The Barrier Framework v6.6: Structural Refinement, Controlled Embeddings, and No-Bypass Topology

This paper presents Version 6.6 of the Barrier Framework, a structural approach to obstruction geometry in analytic and arithmetic settings. This revision introduces: • Controlled embedding refinements• Lyapunov-style descent clarifications• No-Bypass Topological Lemma• Structural decomposition tools• Clarified separation between heuristic energy landscapes and formal bounded theorems This work does not claim resolution of classical open problems.Instead, it establishes bounded structural results intended to strengthen the internal coherence and future extensibility of the framework. DOI: 10.5281/zenodo.18611872