Bose-Einstein correlations (BECs) of identical hadrons reveal information about hadron creation from the strongly interacting matter formed in ultrarelativistic heavy-ion collisions. The measurement of three-particle correlations may in particular shed light on hadron creation mechanisms beyond thermal/chaotic emission. In this paper, we show the status of PHENIX measurements of three-pion correlations as a function of momentum differences within the triplets. We analyze the shape of the correlation functions through the assumption of Lévy sources and a proper treatment of the Coulomb interaction within the triplets. We measure the three-particle correlation strength (λ 3), which, together with the two-particle correlation strength λ 2 , encodes information about hadron creation mechanisms. From a consistent analysis of two-and three-particle correlation strengths, we establish a new experimental measure of thermalization and coherence in the source.