A Provably Stable Geometric Bayesian Self-Healing Framework for Deep-Space Cyber-Physical Systems: SO(3) Attitude Dynamics, Multi-Physics Energy–Thermal Coupling, and Lessons from the 2025 Lunar Trailblazer Catastrophe

Background and Motivation.The total loss of NASA's Lunar Trailblazer spacecraft in February 2025—caused by a solar-array pointing inversion coupled with cascading fault-management errors—exposed a critical gap in deep-space fault-tolerance: autonomous self-healing architectures that are both mathematically provable and physically faithful. Contributions.We present a unified, closed-form, and fully reproducible self-healing framework with four core contributions: (i) a complete rigid-body attitude model on the special orthogonal group SO(3) with Lyapunov-guaranteed global asymptotic stability (GAS) and input-to-state stability (ISS) under bounded disturbances; (ii) a coupled multiphysics energy–thermal model combining a single-diode solar-cell equivalent circuit, a second-order Thévenin battery model with electro-thermal feedback, and a radiative heat balance that captures eclipse and albedo effects; (iii) a Geometric Model Predictive Controller (Geometric-MPC) on SO(3) with torque, power, and state-of-charge constraints, discretised via fourth-order Runge–Kutta; and (iv) a Bayesian self-healing recovery index (GSHRI) integrating Sobol global sensitivity analysis and Markov Chain Monte Carlo (MCMC) posterior inference, with full convergence diagnostics. Results.Applied to authentic Lunar Trailblazer parameters (72 kg mass, 100 Wh battery, 180° pointing-inversion fault), the Geometric-MPC achieves battery SOC recovery to 92.3% (versus total depletion without healing). Sobol analysis identifies fault-detection latency as the dominant uncertainty driver (S1 = 0.712). Metropolis–Hastings MCMC (N = 10^5 samples, Gelman–Rubin R = 1.002) yields a posterior recovery probability of π = 0.9992 (95% credible interval[0.9971, 0.9999]), corresponding to GSHRI = 0.999. All derivations, Monte Carlo ensembles, MCMC chains, and TikZ/PGFPlots visualisations are self-contained and reproducible to machine precision. Recommendation.We advocate mandatory certification of GSHRI >= 0.95 through exhaustive adversarial digital-twin testing prior to launch of all Artemis-era and future deep-space missions.