OpenMemory is an open-source, self-hosted AI memory engine that provides persistent semantic memory for LLM applications using a Hierarchical Memory Decomposition architecture. It features multi-sector embeddings, single-waypoint graph linking, and composite similarity retrieval, delivering 2-3× faster contextual recall and 6-10× lower costs compared to SaaS alternatives. Built with TypeScript and SQLite, it supports multiple embedding providers (OpenAI, Gemini, Ollama) and offers explainable recall paths with full data ownership and privacy control.