Formal Axiomatization of Emergent Physical Laws: An Agent-Based Approach

This work presents a formal axiomatization of emergent physical laws derived from the local decision-making of discrete agents. By postulating a set of foundational axioms—including Locality, Internal Persistence, Minimal Consensus, Strategic Indeterminacy, Temporal Compatibility, Equitable Exchange, and Historical Optimization—the framework rigorously establishes how microscopic stochastic interactions and variational principles give rise to macroscopic phenomena such as conservation laws and wave dynamics. The approach integrates concepts from classical mechanics, variational calculus, and game theory to bridge local agent behavior with global emergent order, providing a unified description applicable to both classical and quantum regimes.