An Axiomatic Variational Framework for the Emergence of Time, Space, and Topology

This paper presents a formal axiomatic framework in which the principle of action functions as a global criterion of physical realizability. Starting from a pre-geometric setting without assumed temporal orientation, spatial geometry, dimensionality, or topology, the framework derives these structures as consequences of stable extremal histories of a global action functional. Temporal orientation emerges through stability selection, spatial geometry arises via Euler–Lagrange structure, dimensionality is constrained by global stability requirements, and topology is selected by the absence of unstable global deformation modes. The framework positions established physical theories as effective intra-history descriptions and provides a deductive foundation for understanding spacetime structure as an output of variational selection. Keywords:variational principles; axiomatic foundations; arrow of time; spacetime emergence; dimensional selection; topology