Update on the intermediate arrival-direction analyses of the Pierre Auger Observatory

We present an update on the arrival-direction analyses conducted on intermediate angular scales using the complete Phase I data of the Pierre Auger Observatory up to the end of $2022$ with a total exposure of $135{,}000\,\text{km}^2\,\text{sr}\,\text{yr}$. We show the arrival-direction distribution of the ultra-high-energy cosmic rays along the supergalactic plane above $20\,\text{EeV}$, and an update in the search for magnetically-induced signatures in the arrival directions. Furthermore, we present the potential of introducing estimators for the rigidity ordering of the events to enhance arrival-direction analyses on small to intermediate angular scales. To achieve this, we take advantage of two estimators working on the response of the surface detector: an analytical fit based on air-shower universality and a deep neural network.