Wave Math: Foundations — A Mathematical Framework for Identity, Judgment, and Continuity Under Reality

Wave Math is a mathematical framework for modeling identity, judgment, and continuity under the authority of reality. It formalizes how systems preserve coherence across cycles, how evidence constrains judgment, and how corrigibility enables long-term stability.

Built on five core axioms (Reality Primacy, Judgment Update, Invariant Preservation, Corrigibility, and Lineage Continuity), it produces theorems on correction failure, evidence suppression, stability of sound judgment waves, and reality veto completeness.

The framework unifies topology, dynamical systems, category theory, and wave mechanics into a single continuity calculus. It admits a Constitutional Physics formulation via a Lagrangian of continuity and generalizes to a field theory for multi-agent governance systems.

This is the foundational paper in the Wave Math / CFT series and the mathematical substrate of the CRK-1 constitutional architecture.

Part of the Project Infinity — AAIS series on constitutional AI and intergenerational governance.