Angell Framework, Vol. 1 Part II: Unified Operator Form

This document extends the ℕᴿ Framework established in Part I (DOI: 10.5281/zenodo.17925583) by formalizing the Unified Operator Form—a master equation architecture from which all domain-specific activation and growth equations derive as instantiations.

The framework decomposes into four canonical operator families:

• Gate (bifurcation / threshold / band-pass)
• Brake (resource drag and capacity clamping)
• Phase (alignment modulation)
• Growth (bounded ascent kernel)

The central claim is that apparent "different equations" across physics, biology, economics, and cognition are not independent discoveries but projections of a single mathematical architecture. Domain-specific equations are obtained by selecting operators from each family and specifying which observables are rendered.

Three Unified Laws are structurally enforced by the operator form itself: Bounded Transcendence, Thresholded Emergence, and Phase Governance.