RFW-Orthotope Addressing Algorithm: Bounded Self-Similar and Deterministic Partition Primitives for High-Dimensional Large-Scale Data

This paper proposes RFW-Orthotope addressing algorithm, a deterministic geometric primitive for high-dimensional space partitioning. Given a high-dimensional point \(x\in\mathbb{R}^N\) and a splitting depth \(m\), RFW Addressing outputs an \(m\)-bit bucket address with the following core properties: (1) determinism; (2) equal-volume partitioning within the ideal RFW domain; (3) bounded self-similarity; (4) under the uniform-in-bucket assumption, data migration volume during re-sharding can be precomputed; (5) metadata complexity is \(O(N+2^m)\), independent of dataset size. This primitive originates from the RFW-Orthotope, a class of self-similar convex geometric bodies whose edge lengths follow a geometric progression. This work distinguishes continuous RFW and integer-lattice RFW: continuous RFW is defined over real space and satisfies strict self-similarity as an idealized mathematical model; integer-lattice RFW targets finite-precision computer implementations and satisfies bounded self-similarity with geometric error of \(O(2^{-K})\), converging to continuous RFW as the discretization scale parameter \(K\to\infty\). We present a unified invocation API, analyze algorithmic complexity, formulate numerical boundary rules and precision budgets, propose an effective depth constraint for low-cardinality data scenarios, and outline application blueprints across storage, routing, distributed training and database systems. RFW Addressing aims to serve as a geometrically equivalent, composable primitive for hash functions in high-dimensional settings, remedying inherent limitations of conventional indexing primitives under ultra-high-dimensional and cross-scale massive data workloads. As a primitive-focused paper, this manuscript contains no experimental results; related empirical evaluations will be reported in follow-up application papers.