Four Methodological Foundations for Open Systems: A Manifesto on Memory Organization, Non-Global Gluing, Information Budgeting, and Distributed Kinetics

Contemporary scientific foundations across artificial intelligence, mathematical logic, cybernetics, and distributed computing face a common impasse rooted in an unexamined ontology: the postulate of the monolithic global context. This dogma presumes that open systems can be understood by embedding them within a single ambient space—an undifferentiated weight vector optimized against a scalar loss, a global probability space where local observations universally glue, an omniscient state vector observable at zero cost, or an ad-hoc combinatorial queue network. In this manifesto, we synthesize our laboratory’s recent cross-disciplinary inquiries into four general methodological foundations: (I) Cognition and Learning: intelligence is the structural organization of memory—encompassing both content organization and relational organization—wherein computational modes (autoregressive or non-autoregressive) are context-dependent choices rather than ideological absolutes, and computational depth is bought with environmental silence; (II) Foundations of Natural Science and Mathematics: global gluing is not a universal law of nature or logic, as demonstrated by quantum contextuality, Bell non-locality, and non-amalgamating multiverses, establishing that formal theories must treat gluing failure as an explicit, measurable physical and topological invariant; (III) Generalized Decision Systems: state observation is an active, physical act, meaning total operational cost must budget sensing overhead against decision quality, rendering intentionally bounded local perception strictly optimal under non-zero sensing costs; and (IV) Complex Collectives and Distributed Systems: decentralized dynamics map onto kinetic field landscapes, where pull mechanisms act as attractors, push mechanisms act as repellers, and cooperative buffers act as intermediate potential wells. Together, these four theses establish an integrated paradigm for formalizing, analyzing, and engineering open, non-equilibrium, and resource-bounded intelligent systems.