Defect-Driven Selection of Irreducible Winding States

This work interprets prime numbers as candidate outcomes of a structural transition in a variational–topological framework. Interacting components give rise to competing phase-locking conditions, leading to incompatible configurations within a single smooth state. Through defect formation and recombination, these configurations may collapse into a single irreducible branch. This terminal state is characterised by topological locking and energy minimisation, where no further decomposition is possible. Within this framework, primality appears not as a purely static property, but as a structural consequence of resolving competing constraints, conditional on the defect formation mechanism.