Recursive Context Collapse: A Topological Dynamics Framework for Paradox Emergence and Resolution
Theory of Paradox (Revised Formal Draft) V2 Author: John Gavel Title: Recursive Context Collapse: A Topological Framework for Paradox Emergence and Resolution Core Premise Paradoxes do not indicate logical failure—they are signs of recursive conflict between coexisting informational systems. They emerge when two or more contextual systems interact, but their recursive flows cannot be simultaneously maintained. We define a paradox as a collapse in recursive coherence between systems that differ in context, invariants, or semantic structure. 1. Mathematical Structure Let two interacting systems be denoted S₁ and S₂. Define: = contextual influence between systems I ( S 1 , S 2 ) = shared invariants between systems M ( S 1 , S 2 ) = paradox tension metric Then: M ( S 1 , S 2 ) = C ( S 1 , S 2 ) / I ( S 1 , S 2 ) When M exceeds a topology-dependent threshold, paradox emerges. Units: C and I are dimensionless but derived from measurable semantic flow coherence and alig...