Resolution of (Heavy) Primaries in Ultra High Energy Cosmic Rays

Measurements of Ultra-High Energy Cosmic Rays (UHECR) suggest a complex composition with significant contributions from heavy nuclei at the highest energies. We systematically explore how the selection and number of primary nuclei included in the analysis impact the inferred UHECR mass composition. Introducing a distance measure in the space of $X_{\mathrm{m}\mathrm{a}\mathrm{x}}$ distribution moments, we demonstrate that limiting the analysis to a few primaries can introduce significant biases, particularly as observational data improves. We provide lists of primaries approximately equidistant in the new measure, which guaranty unbiased results at given statistical confidence. Additionally, we explore consistent inclusion of nuclei heavier than iron and up to plutonium, deriving first observational upper bounds on their contributions to UHECR with the Pierre Auger Open Data.