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The Ultimate Unified Equation and Dark Energy: A Verification Model of Cosmic Evolution Based on Informational Dynamics

7/8/2025

By John Chang
Abstract:
This paper proposes a Unified Evolution Equation of the form dM/dt = ⋅∇M +⋅I(E,S,C) + ⋅Q(x) to model the evolution of the universe driven by dynamic dark energy. The equation integrates information gradients, energy-structure interactions, and quantum-level perturbations to describe self-organizing phenomena in cosmology. Unlike the ΛCDM model, which assumes a constant dark energy density, this formulation introduces time-variant behavior through the term Q(x), aligning with recent observational evidence from DESI and Planck. The model offers a novel interdisciplinary perspective that connects cosmic expansion, structural formation, and informational dynamics. Further investigation is needed to assess its predictive power and its applicability in a general theory of the universe.

Keywords: dark energy, information theory, cosmic evolution, self-organization

DOI：10.5281/zenodo.15702146

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Theoretical Foundations of Science: A Unified Framework Based on the Cosmic Law and Recursive Evolution

7/1/2025

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Author: John Chang (Hai Zhi Tao)
Email：[email protected]

Abstract：

   This paper proposes a unified scientific framework based on the Cosmic Triplet Law (•, |, Ο), introducing a recursive structural equation:

     M(x) = f(M(x−1), M(x−2), ..., R)

   to model the evolution of natural, social, and intelligent systems.
   Building upon a Nine-Level Theory of Structure, we derive nine discipline-level equations and compress them into three meta-level dynamics:

A Structural Evolution Equation unifying mathematics, physics, and chemistry;
A Social Dynamics Equation capturing political, economic, and behavioral systems;
A Life Adaptation Equation describing gene–environment–complexity interaction.

   These are further unified as a Universal Evolution Equation:

     dM/dt = ⋅∇M + ⋅I(E,S,C) + ⋅Q(x)

This equation also represents the Intelligent Wave Equation □M = S(x), proposed as the third fundamental wave — alongside gravitational and electromagnetic waves — governing the evolution of information and meaning across scales.
   Our model bridges recursion, entropy, and feedback into a common evolution law, forming a closed-loop structure from cosmic origin to intelligent systems. It offers a mathematically compact, cross-disciplinary foundation for unifying science across physics, cognition, society, and life.

DOI: 10.5281/zenodo.15478979

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The Ultimate Unified Equation and Dark Energy: A Verification Model of Cosmic Evolution Based on Informational Dynamics

Theoretical Foundations of Science: A Unified Framework Based on the Cosmic Law and Recursive Evolution

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