Entanglement Network Gravity: Field-Level Entanglement as a Substrate for Emergent Gravity

This paper identifies field-level entanglement, the internal correlation structure of a single unified quantum field, as the proposed primitive substrate of emergent spatial geometry, explicitly distinguished from particle-level entanglement (correlations between distinct quantum systems) that figures in much of the entanglement–geometry literature. The deviation of this structure from its vacuum baseline is defined operationally as a coarse-grained density of relative entropy evaluated at the substrate's discrete ultraviolet scale, finite by Araki's theorem and computable in regulated quantum field theory. The same scale controls the parameterized Lorentz-violation prediction and the discreteness-fluctuation estimate of the cosmological constant, fixing one scale across the framework rather than three independent ones. Combined with Jacobson's derivation of the Einstein equations from local Rindler-horizon thermodynamics, and with the Bekenstein–Hawking area law taken as input, this identification recovers the full nonlinear Einstein equations, the Newtonian potential, and the standard observational tests of general relativity, with no additional fitting parameters. Sorkin's order-of-magnitude argument for the cosmological constant is inherited as a consistency check, with the inherited sign problem acknowledged. The functional form of the saturating potential, the resulting strong-field metric (anticipated to be of Hayward type), and the microscopic structure of the substrate are developed in extension papers within the same research program. Categories of claim are tagged inline: established results (standard QFT, GR), framework hypotheses (the substrate proposal, the operational identification), and inherited machinery (Jacobson 1995, Bekenstein–Hawking, Araki, Hollands–Sanders, Bisognano–Wichmann, Casini–Huerta–Myers, Faulkner et al., Sorkin) are distinguished throughout.