Quantifying tectonic–climatic circumscription: a reproducible spatial-statistical test at primary-state locations

A long-standing question in comparative archaeology is whether environmental circumscription — the bounding of productive land by uninhabitable terrain — statistically co-locates with the independent emergence of primary states (Carneiro, 1970; Force, 2008). Neither the original hypothesis nor its tectonic extension has been operationalised as a quantitative global metric tested against explicit null distributions. Here we operationalise one narrowly defined mechanism — desert-river tectonic–climatic circumscription — as a multiplicative Geological Circumscription Index (GCI) computed on a 1° global land grid (15,351 cells) from three public datasets: a plate-boundary model, a global aridity product, and a major-river network. We test whether the seven primary-state locations used in the standard comparative set fall in high-GCI cells, against Monte Carlo null distributions with n = 100,000 trials. The civilizations lie at mean global percentile 95.0% (p = 0.00007); their mean GCI is 24.4 times the global land mean (p = 0.00004); the four desert-river cases in the set reach 42.8 times (p < 0.00001). Three cases score GCI = 0 because each lacks one of the three components, consistent with the index operationalising desert-river circumscription specifically rather than circumscription in general. The GCI field is strongly spatially autocorrelated (Moran's I = 0.892) and geometrically organised along the Alpine–Himalayan–Andean tectonic belt, a direct geometric consequence of plate-tectonic convergence. The result does not constitute a general theory of state formation; it operationalises one mechanism and tests its spatial footprint against explicit nulls. We offer the index and its pipeline as a reproducible tool for further comparative and paleoclimate-adjusted work.