TRUE ALCHEMY: The Universal Law of Balance in Physical, Biological, and Moral Systems

By modeling dual expressions of a single underlying force as paired variables constrained by a conserved invariant, it derives an equilibrium condition using the arithmetic-mean–geometric-mean inequality. The resulting formulation—called the Universal Equation of Balance—appears in electromagnetism, mass–energy equivalence, homeostatic biology, governance theory, and classical philosophical thought. The paper argues that balance is not compromise, but the unique optimal state that minimizes cost and maximizes stability. “True Alchemy” refers to this universal structure of transformation through equilibrium, rather than historical chemical practices.