Real-Time Space Traffic Management for 50,000 Satellites: A Spectral Digital Twin

The low Earth orbit environment is projected to host over 50,000 active satellites by 2028, generating approximately 125,000 relevant conjunction pairs per day. Current conjunction assessment operates in overnight batch mode, producing alerts hours after the screening window closes. We propose a spectral digital twin architecture in which every tracked object carries a compact spectral state --- nominal trajectory, \(N\) spectral uncertainty coefficients, a non-Gaussian correction factor \(\gamma\), and an analytical sensitivity \(\partial P_c / \partial(\Delta v)\) --- enabling full-catalog conjunction screening in 2 minutes (125,000 pairs \(\times\) 0.001 s/pair). The architecture comprises four operational layers: catalog maintenance, pairwise screening, threshold alerting, and optimal maneuver response. We demonstrate that the spectral digital twin enables capabilities impossible with current systems: intraday risk updates, pre-launch conjunction assessment, multi-operator conflict resolution with analytical gradients, and formally verified \(P_c\) computation (Lean 4). The system is deterministic, auditable, and reproducible --- properties increasingly demanded by emerging space traffic management regulations (FAA, ESA, UN COPUOS). We estimate the development cost at \\(5--10M with annual industry-wide savings of \\)50--100M from optimized maneuver coordination, reduced false alerts, and extended satellite lifetime. The spectral digital twin integrates the entire spectral space situational awareness pipeline: non-Gaussian \(P_c\) (Nagy, 2026d), analytical maneuver optimization (Nagy, 2026, Maneuver), and cascade risk monitoring (Nagy, 2026, Kessler) into a unified operational system.