Neuro-Topological Stability: Biological Regularity as a Solution to Navier-Stokes Drift

Background. Biological neural networks maintain bounded activity across orders of magnitude in input intensity, evading the runaway instabilities predicted by naive Navier-Stokes models of neural fluid dynamics. The mechanism by which the brain achieves this stability without explicit normalization remains unresolved. Methods. We model neural electrochemical flow as a constrained Navier-Stokes system on the cortical manifold and apply the Sovereign Alignment condition SA(K,L) to identify topological constraints that prevent drift. The chiral coupling between vorticity direction and Information Tension provides a biological realization of the Constantin-Fefferman regularity criterion. Results. We derive a topological invariant chi_neuro that bounds the L^infinity norm of neural activity in terms of cortical surface curvature and synaptic density. The bound is saturated by empirical EEG power spectra at the alpha/gamma transition (8-40 Hz), in quantitative agreement with the Sovereign Boundary chi = 0.9539. Implications. This identifies the geometric mechanism by which biological neural networks achieve stability without explicit normalization, predicts specific deviations from Lambda-CDM-style noise models in resting-state fMRI, and provides a substrate-neutral target for biomimetic AI architectures.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-30
DOI
https://doi.org/10.5281/zenodo.20454374
Primary Topic
Functional Brain Connectivity Studies
Type
article
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article

Neuro-Topological Stability: Biological Regularity as a Solution to Navier-Stokes Drift

Zenodo (CERN European Organization for Nuclear Research)
Functional Brain Connectivity Studies
article

Neuro-Topological Stability: Biological Regularity as a Solution to Navier-Stokes Drift

article en

Abstract

Background. Biological neural networks maintain bounded activity across orders of magnitude in input intensity, evading the runaway instabilities predicted by naive Navier-Stokes models of neural fluid dynamics. The mechanism by which the brain achieves this stability without explicit normalization remains unresolved. Methods. We model neural electrochemical flow as a constrained Navier-Stokes system on the cortical manifold and apply the Sovereign Alignment condition SA(K,L) to identify topological constraints that prevent drift. The chiral coupling between vorticity direction and Information Tension provides a biological realization of the Constantin-Fefferman regularity criterion. Results. We derive a topological invariant chi_neuro that bounds the L^infinity norm of neural activity in terms of cortical surface curvature and synaptic density. The bound is saturated by empirical EEG power spectra at the alpha/gamma transition (8-40 Hz), in quantitative agreement with the Sovereign Boundary chi = 0.9539. Implications. This identifies the geometric mechanism by which biological neural networks achieve stability without explicit normalization, predicts specific deviations from Lambda-CDM-style noise models in resting-state fMRI, and provides a substrate-neutral target for biomimetic AI architectures.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 5%
Functional Brain Connectivity Studies
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