Folie à deux as a cusp catastrophe in coupled active inference: a dynamical systems account of shared psychotic disorder.

Prior work in computational psychiatry has identified three failure modes of precision weighting that produce the phenomenology of individual-level psychosis: aberrant precision on priors, aberrant precision on sensory likelihood, and aberrant meta-precision. The coupled, dyadic case has remained outside this framework. We identify a fourth failure mode, dyadic precision migration, in which precision migrates from individual sensory and prior channels onto the coupling channel under conditions of external precision collapse and sustained allostatic load. Mode 4 is a supervenient property of the coupled information geometry and is undefined in the decoupled limit; it is invisible to single-agent models of psychosis. Folie à deux, or shared psychotic disorder, is the canonical clinical instance. Starting from coupled active inference, we derive the reduced order-parameter dynamics via Landau theory expansion and show that asymmetric coupling unfolds the symmetric pitchfork bifurcation into the cusp catastrophe normal form. The bifurcation parameter maps to coupling stiffness; the symmetry-breaking parameter maps to coupling asymmetry. Numerical simulations confirm the characteristic semicubical parabola bifurcation geometry and establish that the shared attractor regime is robust (17.8% to 23.4% of explored parameter space) across coupling functional forms and noise distributions. Hysteresis on the cusp manifold predicts a falsifiable ordering of recovery times by the depth to which the secondary's beliefs are reconfigured: shallow (inference-dominated) cases recover quickly on separation, deep (learning-dominated) cases recover slowly, and cases reflecting two independent pathologies do not remit on separation alone. The framework yields a transdiagnostic account of dyadic delusional convergence and clarifies why folie à deux is structurally rare without requiring rare etiological ingredients.