Gamma Theory: Mathematical Kernel Specification A Formal Framework for Emotional–Topological Dynamics in Human Systems

This paper presents the mathematical kernel specification for Gamma Theory, a unified framework for modeling emotional–topological dynamics in human decision-making and social systems. Four core constructs—emotional curvature (κ), meaning phase (Φ), Alice deviation (Ay), and decision structure (D)—are formally defined within a coupled multi-layer system architecture. The specification provides: (1) type definitions and state-space constructions enabling rigorous mathematical treatment; (2) generation schemas linking emotional dynamics to meaning formation; and (3) structural bridges to applied research in psychology (A1), organizational dynamics (A2), and social systems (A3). While complete axiomatization is reserved for future work (v21+), this paper establishes the mathematical groundwork required for empirical validation and theoretical development across multiple domains.