Stability Geometry of Coherent Modes: Descriptor-Space Boundaries in Viscous Curvature and Neural Coordination Dynamics
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2026
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| _version_ | 1866902093275594752 |
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| author | Smith Jr, Francis G. |
| author_facet | Smith Jr, Francis G. |
| contents | <p>Coherent modes in complex systems often persist within restricted regions of state space be-<br>fore losing stability through damping, diffusion, or boundary-mediated transitions. We develop<br>a descriptor-based framework for comparing such stability structure across physically distinct<br>dissipative systems, using density-dependent viscous curvature perturbations in early-universe<br>cosmology and large-scale neural coordination dynamics as deliberately distant examples. The<br>comparison is methodological rather than ontological: no shared substrate or microscopic dy-<br>namics are assumed.<br>In the cosmological sector, bulk viscosity supplies an explicit scale-dependent damping model,<br>with an effective contribution Γ(ρ, k) ∝ ζ(ρ)k2. In the neural sector, sleep EEG recordings are<br>mapped into a dimensionless descriptor vector D(t) = (Ξ, S, χ, Z), where Ξ measures coordi-<br>nation strength, S spectral entropy, χ connectivity extent, and Z an impedance-like stability<br>proxy. From descriptor occupancy we construct empirical landscapes U (D) = − log P (D), re-<br>duced regime coordinates, support boundaries, and trajectory diagnostics.<br>A pilot sleep EEG analysis shows structured descriptor-space occupancy, subject-held-out<br>support generalization, smoother real trajectories than time-shuffled nulls, and stage-resolved<br>descriptor changes across annotated sleep states. These findings support the feasibility of<br>descriptor-space stability analysis while remaining preliminary at the subject level. Curva-<br>ture tension and quadratic neural damping are treated as falsifiable hypotheses rather than<br>established mechanisms.<br>The framework is weakened if descriptor structure fails to generalize, temporal nulls repro-<br>duce the observed trajectories, support boundaries lack predictive value, or damping-scaling<br>predictions fail in perturbational datasets. The result is a conservative stability grammar for<br>coherent-mode persistence and transition geometry across complex systems.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20287181 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Stability Geometry of Coherent Modes: Descriptor-Space Boundaries in Viscous Curvature and Neural Coordination Dynamics Smith Jr, Francis G. Nonlinear dynamics Complex systems Dissipative systems State-space geometry Neural dynamics Computational neuroscience Dynamical systems theory Stochastic processes Drift-diffusion modeling Empirical potential landscapes Dimensionality reduction Manifold learning Functional connectivity Sleep EEG Spectral entropy Metastability Boundary-constrained dynamics Cosmological perturbations <p>Coherent modes in complex systems often persist within restricted regions of state space be-<br>fore losing stability through damping, diffusion, or boundary-mediated transitions. We develop<br>a descriptor-based framework for comparing such stability structure across physically distinct<br>dissipative systems, using density-dependent viscous curvature perturbations in early-universe<br>cosmology and large-scale neural coordination dynamics as deliberately distant examples. The<br>comparison is methodological rather than ontological: no shared substrate or microscopic dy-<br>namics are assumed.<br>In the cosmological sector, bulk viscosity supplies an explicit scale-dependent damping model,<br>with an effective contribution Γ(ρ, k) ∝ ζ(ρ)k2. In the neural sector, sleep EEG recordings are<br>mapped into a dimensionless descriptor vector D(t) = (Ξ, S, χ, Z), where Ξ measures coordi-<br>nation strength, S spectral entropy, χ connectivity extent, and Z an impedance-like stability<br>proxy. From descriptor occupancy we construct empirical landscapes U (D) = − log P (D), re-<br>duced regime coordinates, support boundaries, and trajectory diagnostics.<br>A pilot sleep EEG analysis shows structured descriptor-space occupancy, subject-held-out<br>support generalization, smoother real trajectories than time-shuffled nulls, and stage-resolved<br>descriptor changes across annotated sleep states. These findings support the feasibility of<br>descriptor-space stability analysis while remaining preliminary at the subject level. Curva-<br>ture tension and quadratic neural damping are treated as falsifiable hypotheses rather than<br>established mechanisms.<br>The framework is weakened if descriptor structure fails to generalize, temporal nulls repro-<br>duce the observed trajectories, support boundaries lack predictive value, or damping-scaling<br>predictions fail in perturbational datasets. The result is a conservative stability grammar for<br>coherent-mode persistence and transition geometry across complex systems.</p> |
| title | Stability Geometry of Coherent Modes: Descriptor-Space Boundaries in Viscous Curvature and Neural Coordination Dynamics |
| topic | Nonlinear dynamics Complex systems Dissipative systems State-space geometry Neural dynamics Computational neuroscience Dynamical systems theory Stochastic processes Drift-diffusion modeling Empirical potential landscapes Dimensionality reduction Manifold learning Functional connectivity Sleep EEG Spectral entropy Metastability Boundary-constrained dynamics Cosmological perturbations |
| url | https://doi.org/10.5281/zenodo.20287181 |