Sparse Mixture-of-Experts (MoE) architectures enable efficient scaling of large language models through conditional computation, yet the routing mechanisms responsible for expert selection remain poorly understood. In this work, we introduce routing signatures, a vector representation summarizing expert activation patterns across layers for a given prompt, and use them to study whether MoE routing exhibits task-conditioned structure. Using OLMoE-1B-7B-0125-Instruct as an empirical testbed, we show that prompts from the same task category induce highly similar routing signatures, while promptsResearch goal: How does AnyExperts' on-demand routing strategy compare to fixed routing baselines in terms of inference latency and throughput across varying batch sizes on standard multimodal benchmarks like VQAv2 and Visual7W?Autonomous synthesis report generated by SOVEREIGN Research Kernel. Tribunal consensus score: 8.5/10.