LatentGauge: Planning-Geometry Attacks in a Measure-Preserving Blind Spot

Latent world models plan by comparing imagined futures with an encoded goal. Accurate prediction and a regular latent distribution constrain the representation, while planning also depends on the geometry delivered to its scorer. Follow- ing the planning equations, we identify an inference-time degree of freedom: a shared coordinate map inserts a metric into the action-side Gauss–Newton ma- trix while the predictive model stays fixed. We introduce LATENTGAUGE, a planning-geometry attack that searches within Gaussian-measure-preserving radial transformations under a displacement budget. Probability conservation determines the admissible construction; spatially varying rotation changes its geometry; an exact cost-shift identity connects that change to candidate ranking. For CEM, the native elite boundary determines calibration, and a finite-round bound links exact score changes to successive mean and variance updates. A shared scoring operation and one constrained ranking objective make this chain executable with- out modifying the encoder or predictor. A shared kernel extension specifies the radial profile; feasible trust-region optimization fits it under the exact displacement constraint. We derive the closed-form map, its induced metric and spectrum, and the separation between displacement and local distortion. Controlled Gaussian and affine-model calculations exhibit an exact ranking reversal within an independently integrated budget and reproduce the geometric invariances. The resulting con- struction links distribution-preserving geometry to candidate selection and native planning updates