Experimental verification of the optimal fingerprint method in a spin resonance system: Implications for complex systems.

The optimal fingerprint method (OFM) serves as a potent approach for detecting and attributing climate change. However, direct experimental validation remains challenging due to the system's inherent complexity. Here we experimentally validate this method using a precisely controlled magnetic resonance system of spins, which serves as a minimal physical analog of forced noise response. Based on linear response theory (LRT), we derived the system's Green's function from spin projection noise measurements and successfully applied it to attribute the magnetic fields, yielding excellent agreement with predictions. Furthermore, our measurements confirm the existence of an optimal detection direction that maximizes the signal-to-noise ratio, a key theoretical prediction underlying the OFM. This work serves as a laboratory demonstration of LRT and OFM in detection and attribution studies, aiming to connect theoretical models with experimental observations. These findings may provide useful references for climate change science and its broader interdisciplinary applications in ecosystems, finance, social sciences, quantum sensing, and other fields.