MEND: Measuring and Constraining Latent Dynamics in World Models

World models used for planning and simulation must preserve dynamics under repeated prediction. In joint-embedding predictive architectures (JEPAs), one-step accuracy does not ensure this behavior. We formulate latent prediction as an approximate semi-conjugacy. In the linear-symplectic setting, this relates dimensional collapse to encoder rank and prediction drift to predictor spectrum. MEND measures frequency, instability, and contraction in latent trajectories and uses these measurements to constrain a new predictor while keeping the encoder frozen. An orbit-averaged log-determinant separates physical dissipation from least-squares attenuation. An autonomously iterated V-JEPA 2 predictor has at least 12 positive finite-time Lyapunov exponents and loses an oscillator signal within $15$ to $21$ steps, while the encoder retains it. On a real pendulum video, MEND constrains a conformal-symplectic predictor in a two-dimensional observable. It extends the open-loop horizon from 21 to 651 steps (0.6 to 18.4 periods), approximately 31 times, while following the observed decay. These results support video-based system identification and prediction of mechanical motion using frozen representations. Extending the constraints to action-conditioned world models could support longer-horizon planning and control.