Omni Axis Tree (OAT): A Clustered Hierarchical Data Structure for Multi-Context Retrieval with O(1) Indexed Access, and Mnemo: An AI Agent Memory System Based Thereon

Modern AI agents and enterprise data platforms require data structures capable of representing complex multi-dimensional relationships while maintaining efficient retrieval semantics. This paper introduces the Omni Axis Tree (OAT), a directed hierarchical graph structure that advances multi-dimensional data representation along three axes: (1) multi-parent relationships at all node levels including branches; (2) strictly directional traversal eliminating cyclic dependencies; and (3) bidirectional indexing via the Memory Path model, enabling O(1) retrieval and O(1) insertion regardless of structure size. Empirical benchmarks demonstrate up to 331,654× faster retrieval than worst-case DAG traversal, 819× faster than linear scan, and 314×–5,202× faster than RAG vector search at 50,000 nodes.