Axial Stratified Algebra: Structure, Dynamics, Validation, and Observability

This work introduces a mathematical framework for axial stratified algebra and structured dynamics. The model explores the emergence of structured states from dynamic systems, linking algebraic operations with observable regimes and stability patterns. The framework is supported by validation experiments and numerical analysis, providing evidence for consistent structured-state transitions under defined operators. This deposit establishes the priority and formalization of the proposed mathematical structure prior to journal submission and arXiv dissemination.