ZeroES: A Practical Implementation of the Zero Pairs Interaction Functional – Zigzag Zero–Fractional Zero Framework for Prime Analysis, Market Forecasting, and Neural Signal Processing

Source abstract

This work presents ZeroES (Zero Ebrahim Elsayed), the first comprehensive practical implementation of the Zero Pairs Interaction Functional – Unified Spectral Alignment and Coherence – Zigzag Zero–Fractional Zero (ZPIF-USAC-ZZFZ) framework. ZeroES is a multi-domain analytical platform that unifies the spectral analysis of prime numbers, financial market dynamics, and neural electrophysiological signals (Electroencephalography, EEG). Unlike conventional tools that operate within a single domain, ZeroES leverages a complete suite of mathematical operators derived from the Zero Pairs Interaction Functional – Unified Spectral Alignment and Coherence – Zigzag Zero–Fractional Zero (ZPIF-USAC-ZZFZ) theory, including quadratic, cubic, quartic, fractional, radical, and logarithmic self-interactions, cross-mode interactions between spectral zeros, and a complete spectrum of Zero Behavior Motions (ZBM). The application integrates all known phenomena of zero behavior, providing users with a powerful tool for discovery and prediction across mathematics, finance, and neuroscience. The framework utilizes the first 100 non-trivial zeros of the Riemann zeta function for high-precision spectral analysis. ZeroES is designed with a user-friendly interface, making advanced spectral analysis accessible to researchers, investors, and clinicians. The framework builds upon the Zero Pairs Interaction Functional – Unified Spectral Alignment and Coherence (ZPIF-USAC) theory, which introduces fractional self-fragmentation of zeros as a fundamental property, where each zero acts as an active spectral entity capable of splitting into multiple fractional components and reuniting through natural alignment dynamics. The application demonstrates that Zero Pairs Interaction Functional (ZPIF) can analyze anything: numbers, letters, words, images, signals, sounds, and even ideas, because everything in the universe has a frequency and vibration, and Zero Pairs Interaction Functional (ZPIF) can read these frequencies and convert them into numbers and meanings.