Informational Cosmology and the Kerr-like Vacuum

This paper develops an exact structural map together with a maximum-entropy constitutive closure for the gravitational sector of the Null-Directional Kinematics (NDK) program. Evaluating the maximum-entropy closure for the directional substrate yields an explicit imperfect-fluid realization of the strain stress-energy tensor. In the isotropic limit, this provides a structural route to an effective vacuum-like sector (p -), while away from isotropy it generates rotational heat-flux/frame-dragging-like contributions and tidal squashing through anisotropic stress. The exact partition function for an aligned Kerr-like informational vacuum is then derived, showing that, within the constitutive model, rotational bias enhances the effective quadrupolar response. Mapping this anisotropic stress into the Sachs optical formalism yields leading-order weak-field, thin-lens scaling predictions for horizon-scale optics, including excess spin-aligned shear, anisotropic convergence, and a quadratic relation between misalignment-induced twist and ellipticity observables in the asymptotic regime.