Hamilton-Jacobi (HJ) reachability provides formal safety guarantees for dynamical systems, but repeatedly solving the HJ partial differential equation in changing environments limits its use in real-time planning. This paper introduces learning-based reachability and an online safety certification that together enable real-time contingency-aware planning in unknown environments with probabilistic safety guarantees. We use Fourier Neural Operator (FNO) to approximate the HJ solution operator under varying obstacle configurations. To certify the learned reach-avoid set, we recast robust scenario optimization as multiple hypothesis testings over its sublevel sets, which yields a simultaneous guarantee across candidate levels and recovers the largest certifiable volume at the prescribed safety level. Within this certified set, the induced recovery policy is guaranteed to return the system to a safe region in finite time under any admissible disturbance. Numerical results show that the learning and certification pipeline updates reach-avoid sets at real-time rates and is demonstrated on youBot simulation.

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