Inequality in college has both structural and psychological causes; these include the presence of self-defeating beliefs about the potential for growth and belonging. Such beliefs can be addressed through large-scale interventions in the college transition (Walton & Cohen, 2011; Walton et al., 2023) but are hard to measure. In our pre-registered study, we provide the strongest evidence to date that the belief that belonging challenges are common and tend to improve with time ("a process-oriented perspective"), the primary target of social-belonging interventions, is critical. We did so by developing and applying computational language measures to 25,000 essays written during a randomized trial of this intervention across 22 broadly representative US colleges and universities (Walton et al., 2023). We compare the hypothesized mediator to one of simple optimism, which includes positive expectations without recognizing that challenges are common. Examining the active control condition, we find that socially disadvantaged students are, indeed, significantly less likely to express a process-oriented perspective spontaneously, and more likely to express simple optimism. This matters: Students who convey a process-oriented perspective, both in control and treatment conditions, are significantly more likely to complete their first year of college full-time enrolled and have higher first-year GPAs, while simple optimism predicts worse academic progress. The social-belonging intervention helped distribute a process-oriented perspective more equitably, though disparities remained. These computational methods enable the scalable and unobtrusive assessment of subtle student beliefs that help or hinder college success. [This research was supported by Stanford's Institute for Human-Centered AI (HAI).]