Kamboj Affective Field Theory: A Mathematical Framework for Synthetic Affective Cognition

Kamboj Affective Field Theory (KAFT) models synthetic emotion not as a discrete heuristic label or prompt modifier, but as a history-sensitive, regulated trajectory within an affective vector bundle over a cognitive manifold. This manuscript establishes a unified mathematical engine for artificial general intelligence (AGI), integrating emotion formation, memory persistence, somatic urgency, and action readiness into a single derivable system. By treating emotional states as continuous, superposed dynamical fields, this framework introduces rigorous physics and topological modeling to cybernetics and cognitive architecture. Key theoretical contributions include the formulation of an affective connection, the definition of emotional rigidity via an affective curvature tensor, the application of fractional calculus for non-Markovian emotional hysteresis, and the Barrett-KAFT free-energy equivalence. Statement of Public Priority & Disclosure Boundary: This document serves as the formal Public Priority manuscript for the Kamboj Affective Field Theory. It is published to establish the central mathematical theorems, prove public consistency results, and define falsifiable scientific consequences of the theory. To protect the commercial implementation and deployment mechanics of the system, this manuscript adheres to a controlled-disclosure boundary. It establishes the complete physical and geometric soundness of the affective engine while explicitly withholding the private constructive apparatus—including proprietary calibration schedules, runtime constants, classifier weights, safety policies, and specific source-code implementations. Every theorem is stated with sufficient mathematical rigor for peer review, preserving academic priority while maintaining the exclusivity of the executable substrate.