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Geodesics in dynamical KPZ models remain confined to an essentially one-dimensional trace under noise perturbations, proving that non-trivial bigeodesics are restricted to an exceptional set of Hausdorff dimension zero.
The directed landscape is no longer strictly static: critical $n^{-1/3}$ scaling of Ornstein–Uhlenbeck percolation yields the first continuous, reversible dynamical limit for the universal geometry underlying the KPZ class.