Beyond GDP: A Three-Axis Theory of National Influence Capacity

Why can a commercially small state exercise influence beyond its output, while a materially large state loses leverage when alliances, payment channels, or administrative reach fracture? This article develops a three-axis theory of national influence capacity: productive capacity, mobilizable surplus, and network position. Historical contrasts motivate the separation before formalization. Conditional on scalar comparison and base-point-independent proportional response, the model selects a multiplicative aggregator. A serial-contest mechanism supplies a strategic interpretation, while threshold dynamics distinguish aggregate decline from the order of operational failures. Separate rejection tests discipline the ontology, scalar representation, mechanism, and dynamic regime for specified tasks and horizons. Working-paper theory article. National supplementary material: https://doi.org/10.5281/zenodo.21347878. Firm-level supplementary material: https://doi.org/10.5281/zenodo.21347880. The analytical results are conditional on their stated assumptions.