The Diffraction Profile of Human Expertise: A Continuous, Constraint-Satisfying Framework for Optimal Cognitive Resource Allocation

Traditional models of skill distribution (I-, T-, Pi-, and Comb-shaped) treat expertise as discrete blocks, inevitably violating the strict biological constraint of finite cognitive energy. This paper introduces the Diffraction Profile-a novel continuous framework borrowed from single-slit Fraunhofer diffraction-that mathematically reconciles absolute mastery in one domain with energy-efficient transfer into adjacent fields, while preserving a generalist floor. Skill depth S(x) is modeled as a normalized squared sinc function plus a baseline, explicitly satisfying the integral energy constraint S(x) dx = E. The resulting profile maximizes peak mastery M while generating natural secondary maxima. Crucially, these secondary lobes map perfectly to structurally isomorphic disciplines-predicting spikes of competence in conceptually distant fields that share underlying architectures, aligning with an updated view of Thorndike's identical-elements theory. The model yields testable predictions for elite performers, resolves long-standing specialization-generalization.