We introduce a set of new multiparticle production variables derived from the energy spectrum
of secondary hadrons in ultra-high-energy proton-air interactions. The distributions of these
variables can be measured within the phase space accessible to particle detectors in accelerator
experiments, and are highly dependent on the hadronic interaction model. Furthermore, we
demonstrate a precise, hadronic-model-independent mapping between these variables and the
joint distribution of the depth of shower maxima and the number of muons in extensive air
showers. This enables the use of air shower measurements to constrain hadron production in
kinematic regimes beyond the reach of human-made colliders.