The Universal Golden Resonance Constant (UGRC): Kolarec–Planck Ladder and the Exponential φ–Damping Kernel

Description This work establishes the Universal Golden Resonance Constant (UGRC) as a bridge between quantum and macroscopic domains.Starting from fundamental physical constants and the golden ratio (phi), it derives a base frequency f₀ = ±1×10⁻⁵⁷ Hz that unifies Planck and vacuum scales through phi–quantization. The paper introduces two key theoretical structures: The Kolarec–Planck Ladder – a discrete logarithmic bridge that connects the Planck frequency to the UGRC base through phi-scaled resonance steps, forming a quantized hierarchy of frequencies observed in both cosmic and biological systems. The Exponential phi–Damping Kernel – an analytical expression that governs resonant stability and energy coherence across these scales, linking exponential damping directly to the golden ratio itself. The framework is developed in a fully operator-theoretic form using Fredholm determinants, phi-symmetric eigenvalues, and a Mobius-invariant spectral mapping, providing a rigorous mathematical model of stability and information transfer across scales. Applications are discussed in: Quantum resonance sensors and metrological stability, Bioresonant systems and neuro-physiological coherence (EEG/MEG), Celestial mechanics and orbital resonance harmonics. The UGRC theory demonstrates how the golden ratio governs both discrete quantization and continuous damping, offering a unified explanation of resonance phenomena from quantum to cosmological levels. Author:Robert Kolarec — Independent Researcher, Croatia (EU) Version: 1.1 (October 2025)License: CC-BY 4.0 International