What question did this study set out to answer?

To interpret prime numbers as stable outcomes of structural transitions driven by noncommutative interactions.

March 28, 2026Open Access

Primality as a Topological Phase Transition

Key Points

To interpret prime numbers as stable outcomes of structural transitions driven by noncommutative interactions.
Analyzed twisted configurations arising from interacting components.
Studied the process of defect formation and recombination.
Examined how configurations collapse into an irreducible state characterized by topological locking.
Prime numbers are characterized as balanced states after resolving noncommutative interactions.
Emergence of primality illustrates a dynamic rather than static property.
Demonstrated that further decomposition beyond this unique state is impossible.

Abstract

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.

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