Which Capacity Fails First? National Evidence for a Three-Axis Model of Influence

Abstract

This paper develops an empirical test of a three-axis theory of national influence. It operationalizes productive capacity pi, mobilizable surplus mu, and network position nu; restricts retrospective classification inputs to information dated before scored crossings; and evaluates the framework through historical transitions, a modern panel, and six prospective tests. Among eleven retrospectively selected transitions, seven completed cases strictly match the ordering implied by their pre-crossing classification, Britain and Tang China are joint-shock partials, Mughal India is an explicit violation, and Russia remains right-censored after its first predicted crossing. Under a common scoring rule, the classifier therefore yields strict matches, boundary cases, a violation, and an unresolved trajectory. In a PWT 11.0 G15 panel, both adjacent eigenvalue-ratio diagnostics exceed the exploratory point threshold, although the strict bootstrap criterion is not met. Because the operator starts from three constructed series, this diagnostic does not identify the number or completeness of the underlying axes. A pre-specified off-diagonal coupling-magnitude map selects the locked exploratory cardinal (0.640,0.175,0.185) from four candidates, with its interpretation conditional on the constructed axes, VAR(1), transferred contest parameters, and leakage normalization. The prospective registry fixes observables, horizons, triggers, and rejection levels for six future tests. The results indicate that the theory can distinguish national trajectories and generate prospectively testable predictions beyond GDP rankings. They support continued evaluation of the regime classifier while leaving axis completeness, causal identification, and the cardinal map open to held-out rejection. Exploratory national supplementary study for https://doi.org/10.5281/zenodo.20036716. The constructed-axis diagnostic does not establish axis completeness; the strict bootstrap result remains unfavorable. This record is a working paper, not an independent preregistration.