Temporal Action Structure Controls Representation Identifiability in Predictive World Models

World models learn from trajectories generated by a behavior policy, yet that policy is often summarized only by marginal action frequencies. We show that the missing temporal information—how actions are composed—can decide whether a predictive objective recovers linear state coordinates or prefers an invertible nonlinear reparameterization of the same state. In a stationary Gaussian controlled world, this choice is governed by a spectral gap between the least predictable linear direction and the most predictable quadratic feature. We prove a sharp phase transition over the full class of standardized square-integrable encoders: a positive gap uniquely selects the state up to rotation and controls near-optimal solutions, whereas a negative gap admits an arbitrarily close, smooth, well-conditioned nonlinear improvement. We then construct two full-support distributions over length-five action sequences that match every interaction among up to three positions and the complete linear prediction operator, but have opposite gap signs. The separation also survives nonlinear Gaussian-stationary dynamics, while an independent construction shows that exact marginal Gaussianization is not sufficient in general. In a controlled visual world, finite-sample spectral learning and a 689K-parameter CNN recover the predicted coordinate switch directly from images. In that same controlled visual world, released LeWorldModel predictor modules retain and use these coordinates; after fresh heads receive equal coverage of all 32 action sequences, the two representations incur normalized action-selection regret $0.073$ and $0.366$. Finally, the same gap yields a semidefinite program for sequence-aware behavior design. Thus marginal normalization constrains representation geometry, while temporal behavior controls which geometry prediction rewards.