Contextual Information Systems: A Topological Framework
Contextual Information Systems: A Topological Framework By John Gavel (acknowledgements AI structed authors work for clarity) Abstract We introduce a mathematical framework for studying information-processing systems where meaning emerges from recursive contextual embedding. The framework combines graph theory, dynamical systems, and algebraic topology to model how information maintains coherence and resolves contradictions through topological reconstruction. 1. Definitions and Basic Structures Definition 1.1 (Primitive Context) A primitive context \( \Psi_0 \) is a context structure that does not depend on any prior information elements: Empty context: \( \Psi_0 = (\emptyset, \emptyset, \emptyset) \) — neutral background Seed context: \( \Psi_0 = (\{s\}, \{(s,s)\}, \{w(s,s) = 1\}) \) — self-anchored datum Axiomatic context: \( \Psi_0 \) = predefined graph encoding ontological constraints Definition 1.2 (Hierarchical Context Construction) Given base differ...