting across the
mass spectrum of axion-like particles, many of which require detailed knowledge
of axion structure over a wide range of scales. Current understanding of axion
structures is far from complete, however, due largely to controversy in
modeling the candidate's highly-degenerate state. The series Axion Structure
Formation seeks to develop a consistent model of QCD axion dark matter dynamics
that follows their highly-degenerate nature to the present using novel modeling
techniques and sophisticated simulations. This inaugural paper presents the
problem of describing many non-relativistic axions with minimal degrees of
freedom and constructs a theory of axion infall for the limit of complete
condensation. The derived model is shown to contain axion-specific dynamics not
unlike the exchange-correlation influences experienced by identical fermions.
Perturbative calculations are performed to explore the potential for imprints
in early universe structures.

Cosmology and Nongalactic Astrophysics;Astrophysics of Galaxies;High Energy Physics - Phenomenology