Proposal of a New Cosmic Function as a Reinterpretation of Einstein's E=mc² : Equiangular Spiral-Waveguide Unified Function - R = r₀·e^(±bθ)·e^(±iφ)·e^(±jψ) = r₀·G·Rₒₜ·T_w

Abstract:This paper reinterprets Einstein's mass-energy equivalence E=mc² not as a static equivalence, but as a dynamic resonance condition combining Growth, Rotation, and Twist within a three-dimensional spherical waveguide. We propose a new cosmic function: R = r₀·e^(±bθ)·e^(±iφ)·e^(±jψ) = r₀·G·Rₒₜ·T_w, where ln R = ln r₀ ± bθ ± iφ ± jψ. Dynamic equilibrium is achieved at the minimum resonance condition cosθ=2/3, b=√5/2≈1.118, and pitch angle α≈41.81°. This function serves as a multi-scale logarithmic spiral solution applicable identically from atoms (microscopic waveguide black holes) to our galaxy and multiverse cluster waveguides. Depending on whether the speed of light c is viewed as a cutoff frequency (limiting mode) or group velocity (phenomenon), the multiverse bifurcates into a converging (-bθ) oscillating multiverse or a diverging (+bθ) eternally inflating multiverse. Clarification Note for v1:- To avoid confusion, the original notation R = r₀·G·R·T has been clarified to R = r₀·G·Rₒₜ·T_w (R=total complex radius, Rₒₜ=Rotation, T_w=Twist). The conceptual content is identical to the original.- j is defined as a second imaginary unit orthogonal to i, quaternion system: i²=j²=k²=ijk=-1, ij=-ji=k. Keywords: Equiangular Spiral, Waveguide Cutoff, Complex Logarithmic Radius, Multiverse Bifurcation, cosθ=2/3, pitch angle 42 degrees, de Sitter / Anti-de Sitter Author: Sungbae Im / Independent ResearcherDate: 2026-05-13 (First drafted) / 2026-10-06 (Zenodo upload)Related work: EGU EGUsphere-2026-5961 (Under Review) - Quantitative Research Proposal on Tidal-Atmospheric Resonance Hypothesis for Typhoon Genesis License: CC-BY 4.0