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Fully homomorphic encryption (FHE) allows computations to be performed directly on encrypted data without decryption, offering strong privacy guarantees for sensitive data analysis. This capability is important for privacy-sensitive applications like secure cloud computing, finance, and healthcare. The complexity of FHE schemes, however, has hindered their practical adoption. To make FHE accessible to a broader range of developers, a new generation of specialized frameworks has emerged to translate high-level FHE programs into complex FHE operations, introducing a new programming paradigm. However, the inherent complexity of FHE frameworks makes them prone to incorrect implementation logic. Unlike mere crashes, logic bugs in these frameworks can silently corrupt encrypted computation, potentially leading to severe financial losses and security vulnerabilities in FHE-enhanced applications. In this work, we introduce HERTA, the first automated testing tool tailored for FHE frameworks. HERTA leverages metamorphic testing to uncover deep-seated implementation bugs and vulnerabilities across the multi-layered FHE software stack. To that end, we design a set of novel metamorphic relations (MRs) derived specifically from FHE semantics. These MRs stress the most challenging aspects of the pipeline, enabling automated correctness testing without the need for a manual ground truth. Our evaluation of HERTA on 3 leading industry frameworks discovered 21 previously unknown bugs, several of which have already been confirmed and fixed by developers. Furthermore, our hazard analysis reveals the critical security impact these bugs pose to the integrity and availability of FHE-based services.