The ℒ-Mobility Principle

The ℒ-Mobility Principle presents a geometric view of evolution in which admissibility, not physical time or fixed dynamics, determines how systems move, branch, and collapse. It develops the ideas of an admissibility functional, an evolving admissibility metric, and a regime-evolution operator to show that mobility is governed by geodesic motion on an admissible manifold equipped with its own geometry-attached time. This framework explains how multiple admissible futures appear when the underlying geometry becomes multi-layered, how regime transitions arise when admissibility reorganizes, and how collapse occurs when admissibility disappears entirely. Appendix X provides a clear explanation of all technical terms, making the principle self-contained and applicable to physical, cognitive, organizational, and high-dimensional systems.