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A major obstacle in the attempt to understand high-temperature superconductivity in cuprate superconductors has been distinguishing universal features and trends in experimental signatures from those that are materials or technique-dependent. Towards that end, we have pursued angle-resolved photoemission spectroscopy (ARPES) studies on the model cuprate HgBa₂CuO_4+δ (Hg1201), which has a simple crystal structure, high optimal T_c, and is well characterized by other techniques. Here, we provide an ARPES study of doping-, temperature- and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201, revealing a hierarchy of three distinct energy scales. These establish several universal phenomena connecting multiple experimental techniques with comparable spectral features across different cuprates