Hope influences learning engagement through generative AI acceptance among Chinese college students: conditional direct effect of growth mindset

College students' learning engagement is widely regarded as an important indicator of learning quality and academic development. Understanding the psychological and technological factors associated with learning engagement has become increasingly important in AI-supported learning environments. This study examined the relationships among hope, generative AI acceptance (GAA), growth mindset (GM), and learning engagement (LE) by proposing and testing a conditional direct effect model. Data were collected from 478 Chinese college students through an online questionnaire survey. SPSS 26.0, PROCESS 4.2, and AMOS 24.0 were used to conduct descriptive statistics, reliability and validity analyses, confirmatory factor analysis, correlation analysis, and conditional direct effect analysis. The results indicated that hope was positively associated with learning engagement. Generative AI acceptance partially mediated the relationship between hope and learning engagement. In addition, growth mindset significantly moderated the direct association between hope and learning engagement. Specifically, the positive association between hope and learning engagement was stronger among students with lower levels of growth mindset and weaker among those with higher levels of growth mindset, suggesting a compensatory pattern between these two psychological resources. The findings highlight the complementary roles of psychological resources and technology acceptance in understanding learning engagement in AI-supported learning environments. This study contributes to the literature by integrating hope, generative AI acceptance, and growth mindset within a single framework and provides empirical evidence regarding the psychological and technological factors associated with learning engagement among college students. The findings also offer practical implications for higher education institutions seeking to support student engagement in the generative AI era.