  In extensive air shower experiments, the number of muons crossing a detector
at a given position, as well as their arrival time, arrival direction, and
energy, are determined by a more fundamental 3-dimensional distribution linked
to the hadronic core of the shower. Muons are produced high up in the
atmosphere after the decay of mesons in the hadronic cascade. The distributions
of production depth, energy, and transverse momentum of muons are enough to
fully predict the muon component of air showers in any particular observational
condition. By using air-shower simulations with the state-of-the-art hadronic
interaction models, the mentioned distributions at production are analyzed as a
function of zenith angle, primary mass, and hadronic interaction model, and
their level of universality is studied and assessed in an exhaustive manner for
the first time.
