Ultra-high energy cosmic rays interact with nuclei of the Earth’s atmosphere at $\sim 10 \times \sqrt{s}$ of proton-proton collisions at the LHC and in extremely high rapidity regions, providing a unique opportunity to probe hadronic interactions in poorly explored regions of the kinematic phase space of p-air interactions.

In this contribution, we show that fluctuations in the muon content of Extensive Air Showers correlate with fluctuations of the fraction of the primary energy that goes into hadronic channel of the primary p-air interaction. Furthermore, we show that measurements of the slope of the low tail of the muon number distribution in EAS constrain the forward inclusive cross-section for the production of neutral pions in-pair interactions at $\sim 450$ TeV.

Moreover, we explore the joint $X_{\max}-N_{\mu}$ distribution, demonstrating that the slope of the tail of the muon number distribution is sensitivity to $X_{\max}$, in such a way that hadronic models converge for shallower $X_{\max}$ and diverge for deeper showers. In particular, we hint at the connection between these regimes and the presence of diffraction in p-air interactions.