Stability Geometry of Coherent Modes: Descriptor-Space Boundaries in Viscous Curvature and Neural Coordination Dynamic

Coherent modes in complex systems often persist within restricted regions of state space before losing stability through damping, diffusion, or boundary-mediated transitions. We develop a descriptor-based framework for comparing such stability structure across physically distinct dissipative systems, using density-dependent viscous curvature perturbations in early-universe cosmology and large-scale neural coordination dynamics as deliberately distant examples. The comparison is methodological rather than ontological: no shared substrate or microscopic dynamics are assumed. In the cosmological sector, bulk viscosity supplies an explicit scale-dependent damping model, with an effective contribution Γ(ρ, k) ∝ ζ(ρ)k2. In the neural sector, sleep EEG recordings are mapped into a dimensionless descriptor vector D(t) = (Ξ, S, χ, Z), where Ξ measures coordination strength, S spectral entropy, χ connectivity extent, and Z an impedance-like stability proxy. From descriptor occupancy we construct empirical landscapes U (D) = − log P (D), reduced regime coordinates, support boundaries, and trajectory diagnostics. A pilot sleep EEG analysis shows structured descriptor-space occupancy, subject-held-out support generalization, smoother real trajectories than time-shuffled nulls, and stage-resolved descriptor changes across annotated sleep states. These findings support the feasibility of descriptor-space stability analysis while remaining preliminary at the subject level. Curvature tension and quadratic neural damping are treated as falsifiable hypotheses rather than established mechanisms. The framework is weakened if descriptor structure fails to generalize, temporal nulls reproduce the observed trajectories, support boundaries lack predictive value, or damping-scaling predictions fail in perturbational datasets. The result is a conservative stability grammar for coherent-mode persistence and transition geometry across complex system