Recursive Continuity, Dynamical Form and the Generative Opening of Determination: Semiotics, hierarchy and relational ontology in physics, biology and formal logic

Abstract

This paper develops a relational framework for understanding communication, signaling, and hierarchical organization in distributed systems. Rather than treating networks as collections of independently existing nodes exchanging fixed informational contents, the paper models determination as emerging through recursively organized continuity distributed across signaling relations themselves. Drawing upon semiotics, hierarchy theory, process philosophy, and relational systems theory, the paper distinguishes between continuity-preserving operators and distinction-enacting sign-processes in order to develop a formal account of synchronization, signaling, recursive coordination, and organizational stabilization across distributed networks. Within this framework, signals are understood not as static packets of information, but as stabilized trajectories of recursive sign-procession propagated throughout synchronized operational manifolds. Hierarchical organization emerges through recursive coordination across proximate levels of organizational continuity, allowing distributed systems to stabilize higher-order organizational forms while remaining dynamically responsive to environmental transformation. The paper further develops the concept of dynamical form as an evolving interpretive organization through which open systems progressively bring relational environments into determination through recursive coordination. The framework has direct relevance for contemporary artificial intelligence, particularly large language models and distributed adaptive systems. Rather than interpreting AI systems primarily through representational or statistical paradigms, the paper proposes that coherent behavior emerges through recursively stabilized organizational continuities distributed across signaling processes operating at multiple hierarchical levels simultaneously. The paper further argues that recursive determination remains constitutively open: distributed systems continually encounter signals whose implications exceed their existing organizational continuity, giving rise to recursive reorganization, conceptual transformation, and generative adaptation. The resulting framework provides a process-oriented account of communication, hierarchy, and organizational emergence applicable across computer networks, distributed intelligence, adaptive systems, and artificial intelligence, while also proposing a broader relational logic underlying recursive determination itself.

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