Recent research on curricular analytics suggests that the structure of a college major may impact major persistence and degree completion. Contributing to this line of research, we propose and test a new measure of the "lived curriculum" that captures the extent to which cohorts within a major take the same exact course-taking path as they advance from matriculation to graduation (or institutional exit). First, we describe variation in path homogeneity across both STEM and non-STEM majors at one public research-intensive institution. Second, we show that a major's level of path homogeneity is correlated with the percentage of "locked" requirements in its stated curriculum, but that the stated curriculum cannot account for all observed differences in path homogeneity. Third, we conduct a correlational analysis of early exposure to path homogeneity and graduation likelihood. Findings show that students with average levels of academic preparation are less likely to graduate if enrolled in path-homogeneous majors compared to more path-heterogeneous (i.e., flexible) majors, and that negative outcomes associated with a path-homogeneous major are exacerbated for students with below-average preparation. Supplemental analyses show that this relationship holds for STEM and non-STEM majors, cannot be explained away by the competitiveness of a major, and that students generally switched from more to less path-homogeneous majors over the course of their college careers. Taken together, these findings urge re-examination of the ways college majors can promote retention.