Quantum Prime--Zeta Quantum Impact Factor: A Universal Framework for Engagement Measurement

This paper generalizes the quantum measurement framework established in "Quantum Prime--Zeta Riemann Zeros: A Direct Application to Bibliometrical Data" to create a universal system for engagement quantification across digital domains. Building upon the operator equation $t_n = \mu + n \cdot \Delta + \sin(\theta_n)$--originally developed for generating Riemann zeta zeros and first commercially applied to bibliometrics--we introduce the Quantum Impact Factor (QIF), a continuous metric derived from prime number theory that precisely measures engagement states in any attention-based system. We demonstrate immediate applications in social media analytics, digital marketing, e-commerce, and financial markets, showing how the QIF framework provides a unified mathematical language for quantifying human attention, the most valuable commodity of the digital age. This work transforms the theoretical foundations of prime number theory into practical tools for measuring modern engagement economies.