Signal-Level Witnessing of SU(1,1) Pair Dynamics in Brain Proton Spin Ensembles

Non-compact symmetries such as SU(1,1) govern amplification and squeezing, yet have not been directly identified in macroscopic spin ensembles. Here we apply a symmetry-based analytical framework to previously published magnetic-resonance data acquired from proton spin ensembles in the living human brain. By reanalyzing the detected signal within this framework, we identify a non-compact SU(1,1) pair sector of the full SU(4) spin algebra whose generators carry double-quantum coherence order, and exclude compact SU(2) exchange pathways as an explanation of the observed dynamics. Although the SU(1,1) pair coherence resides in the double-quantum sector, the 45{degrees}-gradient-45{degrees} readout block converts it into a detectable signal through a specific coherence-transfer pathway. We argue that the primary significance of the detected signal is as a witness of entry into a deep metric regime in which purely singlemode compression is no longer sufficient and cross-mode squeezing-like structure becomes necessary. In this sense, the signal functions first as a metric-regime witness and, more specifically, as a witness of non-compact pair-sector multiple-quantum coherence and squeezing. We then show that any strictly bipartite evaluation is obstructed in the high-temperature bulk-NMR setting, and that the appropriate entanglement framework is instead a macroscopic multiple-quantum-coherence witness. The observed signal features are consistent with metric-driven SU(1,1) pair dynamics, while definitive certification of many-body entanglement remains conditional on pathway-corrected calibration of the transfer coefficient and on evaluation of the corresponding separable MQC bound.