† Authors contributed equally to this work.URu2Si2 exhibits a clear phase transition at THO = 17.5 K to a low-temperature phase known as "hidden order" (HO). Even the most basic information needed to construct a theory of this state-such as the number of components in the order parameter-has been lacking. Here we use resonant ultrasound spectroscopy (RUS) and machine learning to determine that the order parameter of HO is one-dimensional (singlet), ruling out a large class of theories based on twodimensional (doublet) order parameters. This strict constraint is independent of any microscopic mechanism, and independent of other symmetries that HO may break. Our technique is general for second-order phase transitions, and can discriminate between nematic (singlet) versus loop current (doublet) order in the high-Tc cuprates, and conventional (singlet) versus the proposed px + ipy (doublet) superconductivity in Sr2RuO4. The machine learning framework we develop should be readily adaptable to other spectroscopic techniques where missing resonances confound traditional analysis, such as NMR.