A Recurring Capture Pattern in Education Systems: Why separated purposes between academic learning and extracurricular sports activities drive domain-specific optimization instead of shared capability development

Learners tend to develop domain-specific behaviors rather than shared capabilities when academic learning and extracurricular sports activities are structured under separated purposes within the same education system. This paper documents a Recurring Capture Pattern (RCP) observed in education systems. Under the institutional condition of a purpose-separation structure in which academic learning and school-based sports are operated under different institutional objectives within a single education system, individually rational behavior systematically converges not toward the development of shared, cross-domain capabilities required in both learning and practice but toward domain-specific adaptive behaviors that are optimized for evaluation within each sub-domain. As these behaviors accumulate, they alter the operational conditions of the system itself, resulting in reinforced separation between academic and athletic domains, reduced visibility of shared capabilities, and increasing difficulty in integrating learning and practice, and reinforcing the same behavioral convergence through a recursive institutional feedback loop. The pattern ultimately produces fragmentation of capability development, binary trade-offs between study and sports, and structural disconnection between learning and embodied practice, indicating a structural misalignment between institutional objectives and rational behavioral adaptation. This paper analytically describes the structural relationship between institutional design and rational behavioral adaptation.