The Unified Scientific Framework of Eternal Equilibrium presents a theoretical and preliminary proof-of-principle model for the Eternal-Life Equation (G = T × E). This framework establishes a unified approach to understanding coherent system stability and self-sustaining equilibrium across physical, biological, energetic, and conceptual systems. The framework formalizes equilibrium as an active, self-regulating process governed by time-energy coherence, adaptive feedback, and relational alignment among system variables. It demonstrates that system persistence, resilience, and regeneration emerge from maintaining dynamic equilibrium rather than relying on static stability or external energy inputs. This white paper documents the mathematical formulation, theoretical foundations, and preliminary proof-of-principle for the Eternal-Life Equation, providing a cross-disciplinary reference applicable to fields including systems science, thermodynamics, complexity theory, energy modeling, and life sciences. Released as Version 1.1, this work is intended to support scholarly discussion, citation, and further development of a unified framework for eternal system equilibrium and regenerative modeling.