Scale‐Conditioned Geometry: How Measurement Resolution Induces Distance, Proximity, and Spatial Dependence

Scale is central to inference in natural and social systems, and geography and ecology have treated it as an explicit object of theory for decades. This paper builds on that work with a formal view in which scale is a degree of freedom of description, parameterizing both the mappings between representations and the metric defining distance and neighborhood. Distance is induced by the representation and can change with resolution even when the underlying system is unchanged. In simulated autocorrelated fields aggregated across seven block sizes (30 Monte Carlo replications), Moran's I declines by a factor of 3.4 while a correlation‐threshold range proxy remains comparatively stable. An explicit metric on the family of representations (Fused Gromov–Wasserstein) shows that scale and zoning are distinct, measurable directions. A change‐of‐support null describes the change expected from information loss under a single correlation structure; a mixed‐scale scenario departs from it at six of seven scales, which rejects that null without by itself establishing a change in coupling. Two observational datasets, each analyzed at a single support, show that the induced metric changes global and local dependence. These results motivate a scale‐explicit workflow that treats proximity and dependence as conditional on representation.