Super-Barriers and Spine Confinement: Invariant Keys for Ordering Solver-Induced Complexity

This work develops a dynamic theory of Super-Barriers: laminated constraint structures arising in extremal and rigidity-driven settings. While the ambient configuration space may exhibit metastability and solver-induced basin complexity, we show that the introduction of appropriate invariant keys canonically confines tightening dynamics to a distinguished critical spine. On this spine, the induced dynamics becomes ordered—either contractive or strictly Lyapunov-descending—thereby suppressing chaotic basin interleaving and enforcing non-overlap on the invariant core. The framework reconciles global complexity with local rigidity and provides a principled mechanism for barrier control and future unlock strategies without assuming problem-specific conjectures. References to chaotic overlap or attraction describe solver-induced basin geometry rather than literal self-intersection of barrier walls. All non-overlap claims apply to the confined dynamics on the critical spine and are conditional on stated ordering hypotheses.