Optimisation as Admissibility Navigation

This paper interprets optimisation processes through the admissibility framework of the Paton System. Traditional optimisation methods search for optimal solutions within a defined parameter space subject to constraints. The admissibility interpretation recognises that only configurations satisfying governing constraints are structurally permitted to exist within the solution space. Optimisation therefore becomes a process of navigating an admissible manifold defined by these constraints. Solutions correspond to stable or extremal regions within this admissible space. This perspective clarifies why optimisation methods converge toward particular structures and explains the geometric character of constrained search processes.