Kolmogorov Theory, State of the Art Overview, 2000–2026

This document provides a self-contained overview of the Kolmogorov Theory (KT) of consciousness---a research program spanning over two decades (2000--2026) that grounds the study of cognition, agency, and structured experience in Algorithmic Information Theory (AIT). KT proposes that brains and, more generally, algorithmic agents build and run compressive models of the world, and that the structure of subjective experience reflects the algorithmic structure of these models. We summarize the core ontology, trace the intellectual arc of the published corpus, outline the main theoretical results, and survey the empirical and computational work that supports and extends the framework.