Irreversible Geometry of Order Parameter Spacetime — Higher-Dimensional Unification and the Information–Geometry Closed Loop

We construct the higher-dimensional unified framework of the order parameter spacetime theory, completing the information–geometry logical closed loop. Three core results are established. First, gauge forces are geometrized: by introducing internal space dimensions, gauge interactions are proved to be the four-dimensional projection of non-dissipative geodesic motion in higher-dimensional spacetime. Second, a candidate form of the information–Einstein equation is proposed: the information dissipation tensor becomes a source of spacetime curvature, with the information energy–momentum tensor determined by four physical requirements. Third, the framework structure of the information–geometry closed loop is established: the information dissipation tensor simultaneously describes the inscription of geometric texture and the irreversible loss of information. As natural consequences, we present three physical results: the contribution of information dissipation to the dark energy density is of the same order as observations on cosmological scales; black hole entropy is reinterpreted as the equation of state of the information–Einstein equation at the horizon; and the traceless part of the tensor leads to polarization-dependent attenuation of gravitational waves. With this, all theoretical threads proposed in the foundational framework—geometrization of gauge forces, information bottleneck, and spacetime emergence—are closed within the higher-dimensional unified framework. This paper builds upon prior works in the series [10.5281/zenodo.21325459, 10.5281/zenodo.21499343, 10.5281/zenodo.21499696].