Candidacy and Trigger: A Two-Phase Empirical Model of Hierarchical Collapse

We test a dynamic ODE model of hierarchical asymmetry on a panel of 260 countries over 1960-2023, drawing on World Bank, Penn World Table, V-Dem and World Inequality Database sources. In cross-section the model holds partially: trade openness and bottom-of-distribution health suppress within-country asymmetry. The annual time-evolution equation fails, with out-of-sample R^2 at or below zero across five functional forms. The same state vector, augmented with market, debt and trajectory features, is much more successful as a discriminator: a four-layer leave-one-collapse-out classifier separates 29 historical collapses from 60 stable controls at a nested cross-validated AUC of 0.91. The signal splits into a chronic risk profile visible a decade before the event and an acute inflection three to five years before. Three independent tests reject the endogenous-drift reading of collapse. What remains is a candidacy-and-trigger picture in which structural variables identify the high-risk countries while collapse timing is set by shocks outside the modelled system. A separate strand documents a lagged co-movement between global fertility and global asymmetry on a single n=63 aggregate series; taken alone this would suggest a selection-pool channel. The same pattern is then tested within countries, within demographic strata, inside a two-way fixed-effects panel and through a migration-mediated cross-country interaction model, and the directional reading fails in each. The aggregate co-movement is a compositional effect rather than a causal channel. A global event-study on 7,316 peer-event observations confirms regional spillover in asymmetry and a novel post-collapse degradation of bottom-of-distribution health in regional neighbours. A pre-registered forward-look produces a top-20 / bottom-20 ranking to be evaluated over 2026-2036.