Simulation-ready world reconstruction demands physical interactivity beyond visual realism, which existing black-box 3D generation fails to deliver. We present NeoWorld-3, a coding-agent framework that reconstructs interactive 3D worlds from visual observations via tunable, executable programs. At its core, NeoSDK provides the underlying computational engine for low-level geometries, part composition, differentiable parameter refinement, and physics validation. At the same time, NeoMCP exposes these capabilities as structured, tool-callable APIs for vision-language agents to visually inspect, edit code, and iteratively refine programs. Through a hierarchical coordinator-worker architecture, the framework scales seamlessly from standalone articulated objects to complex compositional scenes. Evaluations across object-level and scene-level reconstruction benchmarks demonstrate that NeoWorld-3 achieves state-of-the-art geometric fidelity and physical readiness. Crucially, manipulation trajectories planned within our reconstructed twins achieve successful zero-shot execution on a physical dual-arm robot, completing the Real-Sim-Real loop.