This paper proposes a rigorous framework to examine the two-way relationship between artificial intelligence (AI), human cognition, problem-solving, and cultural adaptation across academic and business settings. It addresses a key gap by asking how AI reshapes cognitive processes and organizational norms, and how cultural values and institutional contexts shape AI adoption, trust, and use over time. We employ a three-wave longitudinal design that tracks AI knowledge, perceived competence, trust trajectories, and cultural responses. Participants span academic institutions and diverse firms, enabling contextual comparison. A dynamic sample continuous, intermittent, and wave-specific respondents mirrors real organizational variability and strengthens ecological validity. Methodologically, the study integrates quantitative longitudinal modeling with qualitative thematic analysis to capture temporal, structural, and cultural patterns in AI uptake. We trace AI acculturation through phases of initial resistance, exploratory adoption, and cultural embedding, revealing distinctive trust curves and problem-solving strategies by context: academic environments tend to collaborative, deliberative integration; business environments prioritize performance, speed, and measurable outcomes. Framing adoption as bidirectional challenges deterministic views: AI both reflects and reconfigures norms, decision-making, and cognitive engagement. As the first comparative longitudinal study of its kind, this work advances methodological rigor and offers actionable foundations for human-centred, culturally responsive AI strategies-supporting evidence-based policies, training, and governance that align cognitive performance, organizational goals, and ethical commitments.
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