Does LeWorldModel Preserve Local Action Geometry?

World models are typically evaluated by prediction or control performance, but these criteria do not reveal whether their local response to nearby actions matches the environment. We study this through the action Jacobian and its induced Gram matrix, $G_t=J_t^\top J_t$, comparing pretrained LeWorldModel (LeWM) with simulator transitions expressed through the same frozen encoder. On Reacher, LeWM preserves the dominant action direction but exaggerates eccentricity; on OGBench Cube, the dominant direction and leading action subspace are substantially misaligned. The Cube mismatch persists across finite-difference scales and outside contact transitions. Thus useful latent prediction does not necessarily imply faithful local action geometry.