Influence Capacity Beyond GDP: An Axiomatic Three-Axis Theory

GDP records output but does not identify the capacity to convert output into strategic effects. This paper develops an axiomatic theory of influence capacity organized around productive capacity, mobilizable surplus, and network position. The claim that these three axes are sufficient is stated as a scoped and rejectable ontology hypothesis; it is not derived from the choice of three variables. Conditional on scalar comparability, strict coordinate monotonicity, and base-point-independent coordinate scaling, the axioms select a multiplicative class. The characterization is dimension-neutral: it selects a functional form, not the number of axes. It also separates unit-invariant conclusions from claims requiring cardinal normalization and explains why exponent estimates are not identified without a locked measurement scale and an external outcome. The product form implies constant elasticities, complementarity in levels, and a boundary bottleneck. A serial-contest mechanism provides a strategic foundation and yields an exact finite-share correction; correlated and parallel contests give explicit rival specifications. For decline dynamics, the paper derives aggregate-capacity paths and coordinate hitting times, then establishes conditions under which a strict threshold order survives small coupling. The theory therefore provides separate rejection conditions for the ontology, scalar aggregator, contest mechanism, and dynamic regime. Companion studies examine national evidence and firm-level portability. The result is a modular conditional theory whose analytic claims, measurement commitments, and empirical bridge claims can fail separately. Version note. Version 4.0 restructures the prior 175-page omnibus manuscript into a three-paper series and contains the axiomatic theory only. National evidence is available at concept DOI 10.5281/zenodo.21347878; firm-level portability is available at concept DOI 10.5281/zenodo.21347880. The immediately preceding omnibus version remains permanently available at version DOI 10.5281/zenodo.20177453. The theory is also maintained on SSRN under DOI 10.2139/ssrn.6716498.