arXiv: ROWBench: Do Video Models Render What the Program Specifies? Programmable world models separate executable dynamics from visual generation, offering a promising foundation for next-generation game engines. However, their visual adherence to explicit rules and interactions remains insufficiently evaluated. Existing benchmarks assess visual quality, controllability, and instruction or physical adherence, but rarely test fidelity to fine-grained, program-specified world events. We introduce PROWBench, comprising 170 programmatically constructed episodes and