Mathematical Foundations of Generative Theory (Gt)

This article presents the condensed mathematical foundations of Generative Theory (GT) — a framework describing how stable structures emerge from unstable generative states through iteration, invariants,and coherence stabilization. GT formalizes the mechanisms by which structures arise as fixed pointsof generative processes, using a categorical and relational mathematical language based on ilons, generative functors, pre‑structures, invariants (Gravit), coherence measures, and meta‑structures. Although the paper focuses on the mathematical core of GT, the same generative principles apply to biological, cognitive, social and technological systems — wherever stable configurations emerge from unstable states. The document provides a unified, domain‑agnostic mechanism of emergence relevant to physics, cosmology, biology, neuroscience, materials science, AI and complex systems research. It also outlines empirical testability through pre‑structural signals, coherence fluctuations and early stabilization patterns, offering a path toward laboratory verification. This is the first open‑access, self‑contained mathematical introduction to GT, intended for researchers across disciplines. Author: Waldemar Superson