A Deterministic Limit for Geomagnetic Saturation: Deriving the Critical Flux Node Radius via Inductive Dissipation

The prediction of catastrophic transformer failure due to Geomagnetically Induced Currents (GIC) from solar flares and High-Altitude Electromagnetic Pulses (HEMP) relies heavily on bulk thermal monitoring and reactive relay tripping. While these frameworks mitigate aggregate overheating, they fail to deterministically define the exact spatial boundary where localized half-cycle DC saturation triggers an irreversible escape of magnetic flux into the structural steel. This paper introduces a strict continuum framework for macroscopic ferromagnetism. By modeling the transformer core as a dynamic kinematic balance between the spatial capacity for flux containment (inductive dissipation) and the localized rate of domain pinning (DC saturation), we derive a universal critical saturation radius (Rsat). We demonstrate that core vaporization is not a probabilistic thermal runaway, but an exact deterministic limit where localized DC saturation strictly overpowers the advective flux-channeling capacity of the surrounding laminated steel. We propose a blueprint for Active Grid Telemetry (AGT) using distributed Hall-effect sensors to provide real-time spatial prediction and neutral blocking prior to catastrophic grid collapse.