Connection Theory: A General Framework for Adaptive Network Dynamics — From Temporally Extended Existence to Emergent Dynamic Properties

Biological organisms and autonomous artificial systems exhibit adaptive behavior through fundamentally different physical mechanisms. This paper proposes Connection Theory, a general framework for investigating organizational dynamics shared by adaptive systems with different implementations. It treats temporally extended organization, rather than an instantaneous configuration, as the primary explanatory object, and develops a progression from interaction, through history-dependent feedback and stabilized connection, to selectively coordinated organization. Adaptation is defined as consequence-sensitive organizational change, not guaranteed improvement. The framework separates four questions often conflated: whether a dynamic property is actively manifested; whether capability-relevant organizational state is retained across bounded inactivity; whether a resumed system preserves Organizational Continuity through a non-forking causal lineage under a specified individuation frame; and whether retained or reconstructed organization remains applicable under current conditions. This separation permits adaptive behavior to be analyzed across interruption, reconstruction, migration, and environmental change without reducing capability to uninterrupted operation or static structure. The framework does not replace mechanism-specific theories or claim empirical validation. Instead, it identifies problems that can distinguish organizational dynamics from static connection inventories or cross-domain analogy: feedback selection under organization-conditioned evidence, update non-commutativity, selective coordination, localization of capability-relevant persistence state, and lineage continuity across interruption. Connection Theory therefore offers a common conceptual basis for developing falsifiable models of learning, adaptation, intelligence, and other dynamic properties in biological and artificial adaptive systems. Its contribution is a disciplined problem structure for empirical comparison across adaptive system classes. This manuscript is a preprint and has not undergone peer review.