Evidence for Bures--Wasserstein Boundary Dynamics in the Living Human Brain
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918426875789312 |
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| author | Kerskens, Christian |
| author_facet | Kerskens, Christian |
| contents | When substrate-constrained covariance flow on the Bures--Wasserstein manifold reaches the Williamson boundary, single-mode compression saturates and further admissible covariance evolution is forced into the cross-mode complement. This paper derives how that substrate boundary transition becomes experimentally visible in an embedded spin probe in the living human brain. We formulate a boundary-conditioned transfer theorem: when the substrate enters the deep boundary regime in a coupled mode, the boundary-selected cross-mode continuation of substrate covariance flow enters the reduced spin dynamics as a nonzero inter-spin correlation block. The spin probe does not inherit the substrate boundary as a state; it detects the boundary indirectly through the transferred cross-mode sector of the reduced dynamics. To leading order, this transfer is selective: it acts through an additive cross-diffusion channel while leaving conventional single-mode NMR observables such as \(T_1\), \(T_2\), linewidths, and the ordinary single-quantum response dominated by the thermal background.
Projecting the induced spin cross-mode structure into the two-spin algebra, we argue that the experimentally relevant dominant recipient is the double-quantum SU(1,1) pair sector rather than the compact zero-quantum SU(2) exchange sector. We then derive the coherence-transfer pathway through which this double-quantum pair coherence is converted into a detectable signal by the \(45^\circ\)--gradient--\(45^\circ\) readout block. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22680 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Evidence for Bures--Wasserstein Boundary Dynamics in the Living Human Brain Kerskens, Christian Neurons and Cognition When substrate-constrained covariance flow on the Bures--Wasserstein manifold reaches the Williamson boundary, single-mode compression saturates and further admissible covariance evolution is forced into the cross-mode complement. This paper derives how that substrate boundary transition becomes experimentally visible in an embedded spin probe in the living human brain. We formulate a boundary-conditioned transfer theorem: when the substrate enters the deep boundary regime in a coupled mode, the boundary-selected cross-mode continuation of substrate covariance flow enters the reduced spin dynamics as a nonzero inter-spin correlation block. The spin probe does not inherit the substrate boundary as a state; it detects the boundary indirectly through the transferred cross-mode sector of the reduced dynamics. To leading order, this transfer is selective: it acts through an additive cross-diffusion channel while leaving conventional single-mode NMR observables such as \(T_1\), \(T_2\), linewidths, and the ordinary single-quantum response dominated by the thermal background. Projecting the induced spin cross-mode structure into the two-spin algebra, we argue that the experimentally relevant dominant recipient is the double-quantum SU(1,1) pair sector rather than the compact zero-quantum SU(2) exchange sector. We then derive the coherence-transfer pathway through which this double-quantum pair coherence is converted into a detectable signal by the \(45^\circ\)--gradient--\(45^\circ\) readout block. |
| title | Evidence for Bures--Wasserstein Boundary Dynamics in the Living Human Brain |
| topic | Neurons and Cognition |
| url | https://arxiv.org/abs/2505.22680 |