Phase Dynamics in Hypergraph Rewriting Systems: Empirical Validation of Energetic First Principles in the Wolfram Physics Project

We report empirical validation of Energetic First Principles (E1P), a structural framework for universal process dynamics, within the computational physics domain of hypergraph rewriting systems. This follows prior validation in AI architecture (Resonant Institute, 2025).

Using the Wolfram Physics Project (WPP) formalism, we operationalized E1P's four-phase cycle (Identity → Polarity → Flow → Separation → Identity) as measurable observables in causal graphs: branching events, merging events, cumulative open branches, and inverse activity.

Systematic testing across 15 hypergraph rewriting rules revealed:

• Phase ordering is universal across all causally invariant (CI) rules (9/9)
• The entropy threshold τ is a discrete phase boundary intrinsic to rule structure
• Four rule classes emerge corresponding to distinct E1P pathways—Generative CI, Conservative CI, FixedPoint, and Causally Variant
• Emergence, measured as exponential growth rate, distinguishes generative (spiral) from conservative (loop) dynamics

These findings demonstrate that E1P phase structure is not imposed interpretation but discovered structure within CI dynamics, extending cross-domain validation and suggesting universal process dynamics may be structural features of any system where divergent paths must reconverge.