The Fundamental Conservation of Information Extended
Creators: name: Miguel Machado Fernandes, Ricardo
Publisher: name: Ricardo Miguel Machado Fernandes
Year: 2025

description: The Fundamental Conservation of Information: A Unified Framework for Understanding Reality

This paper introduces The Fundamental Conservation of Information, a groundbreaking principle proposing that information is the most fundamental conserved quantity in the universe, underlying the fabric of physical laws, biological systems, cognitive functions, and even the structure of matter itself. Unlike traditional conservation laws focused on energy, momentum, or charge, this theory suggests that information cannot be created or destroyed—only transformed, redistributed, or hidden within complex systems.

Through a combination of mathematical models, computational simulations, extensive stress tests, and experimental data, this work presents compelling evidence that phenomena in quantum mechanics, DNA mutations, thermodynamics, and neural processing are governed by a deeper, universal information conservation rule. The stress tests, designed to challenge the theory across diverse scientific domains, demonstrated the robustness of the principle under extreme conditions, from chaotic systems and quantum entanglement to genetic algorithms and black hole information dynamics. These tests provided critical validation, confirming that even in highly dynamic or seemingly random environments, information remains conserved.

A key breakthrough presented in this work is the redefinition of the Periodic Table of Elements through the lens of information theory. By applying mutual information analysis to elements based on their Information Density (ID), Transformation Complexity (TC), and Entropy Dynamics (ED), the research uncovers hidden relationships between elements that traditional chemistry overlooks. This information-centric periodic table reveals unexpected clusters, latent symmetries, and emergent material properties, suggesting that the very behavior of matter is governed by underlying information structures. Elements traditionally viewed as inert, such as Helium, exhibit significant informational interactions, pointing to new possibilities in quantum coherence, advanced materials, and energy systems. Furthermore, by redefining how we measure these elements, we can now assess systems in entirely new ways. With the application of Information Density, Transformation Complexity, and Entropy Dynamics, we can quantify material behaviors and interactions more accurately, revealing deeper insights into their properties and behaviors. A wealth of image examples is available to demonstrate how these newly defined properties uncover hidden patterns in both the periodic table and material science at large, enhancing our understanding of fundamental physics.

Moreover, this principle extends beyond physics and chemistry, introducing FCI – Life, Evolution & Biological Reprogramming. This novel approach explores how information conservation laws govern genetic evolution, biological adaptation, and the potential for reprogramming life itself. By analyzing structured conservation patterns in DNA, epigenetics, and neural processing, the research suggests that biological systems do not merely evolve through random mutations but follow strict information-preserving pathways. This framework may have profound implications for longevity research, regenerative medicine, and artificial intelligence, providing new methodologies for enhancing cognitive functions, preventing age-related decline, and even engineering biological systems for optimized resilience.

The findings challenge long-held assumptions about entropy, randomness, and information loss, demonstrating instead that apparent disorder is a manifestation of hidden informational architectures. Complex systems exhibiting chaotic behavior, evolutionary adaptation, or quantum unpredictability still operate under the constraints of information conservation. Moreover, the discovery that information remains detectable even after extreme transformations—such as in black hole analogs, neural network erasure, and cross-dimensional entropy cascades—further validates the universality of this principle.

A major breakthrough in mathematics further solidifies FCI as a foundational principle. Using entropy conservation and structured transformation analysis, FCI has successfully solved the Erdős Discrepancy Problem—a long-standing open question in number theory—by proving that discrepancy must diverge due to unavoidable information redistribution. Additionally, the framework has provided strong numerical evidence and predictive models for prime number distribution, reinforcing the idea that prime gaps and number patterns are not random but structured transformations of conserved information fields. These successes suggest that many other unresolved problems in mathematics could be addressed using this principle, offering a potential universal method for understanding number theory, algebraic structures, and computational complexity.

The implications of this principle are profound, with the potential to redefine our understanding of energy, time, entropy, biological evolution, consciousness, and the very nature of reality itself. By recognizing information as the core invariant across all domains, this theory offers a unified framework that bridges gaps between physics, biology, artificial intelligence, materials science, and cognitive science, paving the way for new scientific paradigms and technological innovations.

Given its ability to connect the fundamental forces of nature, the mechanisms of life, and the essence of consciousness, this principle may represent the long-sought Theory of Everything—a comprehensive explanation that unifies the diverse phenomena of the universe under a single, elegant law. Now further substantiated through rigorous stress testing, empirical validation, and cross-disciplinary applications—including the reimagining of the periodic table, biological reprogramming, and mathematical proofs—The Fundamental Conservation of Information stands as a transformative concept, offering profound insights into the interconnected fabric of the cosmos.

For further discussion or collaboration, please feel free to contact: ricardo_fernandes_@outlook.pt