The Einsteinian Catastrophe Prevention Manifold

This work presents a universal geometric framework for catastrophe prevention applicable to any observer platform, including planets, spacecraft, habitats, and large-scale engineered environments. Extending the stability invariant introduced in The Einsteinian Orbital Stability Manifold, hazards are modeled as measures on a stratified interaction space and governed by a platform-coupled branching operator. The spectral radius of this operator defines a single criticality scalar that determines whether hazard dynamics are subcritical or self-amplifying. Orbital debris cascades, atmospheric fragmentation, dense belt interactions, and rogue-object threats are shown to belong to the same universality class: supercritical phase transitions in interaction manifolds with endogenous hazard reproduction. Permanent safety is proven equivalent to maintaining subcritical curvature across all observer-coupled interaction basins and relevant scales. The formulation is purely theoretical and non-implementational, introducing no technologies, methods, or operational prescriptions. This manuscript functions as a universal extension of the Ainstein geometric framework, generalizing stability theory from near-Earth orbital space to arbitrary environments and observers.