We present eMEM (Embodied Memory), a hybrid graph-based memory system for embodied agents operating in physical environments. Current agent memory architectures, such as Generative Agents, MemGPT, and A-MEM, treat memory as text streams or knowledge graphs, but embodied agents require memory that is simultaneously searchable by meaning, space, and time. eMEM fills this gap with a multi-index architecture (SQL ITE for structured storage, hnswlib for approximate nearest neighbour semantic search, and an R-tree for spatial queries) unified behind a single graph model. A tiered consolidation pipeline transforms raw perceptual observations into compressed summaries, mirroring hippocampal-neocortical consolidation in biological systems. Ten agent-facing recall tools expose memory retrieval primitives, including concept-to-location resolution and cross layer recall, as first-class operations for LLM tool calling. The system is fully embedded and runs in-process alongside the agent. In addition we introduce eMEM-Bench v1, a benchmark we construct over ProcTHOR-10K scenes for embodied memory evaluation. The benchmark is organised explicitly around eight cognitive-psychology paradigms (DRM lures, pattern separation, pattern completion, source monitoring, context-dependent retrieval, long-horizon interference, serial position, and a foil augmented retention curve), each chosen so that the result is interpretable against the broader memory-systems literature in humans and prior agent-memory systems; a level of diagnostic that surface-task benchmarks like LoCoMo or OpenEQA cannot provide. eMEM scores 80.8 weighted mean over 988 probes, with a flat retention curve at ceiling from 1 h to 1 yr of simulated delay on room-unique items. We show that a pure RAG baseline (the flat_rag ablation) loses 30 pt on context dependent retrieval and 29 pt on DRM lure rejection, isolating the contribution of multi-layer storage and consolidation respectively. We release both the system and the benchmark code.