Black-box LLM fingerprinting aims to decide whether a target model is derived from a known source model using only the models' output to queries. A common strategy perturbs each query slightly and records the response changes of both models, yielding two corresponding sets of variations. These sets contain two sources of information: the relations among changes within each set and the correspondence of changes between the two sets. Existing techniques usually exploit only one of them.\n\nSetPrint is a training‑free method that jointly captures both within‑set relations and between‑set correspondence. It first normalizes each response change by the mean change of its own set, then compares the normalized changes induced by the same perturbation across the two models.\n\nOn the LeaFBench benchmark, SetPrint consistently outperforms current training‑free black-box fingerprinting approaches. Further analysis attributes the gains to the combined use of within‑set relations and between‑set correspondence.\n\nReview