General Behavior Calculus (GB-Calculus) Canonical Mechanical, Semantic, and Geometric Specification

Abstract

General Behavior Calculus (GB-Calculus) represents an effort to formalize the mathematical language used within General Behavior into a consistent and extensible specification. The objective is not to claim that the calculus is complete or that every component has reached its final form. Rather, this work establishes a stable reference point from which the notation, transformations, state relationships, interval structure, and geometric correspondence can be communicated, examined, tested, implemented, and further developed. Formalization became necessary as the framework increased in scope. A shared mathematical specification provides a basis not only for teaching and communicating General Behavior, but also for allowing others to critically evaluate its internal structure, reproduce its relationships, identify limitations, propose improvements, and extend the framework through future research. Establishing explicit types, operators, equations, constraints, and indexing conventions also provides the structure required to translate GB concepts into computational representations and software implementations. This specification should therefore be understood as a foundation rather than an endpoint: a defined version of GB-Calculus upon which subsequent theoretical, empirical, and computational work can build.