Coupling Geometry Case Study VII: The Inca Empire, c. 1438–1572 CE

Coupling Geometry's claims about distribution face their hardest test in the Inca Empire, which ran a centralised redistributive economy without markets, currency, or conventional writing, coordinated through labour obligation, reciprocal exchange, and quipu record-keeping — a system in which allocation was total state provision rather than exchange. Eleven derivations are applied. Three carry the study. The vertical archipelago — complementary production across altitude zones — is neither territorial nor positional, and produces a dependency profile inverted from the territorial norm: diversity that confers resilience against local failure while making every zone reliant on the redistribution connecting them, so that when redistribution failed the portfolio inverted into dependency. The absence of markets in the Andean core, where they existed elsewhere in the Americas, is explained rather than assumed: where goods are non-substitutable complements rather than interchangeable commodities, centralised redistribution outperforms exchange. And cascade speed across four independent cases runs inverse to the capacity to decouple — fragmented Maya polities took roughly 150 years, Egypt survived repeatedly by splitting in two, Rome's east outlasted its west by a millennium, and the Inca, with no decoupling mechanism at all, fell with the capture of one man at Cajamarca. What this establishes is bounded, and the paper states the bounds. This is a portability test, not a predictive one: the derivations were not registered in advance, and the assessment was made by the author who framed them. No aggregate score is reported. One derivation is partly circular — its prediction is testable and held, but its conclusion, that the framework needs a third material-base category, is drawn from this case and cannot be confirmed by it. Three others risked almost nothing. Contested casualty figures that circulate widely in the literature have been removed rather than reproduced, and the vertical archipelago model on which the first finding depends is itself contested by specialists, which the paper records. Adversarial examination by Andeanists is invited. Case Study VI: Ancient Egypt, c. 3000–30 BCE – Case Study VIII: The Venetian Republic, 697–1797 CE