The Dynamic Topology-Algebra Correspondence Principle: From Phase Closure to Galois Theory

Abstract Classical algebra defines the "solution" of an equation as a static coordinate satisfying F(x)=0. This definition rests on two unexamined presuppositions: the existence of a solution requires no dynamical guarantee, and the stability of a solution requires no cooperation from its neighbors. Under this dual presupposition, classical algebraic solutions become a dance on a knife-edge—precise but fragile, formally complete but topologically unclosed. Within the framework of generative mathematics, based on the complete chain "Axiom 4 → group structure → modular automorphism → operator flow" established by L1 dynamic group theory, this paper proposes a generative version of the dynamic topology-algebra…