BST-ID: A Binary Prefix Algebra for Multi-Resolution Spatiotemporal Regions

This study extends hierarchical spatiotemporal identifiers beyond cell identification by using the Binary Spatiotemporal Identifier (BST-ID) as a computational representation for multi-cell regions. BST-ID supports independent resolution along x, y, altitude, and time; normalized finite prefix sets represent regions. We define subsumption, Union, anisotropic Intersection, selective Difference, refinement/coarsening, and neighborhood operations. Chained operations remain in the same BST-ID prefix domain. Full working-grid expansion provides reference semantics; selective execution depends on generated-prefix count K. All 43,444 bounded exhaustive, randomized, property-based, and targeted checks passed. In a synthetic 3D Difference case, selective traversal visited 4.97% of the full grid and reduced serialized size by 93.94%, preserving finest-grid occupancy. The real-world-derived Tsuruga Castle case normalized 31,334 fine XYH cells to 3884 prefixes (87.6% reduction), exactly reconstructing the declared fine-cell set. A dynamic UAS scenario with 34 simulated flights evaluated time-varying reservations, overlap, and conformance. Whole-scenario XYHT normalization reduced fixed-spatial dyadic-time records from 932,090 to 240,360; 75.72% of final prefixes had unequal X/Y zooms. The arbitrary exact-interval baseline remained more compact. Together, these results show that BST-ID provides representational continuity: independently resolved spatial and temporal prefixes support multi-cell region computation in the same prefix domain.