Dynamical clustering of U.S. states reveals four distinct infection patterns that predict SARS-CoV-2 pandemic behavior

The SARS-CoV-2 pandemic has so far unfolded diversely across the fifty United States of America, reflected both in different time progressions of infection "waves" and in magnitudes of local infection rates. Despite a marked diversity of presentations, most U.S. states experienced their single greatest surge in daily new cases during the transition from Fall 2020 to Winter 2021. Popular media also cite additional similarities between states -- often despite disparities in governmental policies, reported mask-wearing compliance rates, and vaccination percentages. Here, we identify a set of robust, low-dimensional clusters that 1) summarize the timings and relative heights of four historical COVID-19 "wave opportunities" accessible to all 50 U.S. states, 2) correlate with geographical and intervention patterns associated with those groups of states they encompass, and 3) predict aspects of the "fifth wave" of new infections in the late Summer of 2021. In particular, we argue that clustering elucidates a negative relationship between vaccination rates and subsequent case-load variabilities within state groups. We advance the hypothesis that vaccination acts as a ``seat belt," in effect constraining the likely range of new-case upticks, even in the context of the Summer 2021, variant-driven surge.