Extensions to local discrete transport and quantitative attractor dimensions

Extend the theory of two-field divergence-free edge-cochain systems with Hodge-Laplacian dissipation and MHD-type trilinear cancellation to local cochain transport interactions, nonlinearities derived from a compatible discrete calculus, and quantitative estimates of global-attractor dimensions.

Background

The paper develops an abstract cancellation framework for finite-dimensional two-field edge-cochain systems and gives an explicit anticommutator realization, but it does not derive a physically or geometrically local transport operator from a compatible discrete calculus. It also establishes existence of compact global attractors under Hodge coercivity, without deriving quantitative fractal- or Hausdorff-dimension bounds. The authors identify extending the framework in these directions—including local cochain transport, compatible discrete-calculus nonlinearities, and attractor-dimension estimates—as unresolved.