Infinitesimal Causality

תקציר מקורי באנגליתarXiv:2606.24621v2 Announce Type: replace-cross Abstract: Interventions can be varied continuously in many causal models. Differentiating a specified smooth intervention protocol produces vector fields on a statistical model, and their Lie brackets describe the noncommutativity of the corresponding local perturbations. We formulate this differential geometry of interventions on smooth statistical models and call the resulting framework infinitesimal causality (IC). Given a constant-rank distribution spanned by visible intervention fields, we define the normal Lie-bracket residual and show that its vanishing is exactly the involutivity condition in the classical Frobenius theorem. We establish the coordinate invariance of the zero-residual property and characterize its dependence on the int