WorldKernel: A World Model is the Coupling Kernel of Admissible Possible Worlds

WorldKernel: Formalizing world models as coupling kernels over counterfactual worlds

A new arXiv preprint identifies a structural failure mode in prediction-based world models: strong predictors can recover the diagonal of a counterfactual coupling kernel (ordinary posteriors) but systematically fail on off-diagonal cross-world couplings, collapsing to point estimates that are sometimes provably inadmissible. The authors formalize a world model as a positive semidefinite kernel K(T,T') over admissible possible worlds, showing the off-diagonal encodes counterfactual structure that more data cannot resolve. They demonstrate that PSD constraints provide partial identification bounds computable in polynomial time, that ontological axioms tighten these bounds, and that targeted constraint learning ('scars') closes the gap faster than untargeted approaches. The work has implications for causal reasoning in AI systems and the theoretical limits of learned world models.