This paper identifies field-level entanglement, the internal correlation structure of a single unified quantum field, as the 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 where the bare entanglement entropy is ultraviolet divergent, and computable in regulated quantum field theory. This finiteness is the respect in which the construction improves on entanglement-equilibrium derivations that take the divergent bare entropy as their variable. 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. The substrate variable is shown to be, at leading order, a quantum Fisher information density, and this identification gives it a role the horizon-thermodynamic argument does not: its positivity and convexity supply the stability structure on which the strong-field saturation of the framework depends, a second-order structure to which the first-order entanglement-entropy variation is blind. 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 microscopic structure of the substrate, the saturating strong-field response, and the resulting Hayward-type regular black-hole geometry are developed in the companion mechanics paper submitted alongside this work, which gives the substrate an explicit discrete dynamics and obtains from it a parameter-free prediction of the dark-energy scale, near 2 meV against an observed value of about 2.3 meV, the emergence of time from substrate reconnection, and an identification of inertial mass with reconnection frequency. This is the foundation paper of the Entanglement Network Gravity research program. The microscopic mechanics are developed in the companion paper (DOI 10.5281/zenodo.21266352) and the matter sector, including the Koide mass relation (DOI 10.5281/zenodo.20771739), in a further companion paper.
Yohannes Dereje Alemayehu (Wed,) studied this question.