Predictive Closure in Coarse-Grained World Models: Memory and Resolution

Coarse-grained 3D scene simulators—including volumetric latent world models, BEV occupancy representations, and voxelised scene dynamics—replace high-resolution scene states with compact macro representations. Predictive insufficiency in such representations can arise from two distinct sources: inadequate temporal context or loss of predictive information during spatial aggregation. We introduce a two-axis predictive closure audit that separates these effects. Track A evaluates memory closure by measuring whether extending a length-$L$ macro history reduces out-of-sample prediction error. Track B evaluates feature-relative resolution closure by testing whether a declared micro-level feature provides additional predictive information beyond the same macro context, using a strictly nested, cross-fitted residual-augmentation procedure. We further establish two theoretical boundaries for predictive closure: the same observed macro law can arise from both strongly lumpable and non-lumpable micro processes, and finite recursive-state dimension does not imply finite observation-window memory. These results motivate testing predictive closure directly rather than inferring it from macro prediction accuracy or state dimension.