Primality as a Topological Phase Transition

This work interprets prime numbers as stable outcomes of a structural transition driven by noncommutativity. Twisted configurations, arising from interacting components, generate competing noncommutative structures. Through defect formation and recombination, these configurations collapse into a single irreducible state. This state is characterised by topological locking and energy minimisation, where no further decomposition is possible. In this framework, primality emerges not as a static property, but as the unique balanced state achieved after resolving noncommutative interactions.