The DAVID System: A Coordinate Representation Framework Based on Shell Anchors and Ω -Geometry

This paper introduces the DAVID System (Directional And Vector-based Integrated Design), a coordinate representation framework that replaces traditional angular coordinates (latitude and longitude) with a non-angular triple (n,Ai,uΩ)(n, A_i, u_\Omega)(n,Ai,uΩ). In this formulation, spatial position is expressed relative to nested shells, structured anchor points, and a dimensionless distance coordinate, eliminating polar singularities and arbitrary angular divisions. The DAVID framework is developed axiomatically and shown to possess desirable mathematical properties, including singularity-free representation, natural vector composability, and scale-consistent behavior across spatial regimes. A normalization constant Ω=π/log⁡(13)\Omega = \pi / \log(13)Ω=π/log(13) is introduced as a geometric scaling factor, distinct from angular units. One admissible shell and anchor model is presented as an illustrative instantiation, and full conversion protocols between DAVID coordinates and standard latitude–longitude systems are provided. A complete worked example for Greenwich, London demonstrates the operational meaning of the coordinate triple using a reproducible computational implementation. DAVID is presented strictly as a coordinate representation framework. Claims regarding physical detectability of shell structures, navigation system performance, or superiority over GPS are explicitly deferred. The work establishes a rigorous mathematical foundation upon which future empirical, engineering, or optimization studies may build.