Artifact 3 — Harmonic Resonance Function (HRF) & Systemic Failure Index (SFI) Protocol

The Harmonic Resonance Function (HRF) and Systemic Failure Index (SFI) are the mathematical foundations of the Commons Foundational Operating System (FOS). These equations establish quantifiable measures of syntropic stability and entropic decay, linking legal and ethical enforcement frameworks (SIB Charter, Artifact 32) to system integrity. This protocol ensures AI systems operate with measurable coherence and defendable accountability. Keywords: HRF, SFI, Harmonic Resonance Function, Systemic Failure Index, syntropic systems, entropic decay, FOS, legal mathematics, Commons IP, ethical AI, structural integrity, Mya P. Brown, Commons Initiative, artifact 3.