AlphaEarth satellite embeddings occupy a low-dimensional, locally rotating manifold

Google AlphaEarth's 64-dimensional satellite embeddings have a participation-ratio effective dimensionality of 13.3 and a local intrinsic dimensionality of about 10 across ~12.1M CONUS samples (2017-2023) [rahman-etal-2026-characterizing-alphaearth-embedding-geometry] This intrinsic-to-ambient ratio is higher than comparable geographic implicit neural representations, whose prior ID was 2-10 in 256-512 ambient dimensions [rahman-etal-2026-characterizing-alphaearth-embedding-geometry] Tangent spaces between adjacent probe locations rotate more than 60 degrees at 84% of sampled locations, indicating a strongly curved (non-affine) manifold [rahman-etal-2026-characterizing-alphaearth-embedding-geometry] A separate local-versus-global comparison finds a mean |cos theta| of 0.169 between local tangent spaces and the global principal axes, a distinct metric from the adjacent-probe rotation [rahman-etal-2026-characterizing-alphaearth-embedding-geometry] Tangent-space instability is highest in mountainous regions with steep environmental gradients [rahman-etal-2026-characterizing-alphaearth-embedding-geometry]