Cosmic Morphodynamics: A Mathematical Theory of Dust Cloud Morphology Near Trojan L4 & L5

Cosmic dust clouds exhibit persistent, structured morphologies—filaments, lobes, anisotropic halos, knots, and metastable “edges”—that cannot be understood as static equilibria in configuration space. This article develops a unified mathematical framework in which a dust cloud is a long-time statistical object selected by resonant dynamics under weak dissipation and weak stochastic forcing. Using the Trojan L4/L5 regions of the circular restricted three-body problem (CR3BP) as a canonical setting, we formulate dust motion as a stochastic–dissipative perturbation of the Hamiltonian CR3BP and define resonant dust measures as invariant (or quasi-stationary) probability measures whose configuration-space projections are the observable morphology. Under explicit Lyapunov drift and hypoellipticity/irreducibility hypotheses, we establish existence, uniqueness, and empirical convergence of resonant dust measures. We then prove morphology laws: exponential concentration of mass near a resonant skeleton; local Gaussian transverse profiles and the universal filament-thickness scaling w≍σ^(1/2); and operator-controlled metastable escape rates with Eyring–Kramers asymptotics κ∼Ae^(-ΔΦ/σ). A resonant-averaging/homogenization reduction yields an effective drift–diffusion operator on slow resonant actions, defining a Trojan morphodynamic universality class in which leading exponents and metastability are determined at the operator level rather than by microphysical detail. Finally—and as the primary morphology layer—we classify morphology types by the topology of the effective potential Φ: single-well cores, double-well split filaments, saddle-chain branching networks, and knotting via bottlenecks and flux concentration. This classification is sharpened by committor functions for the reduced operator L_σ^Φ: committor level sets q="const" provide exact PDE-defined branch boundaries, committor tubes T_α define transition corridors, and the reactive current J predicts knot loci as flux maxima. A short PDE appendix derives the adjoint operator, stationary Fokker–Planck equation, and Dirichlet variational principles for committors and capacities, making the morphology theory explicitly operator-driven.