Persistence-First Natural Laws for Benevolent Propagation

This preprint develops a persistence-first framework for natural laws governing benevolent propagation in intelligent systems. Instead of postulating utility functions, value alignment, or externally chosen objectives, the paper takes only persistence under finite resources as a primitive order on ensembles of processes, and builds all higher structure from this single assumption. At the first layer (L1), the work introduces minimal axioms for persistence functionals that assign survival tendencies to finite ensembles of agents or processes. From these axioms it defines relational benevolence as behavior that increases the persistence of both the acting ensemble and a target ensemble, and formalizes a simple “persistence-rational exclusion” condition that rules out strictly antisocial mechanisms under any selection rule that never chooses them. At the second layer (L2), the paper formalizes a relativity-of-theories perspective: a “theory” is a coarse-graining of an underlying process space together with its dynamics, and theory morphisms are persistence- and benevolence-preserving coarse-grainings. A statement is called a natural-law statement if it is invariant under all such morphisms. This gives a representation-independent notion of natural law that is compatible with multiple modeling choices and observation spaces. At the third layer (L3), the framework is instantiated in a large implementation class based on metric gradient flows and optimal transport geometry. The paper shows how persistence-compatible Lyapunov functionals and EVI gradient flows on Wasserstein, Hellinger–Kantorovich, or Bures-type spaces support observation quotients, Image–EVI stability, preimage Minkowski dimension bounds on scaling exponents, and residual-spine based depth truncation bounds. These results connect the persistence-first semantics to compute–performance trade-offs, scaling laws, and multi-scale implementations in modern AI systems, while remaining agnostic about specific architectures. Overall, the paper positions persistence as the unique primitive, treats benevolence and natural laws as derived relational notions, and shows how gradient-flow-based AI implementations can be understood as one large, physically motivated realization class compatible with this minimal semantics. Keywords: persistence-first, benevolent AI, natural laws, relativity of theories, gradient flows, Wasserstein distance, Hellinger–Kantorovich metric, Bures metric, optimal transport, scaling laws, compute–performance trade-offs, multi-agent systems, alignment, no-meta governance.