Mathematical and Neurobiological Unification of the Core Emotion Framework: A Staged Validation and Architectural Specification

This paper presents a unified mathematical, neurobiological, and mechanical architecture for the Core Emotion Framework (CEF), a structural constructivist model that conceptualizes affective function as a system of ten discrete operators distributed across three autonomous neural hubs: the cephalic, cardiac, and enteric nervous systems. Emotional transitions are formalized using quantum semantic principles by mapping operator dynamics onto the Poincaré–Bloch sphere, where affective states evolve through unitary rotations within a constrained geometric state space. This representation enables a continuous dynamical model in which pathological fusions—such as the Calculating–Constricting entanglement—manifest as topological deformations and attractor states that restrict rotational degrees of freedom. The neurobiological grounding of the tri centric architecture is established through evidence for independent processing capabilities in each neural hub, including the intrinsic cardiac nervous system and the enteric neural plexuses. The framework further integrates a mechanical actuation ecosystem that mirrors emotional polarities through clockwise, counter clockwise, and swing dynamics, enabling somatic affective alignment via physical interaction. A four phase empirical validation roadmap is proposed, spanning mechanical endurance testing, human factors evaluation, operator level fidelity assessment, and longitudinal safety governance. Together, these components establish the CEF as a mathematically grounded, biologically plausible, and mechanically implementable paradigm for affective regulation, psychometric assessment, and human machine emotional synchronization. This paper proceeds in four major parts. First, it formalizes the quantum‑semantic state‑space representation of emotional operators. Second, it establishes the neurobiological grounding of the tricentric architecture. Third, it specifies the mechanical and software systems that operationalize emotional dynamics through physical actuation. Finally, it outlines a four‑phase empirical validation program designed to ensure mechanical reliability, ergonomic safety, operator‑level fidelity, and long‑term developmental suitability. Keywords Core Emotion Framework; quantum semantic affect modeling; Bloch sphere; emotional operators; tri centric neural architecture; cephalic–cardiac–enteric systems; autonomic coherence; somatic mechanical coupling; affective state space dynamics; structural fusions; psychometric validation; human machine interaction; emotional regulation devices.