Wavelet p-Leader States and Directed Tail Hypergraphs in CPEC-Linked Pakistani Equities: A Leakage-Controlled Two-Speed Risk Architecture

Financial risk along the China–Pakistan Economic Corridor may combine fast firm-level scaling changes with slower joint-tail exposure. This study evaluates a leakage-controlled two-speed architecture for seven Pakistani equities during July 2021–June 2026. Causally timed, bounded-influence wavelet p-leader states feed quantile learners, while 13 prespecified directed hyperedges define a structural map. Evidence comprises 999 iterative amplitude-adjusted Fourier-transform (IAAFT) surrogates per node, 999 matched random edge sets, a 249-origin locked Value-at-Risk–Expected Shortfall test, learner-by-feature ablations, moving-block inference, and cost-adjusted portfolios. Robustification removes the legacy KEL spectrum anomaly; only LUCK rejects the IAAFT null after false-discovery-rate control (q = 0.009). No hyperedge has a confirmed increment beyond singleton conditionals and the pairwise-only benchmark. The map’s mean lift is 0.951 versus a placebo median of 0.989 (p = 0.834). The reservoir is competitive in point loss but indistinguishable from the conditional autoregressive Value-at-Risk benchmark (p = 0.420); its p-leader gain does not transfer across learners or survive KEL-block exclusion. The 0.606-percentage-point drawdown difference relative to historical conditional Value-at-Risk (CVaR) is imprecisely estimated (95% interval: [−7.652, 5.648]; p = 0.626). The framework supports robust multiscale measurement and transparent structural mapping, not general forecasting superiority, unique hyperedge information, or reliable portfolio protection.