ATS-CAD Algebraic Topological Swarm Computer-Aided Design

This technical monograph introduces Algebraic Topological Swarm CAD (ATS-CAD), a precision solid modeling paradigm implemented in Rust that eliminates trimmed NURBS, heuristic tolerance bands, and floating-point boundary stitching. Formulated as an exact, non-hybrid kernel, ATS-CAD unifies real semi-algebraic geometry over the rational field Q[x,y,z], stratified CW-complexes stored in arena-allocated generalized combinatorial maps (G-Maps), and a 100% deterministic actor-swarm concurrency engine structured as a Kahn Process Network. Anchored to a dual-space metric framework featuring a discrete 1-nanometer world frame coupled with continuous algebraic number root isolation (A), the kernel guarantees "watertight" manifold closure (d^2 = 0) and crash-proof booleans without geometric healing. Complete architectural blueprints and Rust implementations are provided, establishing world-wide prior art disclosure and a foundation for zero-mesh CNC toolpath generation, ASME Y14.5 GD&T compliance, and verifiable precision engineering.