Unfolding the Energy Spectrum of Ultra-High-Energy Cosmic Rays Using Pierre Auger Open Data

We reconstruct the energy spectrum of ultra-high-energy cosmic rays using the publicly released Pierre Auger Observatory data set. Since event-level Monte Carlo truth information is not included in the open data, we develop a consistent procedure to regenerate a pseudo-Monte Carlo sample directly from the published quantities: the registered event counts $N$, the unfolded spectrum $N_\mathrm{corr}$, and the detector response matrix $R_{ij}$ from the Auger 2020 spectrum data analysis. Using the row-normalized response matrix and the published unfolded spectrum as a truth prior, we construct an absolute-level migration matrix and generate the event-by-event truth and reconstructed-level pairs by drawing from a two-dimensional probability distribution function. The resulting sample statistically replicates the detector response properties of the Pierre Auger Surface Detector. This pseudo-MC sample allows for the application of classical unfolding techniques (bin-by-bin and iterative Bayesian unfolding via RooUnfold) as well as a machine-learning-based unfolding using OmniFold. We demonstrate that using such publicly available information this approach allows the full unfolding procedure.