Topological Persistence of Post-Emergent Hydrological Regimes Across Deep-Time Perturbations

Hydrological variability is commonly interpreted as a stochastic response to atmospheric forcing and surface boundary conditions. In this study, we investigate whether large-scale hydrological regimes instead exhibit structural persistence once established, rather than continuously reconfiguring under perturbation. Using a deep-time diagnostic reconstruction spanning the late Paleocene to early Eocene (−58 to −54 Ma), we analyze post-emergent hydrological behavior across two mid-latitude continental regions under identical physical constraints. The analysis emphasizes structural and topological diagnostics, including causal organization, regime geometry, and robustness to stochastic noise and symmetry-breaking perturbations. Across extensive control ensembles, the system converges to a stable, low-dimensional hydrological structure characterized by invariant topology and non-trivial causal density. While local variability and event-scale fluctuations persist, the global structural configuration remains unchanged across perturbations. These results suggest that post-emergent hydrological regimes behave as topologically stable phase objects, rather than as transient statistical aggregates. This perspective has implications for paleoclimate interpretation, extreme-event clustering, and the conceptual modeling of hydrological memory in both ancient and modern climate systems. All parameters, diagnostics, and outputs associated with this study are provided with the accompanying record to support transparency and reproducibility.