The Post-Calculus Manifesto: From Differentiation to Resonance

Main Framework Abstract This manifesto declares the obsolescence of calculus as a universal framework for modeling emergence. It introduces Coherent Prime Resonance (CPR), the mathematical substrate of CODES—the Chirality of Dynamic Emergent Systems—which replaces differentiation with phase-aligned recurrence. From biology to AI to cognition, structure emerges not from continuity but from resonance thresholds governed by prime intervals and chirality. This paper formalizes CPR, establishes PAS (Phase Alignment Score) as the new metric of lawful emergence, and outlines a full transition strategy across education, computation, and physics.