Part I: The Wave Paradigm - A Universal Framework for Physical Reality

In this foundational work, we introduce a universal framework that reimagines the fabric of reality through the lens of waves. By positioning waves as the fundamental entity underlying all physical phenomena, this paradigm challenges long-standing constructs like particles, fields, and singularities, offering a unified and deterministic alternative.

We derive a novel partial differential equation (PDE) operator that encodes infinite complexity expansions, capable of describing phenomena across quantum and classical regimes. This operator resolves inconsistencies in traditional physics, including the quantum-classical divide and the anomalies of singularities, while ensuring convergence and stability.

This work lays the mathematical foundation for a transformative understanding of physics, setting the stage for applications ranging from quantum mechanics to cosmology. It invites the scientific community to explore a universe where waves, not particles or fields, are the fundamental building blocks of reality.