GIC Network Model: Multi-Substation Faraday Solve

This is the 2D companion to the 3D geomagnetically-induced-current simulator, and it reaches the same space-weather conclusion through a genuinely different computational route. Instead of evaluating a single lumped Ohm's-law formula for the whole corridor, it builds a synthetic magnetometer trace by integrating a driving signal frame-by-frame, recovers dB/dt by numerically differentiating that trace — the way a real magnetometer feed is actually processed — and then feeds the result into a full multi-substation resistor network solved by Kirchhoff's current law, the same Lehtinen–Pirjola method real grid operators use. Each substation is independently grounded to remote earth and each segment of the corridor can carry its own ground geology, so current can inject and return at internal transformers, not just the two ends. A live readout of the summed GIC across every node — which the underlying algebra forces to zero regardless of how the geology is arranged — gives you a running proof that the network solve is self-consistent.