The emergence of locality from fundamentally non-spatial relational dynamics remains an open problem in relational approaches to complex systems and theoretical physics. In particular, it remains unclear whether persistent localized structures can arise from relational memory and interaction history without assuming predefined spatial geometry or neighborhood relations. To address this question, we developed a trace-reinforcement model in which interactions leave relational traces that accumulate and influence subsequent interaction probabilities. We first found that the minimal model generated scale-dependent transitions between globally connected and fragmented regimes. While the minimal model successfully generated global proximity and large-scale recurrent circulation, it did not produce compact localized cyclic units. We therefore extended the model by introducing additional parameters for reciprocal reinforcement, finite coherence persistence, exploratory noise, and loop-specific persistence to investigate the formation and stabilization of localized strongly connected components (SCCs). Systematic simulations showed that stable SCCs emerged under conditions of nonzero reciprocal reinforcement, finite but incomplete coherence persistence, and near-persistent loop stabilization. Thus, global connectivity or circulation alone was not sufficient to generate persistent localization. Instead, localized SCCs appeared as metastable recurrent structures maintained by reciprocal reinforcement and finite memory. Loop-size analysis further showed that reciprocal two-node cycles were exclusively detected under representative conditions, whereas larger cyclic motifs such as triangles and higher-order rings were not observed. Lifetime analysis further indicated that these reciprocal structures persisted for a substantial fraction of the simulation duration, suggesting that they function as long-lived metastable recurrent modes. These findings provide a minimal computational demonstration that effective locality and proto-local recurrent units can arise from relational memory and reinforcement dynamics without predefined geometry. The model may serve as a starting point for future work linking complex-systems mechanisms of emergent organization with relational approaches to physical structure.
KUMIKO SAEKI (Fri,) studied this question.