Abstract — We present a unified computational framework for geometry and physics based on the concept of Computable Coordinate Systems. The central idea is to elevate coordinate systems from passive references to first-class algebraic objects, denoted as coord, which support intuitive operations such as multiplication (∗) and division (∕). This algebraic approach replaces cumbersome matrix and tensor calculus with a natural and efficient formalism for hierarchical transformations. The framework extends naturally i…