Topology of Arising and the Principle of Minimal Action in Admissibility Structures: Level 0 Theoretical Framework

This record presents the theoretical Level 0 framework of the Structured Ontological Mapping of Arisings (SOMA) project. The document develops a formal ontological reconstruction of the minimal structural conditions under which distinguishability, compensation, energy, oscillatory closure, resonant triads, configurational nodes, and ensemble-level organization become admissible. The analysis does not assume physical spacetime, particles, or empirical microphysical laws as primitive givens. Instead, it introduces mathematical expressions as admissibility formalisms and structural proxies for the conditions under which specific forms of organization become possible. The present version is limited to the theoretical part of Level 0. It focuses on the internal architecture of phases A-D, including the transition from distinguishability to oscillatory closure, coherent triadic resonance, node-level stabilization, ensemble-quantum formation, and the ontological bridge toward Level 1 field organization. This upload is intended as the first public version of the Level 0 framework. Future versions of the record are planned to include simulation materials, computational implementations, derived visualizations, and expanded methodological documentation.