The rapid use of generative artificial intelligence (GenAI) in higher education has raised concerns about student responsibility, transparency, and meaningful learning. This study examines how prompt literacy, critical AI literacy, and assessment design contribute to epistemic transparency in AI-supported learning environments. A quantitative cross-sectional survey design was adopted. Data were collected from 649 undergraduate and postgraduate students enrolled in higher education institutions in India. Partial least squares structural equation modeling was employed to test the direct, indirect, and interaction effects. The results show that prompt literacy has a strong positive effect on critical AI literacy and a statistically significant but modest direct effect on epistemic transparency. Critical AI literacy further partially mediates the relationship between prompt literacy and epistemic transparency. Critical AI literacy and assessment design also exert significant positive direct effects on epistemic transparency, with assessment design demonstrating the strongest direct practical contribution. However, the interaction between assessment design and critical AI literacy is not significant, indicating that these factors operate independently in promoting transparent AI-supported learning. This study introduces epistemic transparency as a distinct and measurable learning outcome in AI-mediated higher education. By integrating student competencies with assessment design, it offers practical insights for developing responsible and transparent AI use in higher education.