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One can make a theoretical upper bound by considering the most short-lived star possible $\tau_{short}$, and a large supply of initial hydrogen $M_H$. Then one could calculate the fraction hydrogen that is recycled $r$ after the star ends (with a supernova), and get a total number of generations as $\log (M_{star}/M_H)/\log(r)$. If one uses the solar-mass \$...