Mathematical, Neurobiological, and Mechanical Integration of the Core Emotion Framework: Mapping Intuitive Tri-Centric Dynamics to Formal Architecture

Colloquial models of human psychology frequently rely on intuitive, simplified divisions—characterizing the "Head" as the locus of analytical thinking, the "Heart" as the source of emotional warmth, and the "Gut" as the driver of impulsive action. While these heuristics provide accessible shorthand for everyday self-reflection, they lack the mathematical, biological, and mechanical precision required for clinical diagnostics, affective computing, or targeted psychotherapeutic design. The Core Emotion Framework (CEF), a structural-constructivist paradigm developed to unify affective science, systematizes these intuitive heuristics by translating them into a mathematically explicit, neurobiologically grounded, and mechanically actuated architecture. Rather than treating emotions as fleeting, subjective states, the CEF models affect as a system of ten discrete functional operators distributed across three autonomous neural hubs. By mapping these operators onto the geometric state-space of the Poincaré-Bloch sphere and aligning them with physical hardware, the CEF bridges the historic divide between classical innate emotion theories and modern psychological constructionism.