Tripartite Framework Comparison: De Rham Cohomology, Artin Stacks, and Markov Chains

This paper presents a comparative analysis of three fundamental frameworks—De Rham cohomology, Artin stacks, and Markov chains—through the lens of formal language and domain-specific abstraction. We examine their structural, functional, and computational characteristics, highlighting the intersections and divergences in expressing topological, geometric, and stochastic phenomena. The analysis situates each framework within a conceptual hierarchy, clarifying its role in mathematical and applied reasoning.