Title: Orbital Polarimetric Tomography of a Flare Near the Sagittarius A* Supermassive Black Hole

Abstract: The interaction between the supermassive black hole at the center of the Milky Way, Sagittarius A*, and its accretion disk occasionally produces high-energy flares seen in X-ray, infrared, and radio. One proposed mechanism that produces flares is the formation of compact, bright regions that appear within the accretion disk and close to the event horizon. Understanding these flares provides a window into accretion processes. Although sophisticated simulations predict the formation of these flares, their structure has yet to be recovered by observations. Here we show the first three-dimensional (3D) reconstruction of an emission flare recovered from ALMA light curves observed on April 11, 2017. Our recovery shows compact, bright regions at a distance of roughly six times the event horizon. Moreover, it suggests a clockwise rotation in a low-inclination orbital plane, consistent with prior studies by GRAVITY and EHT. To recover this emission structure, we solve an ill-posed tomography problem by integrating a neural 3D representation with a gravitational model for black holes. Although the recovery is subject to, and sometimes sensitive to, the model assumptions, under physically motivated choices, our results are stable, and our approach is successful on simulated data.