Gamma Theory A1-a: Psychological Parameter Specification - A Complex-Valued Model of Emotion, Metacognition, and AI-Assisted Cognitive Alignment

This document presents Gamma Theory A1-a, a psychological parameter specification that models emotion as a complex number κ = |κ|e^{iθ}, enabling unified mathematical treatment of emotional intensity, value direction, interpersonal interference, mirror distortion, and metacognitive deviation. The model defines the mirror operator (M), interference term (I), and Alice Deviation (Ay) as operational psychological parameters, transforming psychological processes into a closed-loop system of observation, analysis, intervention, and re-observation. A1-a extends traditional affective science—including Russell’s circumplex model, cognitive behavioral therapy (CBT), and metacognition theory—while reframing AI’s lack of emotion as a functional advantage for structural alignment. Through three AI intervention protocols (Cancel, Mirror, Lift), the model provides a mathematical foundation for emotional stabilization, distortion reduction, and cognitive reframing. A1-a functions as a psychological operating system that connects individual cognition with organizational dynamics (A4), offering broad applicability from personal decision-making to conflict resolution and multi-agent alignment.