The Velado Algebra: A Novel Non-Associative Algebraic Structure on the Probability Simplex

We introduce the Velado algebra, a novel non-associative algebraic structure arising from trust aggregation dynamics on the probability simplex. The algebra is defined by the normalized sum operation Φ(a,b) = (a+b)/‖a+b‖₁ and possesses a closed-form associator φ(a,b,c) = (c−a)/4 that is independent of the middle argument. This independence property appears to be unique in the non-associative algebra literature. We prove that this structure does not correspond to any standard named algebra class—including Jordan, alternative, genetic, and composition algebras—establishing it as a genuinely novel algebraic object. Key results: • Closed-form associator φ(a,b,c) = (c−a)/4 • Associator independent of middle argument (unique property) • Commutative, flexible, power-associative, and baric • NOT Jordan, alternative, or composition algebra • Applications in AI governance and multi-agent consensus Related patent: U.S. Provisional Application No. 63/948,782 (December 26, 2025)