Cardiac-Phase-Dependent Spin Coherence as a Probe of Boundary Covariance Geometry in Neural Tissue

arXiv:2505.22680v2 Announce Type: replace
Abstract: A recently proposed geometric framework predicts that the transition from distributed belief to committed action involves a metric regime change, culminating in a boundary regime where cross-mode structure becomes algebraically necessary for continued state-space compression. This paper examines whether reported magnetic resonance measurements of proton spins in neural tissue provide an empirical probe of this regime. A companion analysis identifies the detected signal as the readout-converted signature of double-quantum SU(1,1) pair coherence, which correlates with short-term memory performance and cardiac-phase dynamics during wakefulness. We show that the mathematical bridge between the abstract transport framework and the physical spin system is the Bures metric, which natively governs both Gaussian Wasserstein geometry and quantum density matrices. We argue that the observed signal is best understood as a probe of entry into a deep boundary regime where single-mode compression is exhausted and collective cross-mode squeezing emerges. Because high-temperature bulk NMR obstructs strictly bipartite entanglement witnesses, we contextualize the signal within a macroscopic multiple-quantum-coherence (MQC) framework. Consequently, the current data provide evidence for the metric-driven onset of collective non-compact SU(1,1) structure, establishing the necessary physical foundation for future macroscopic many-body entanglement certification.