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This study examines whether a generic core underlies problem-solving (PS) competence, addressing longstanding fragmentation in PS research. Using psychometric modeling on the PISA 2012 Computer-Based Assessment dataset, we investigate the relationships among generic, domain-specific, and domain-general PS constructs. Three models—the Bifactor, Subdimension, and Composite—are compared. Findings indicate that the Composite model most accurately and interpretable represents PS across assessments. This evidence substantiates an integrated PS structure, advancing theoretical debates and guiding assessment and curriculum frameworks. By bridging past debates and informing future research, this study contributes to equipping students with adaptive, cross-domain problem-solving skills essential for addressing complex global challenges