TITLE:
A Reduced Kinetic Stability Model for the Dark-Matter Cosmic Web
AUTHORS:
Nikolay N. Fimin
KEYWORDS:
Kinetic Stability, Cosmic Web, Dark Matter, Characteristic Flow, Symplectic Invariants, Vlasov-Poisson-Λ System
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.8,
August
24,
2026
ABSTRACT: We formulate a reduced kinetic stability model for the dark-matter cosmic web in a deliberately restricted finite-time sense. The object is the tangent deformation of prescribed Vlasov characteristics, not spectral or nonlinear stability of a self-consistent Vlasov-Poisson solution. Six-dimensional geodesic-deviation and phase-space-distortion integration is already established; the present addition is a morphology-labeled reporting protocol for an available tangent propagator. A Gaussian-smoothed T-web supplies void, wall, filament, and node labels, while the complete effective Hessian determines the local dynamics. For a frozen conservative physical-coordinate cell, Hessian inertia and quadratic first integrals identify hyperbolic, neutral, and elliptic sectors; comoving behaviour is determined by the full Hubble-containing generator. Finite-time amplification is measured by the standard largest singular-value/FTLE quantity in one fixed full-state metric and on maximal contiguous morphology intervals after exact substep composition. The smoothing length controls the reconstructed Hessian and labels, but its common scalar factor cancels from the induced gain; the position-velocity weighting is set by a declared time scale. The propagator bound is label-blind, so morphology sums are residence-time-labeled bookkeeping rather than causal environmental contributions. Homogeneous expansion is removed with an interaction-picture propagator. Common-anchor factors telescope globally, but their norms depend on the anchor; local two-point factors and a transported-metric interpretation are therefore distinguished. A fully three-dimensional benchmark tests changing eigenframes, classifier-Hessian misalignment, a near-neutral gap, partitioning, anchor dependence, metric choice, and classification tolerances. At a fixed matter Hessian, the cosmological constant gives the usual local downward curvature shift. The paper provides a formal construction and validation protocol, not an empirically validated cosmic-web diagnostic.