The Shape that Survives: Topological Invariants of Equilibrium under Observational Equivalence

Recovering an economy's structure from data usually pins down only part of it. Which features of its equilibria, its self-reproducing states, survive that ambiguity? The economy's dominant strength and direction of dependence are firmly pinned down, but the individual links between its parts are not. The answer is an asymmetry. The global shape of the set of equilibria, captured by topological quantities such as the fixed-point index sum and the Euler characteristic, is the same for every structure the data cannot tell apart. As a result, in the typical case the number of equilibria is forced to be odd, even where the links are unidentified. The exact count, and where each equilibrium sits, are not pinned down. A coda reads the Chichilnisky impossibility of fair preference aggregation as a fact about the shape of the preference space. Counting equilibria is not the same as determining which one the economy reaches, and nothing here is a forecast; a reproducible, illustrative worked example is included.