Why Does the Future Branch? Identifiable Closure Tests for Stochastic Physical World Models

This paper argues that ordinary transition data cannot identify why a stochastic world model produces multiple futures: the ambiguity may come from observation aliasing between different physical states or from irreducible process noise after the full state is fixed. It introduces ClosurePairs, an interventional protocol that crosses compatible microstates with repeated exogenous disturbances. A two-way variance decomposition separates state aliasing, process noise, and their interaction. Reported experiments include 18 nonlinear Langevin conditions, a pixel-conditioned recurrent model, and a matched-variance REFINE/BRANCH routing test. ClosurePairs improves attribution and sensing metrics without changing forecast NLL.