Why does massive AI investment fail to generate commensurate productivity gains? We argue the paradox is theoretically generated: prevailing production function frameworks encounter a structural boundary by treating AI as a separable factor of production without modeling the cognitive mediation through which AI generates productive value. This directs investment toward deployment when productivity requires prior development of what we term convergence capacity (C). We propose the Intellectually Converged Human (ICH) framework, a fifth-stage framework for production function theory: H-hat = H[1 + phi(A,C)], where effective productive capacity equals human capital (H) scaled by an augmentation factor [1 + phi], with phi jointly determined by AI utilization intensity (A) and convergence capacity (C), a four-dimensional cognitive construct encompassing embodied understanding, metacognition, temporal integration, and integrative thinking. The production function Y = F(K, H-hat) provides a human-centered mechanism for Solow's TFP residual: A_Solow = [1 + phi(A,C)]^(1-alpha). The framework predicts three augmentation regimes with distinct policy implications. Descriptive cross-national analysis of 20 OECD economies shows the AIxC interaction is associated with 86% of TFP variance versus 31% for AI alone, a pattern-consistent finding in the small-n theoretical tradition. South Korea exemplifies national-scale under-augmentation: high H, substantial A, low C produce phi = 0. We distinguish convergence capacity from adjacent constructs, absorptive capacity, dynamic capability, and human capital, and demonstrate that C constitutes the specific cognitive mediator that prior frameworks have left implicit. We derive C-first policy prescriptions and offer three empirically testable propositions with a falsifiable 10-year forecast.

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