The standard formulation of General Relativity models gravity as the curvature of spacetime dictated by the classical stress-energy of matter. However, treating mass as an intrinsic, fundamental property rather than a derived thermodynamic state creates severe theoretical friction when attempting to unify macroscopic geometric mechanics with discrete quantum theory. In this paper, we propose a structural replacement for classical mass, defining it strictly as localized informational density computed via renormalized entanglement entropy, S_eff. We mathematically redefine the observable spatial continuum not as an independent manifold, but as an induced Z_2-symmetric orbifold boundary embedded within a five-dimensional purification space governed by a zero-sum global entropy mandate (S_global = 0). By imposing universal entanglement equilibrium across all ball-shaped regions of this boundary—a structural consequence of the Z_2 topology rather than an empirical thermodynamic assumption—we demonstrate that the linearized Einstein field equations emerge as the unique local consistency condition, with Newton's constant determined directly by the area-law prefactor of the entanglement entropy. As an independent confirmation, we evaluate the extrinsic geometry of the Z_2 boundary via the Israel junction conditions and recover Poisson's equation for Newtonian gravity from the embedding data alone. Demanding consistency between the intrinsic and extrinsic derivations establishes a rigid constraint between the boundary tension and the bulk curvature scale, collapsing the framework's parameter space from three phenomenological variables to a single bulk-geometric degree of freedom. Crucially, because the geometric deformation couples to spatial entanglement rather than raw energy alone, the framework predicts that gravity acquires state-dependent corrections at subleading order in the entanglement expansion, structurally distinguishing it from General Relativity.