Formal Derivation: E=mc² from Information Dynamics

This paper presents a novel derivation of Einstein's famous equation E=mc² from first principles based on information theory rather than relativity. Working within the Pentagonal Quantum Information Substrate (PQIS) framework, we demonstrate that mass-energy equivalence emerges naturally from the dynamics of information processing in a discrete network with pentagonal (D₅) symmetry. We formally define mass as localized, stable information patterns with excess information depth above a baseline value, while energy corresponds to the same information in propagating form. Through rigorous mathematical analysis, we establish that the maximum information propagation speed equals the speed of light c, and derive the exact value of the information-mass conversion constant m₀ = φ²/(5c²), where φ is the golden ratio. When stable information patterns dissolve completely into propagating waves, the energy released is exactly E = m·c². We also identify quantum corrections for finite-sized systems and modifications at high energies. Our derivation suggests that mass-energy equivalence is not merely a property of specific physical systems but a logical necessity arising from information conservation, with significant implications for our understanding of fundamental physics.