Emergence and Collapse of Spatial Geometry from Temporal Coherence: Evidence from Atomic Clock Networks

This work presents an empirical analysis of the informational role of spatial geometry using publicly available atomic clock data from the BIPM Circular T archive. By analyzing relational time differences between UTC(k) laboratories, we test whether spatial distance consistently carries predictive information or whether its relevance depends on the coherence of the underlying temporal structure. We introduce a non-parametric geometric information metric that quantifies the coupling between spatial distance and relational time dynamics, alongside an independent permutation-based measure of temporal coherence (TDI). Using rolling-window analysis across a global network of atomic clocks, we identify distinct regimes in which spatial distance is informative and regimes in which this information collapses. The results show that spatial geometry carries predictive information only during temporally coherent intervals. When temporal coherence breaks down, the distance–relation coupling vanishes, despite the continued presence of measurable time signals. This indicates that geometry behaves as an emergent, coherence-dependent informational property rather than as a fixed background structure. All data used in this study are publicly available through the BIPM Circular T dataset. The analysis is fully reproducible and relies solely on empirical measurements and non-parametric statistical methods.