Effective embodied exploration requires agents to accumulate and retain spatial knowledge over time. However, existing scene representations, such as discrete scene graphs or static view-based snapshots, lack \textit{post-hoc re-observability}. If an initial observation misses a target, the resulting memory omission is often irrecoverable. To bridge this gap, we propose \textbf{GSMem}, a zero-shot embodied exploration and reasoning framework built upon 3D Gaussian Splatting (3DGS). By explicitly parameterizing continuous geometry and dense appearance, 3DGS serves as a persistent spatial memory that endows the agent with \textit{Spatial Recollection}: the ability to render photorealistic novel views from optimal, previously unoccupied viewpoints. To operationalize this, GSMem employs a retrieval mechanism that simultaneously leverages parallel object-level scene graphs and semantic-level language fields. This complementary design robustly localizes target regions, enabling the agent to ``hallucinate'' optimal views for high-fidelity Vision-Language Model (VLM) reasoning. Furthermore, we introduce a hybrid exploration strategy that combines VLM-driven semantic scoring with a 3DGS-based coverage objective, balancing task-aware exploration with geometric coverage. Extensive experiments on embodied question answering and lifelong navigation demonstrate the robustness and effectiveness of our framework

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