Dust Theory Vol. 1: Gradient Cosmos Ontology: Axiomatic Construction and Endogenous Evolution of Difference-Based Reality (Gradient Cosmos Research Series)

This paper presents a unified foundational theoretical study spanning fundamental physics and cognitive science. The fundamental bottleneck in complex systems research lies in the absence of microscopic endogenous evolutionary mechanisms. All existing theories presuppose time, space, and substance as a priori backgrounds, and thus cannot derive all order endogenously from the simplest relations. Grounded in methodological constructivism as its meta-principle, this paper proposes Gradient-Relational Ontology (referred to as Dust Theory)—an axiomatic monistic ontological doctrine. Taking primitive gradient relations as its sole undefined primitive, the doctrine presupposes no independent entities, spacetime background, or external rules. Relying only on five minimal operational postulates and well-defined coupling functions, it endogenously derives three fundamental system properties: relational continuity, potential infinite nesting, and a steady-state continuous spectrum. Building on this foundation, this paper reveals the path-rule duality principle and the two-level bootstrapping evolution mechanism. It proves that discrete conduction paths can spontaneously condense into stable operational rules, and that systems can achieve self-upgrading of rules through continuous microscopic modification and macroscopic structural transition. The trend of structural free energy minimization provides a non-teleological statistical direction for evolution. This doctrine offers a unified ontological explanation for order generation across mathematical, physical, biological, cognitive, and social systems, and provides a brand-new relationalist framework for reconstructing the fundamental question of how order emerges endogenously. Starting from its axiomatic system, the core conclusions of quantum mechanics and relativity can be derived, and the framework yields experimentally testable falsifiable predictions.