Entanglement-Density Gravity: The vacuum does not gravitate — Einstein's equation as an entanglement balance, and the structure-correlated dark energy it predicts

We propose that gravity is the thermodynamics of vacuum entanglement, applied to the multi-sector vacuum of realistic physics. Adopting the entanglement-equilibrium hypothesis — that the vacuum maximizes entanglement entropy in small causal regions — Einstein's equations follow as a balance between the entanglement surplus carried by matter and the geometric entanglement deficit carried by curvature, with the cosmological constant entering as the entanglement density of the vacuum. Three results follow: the equivalence principle becomes a theorem rather than a postulate; gravity couples only to departures from each sector's vacuum, so the Standard Model vacuum energy does not gravitate and the cosmological constant problem dissolves, with the observed dark energy emerging as the entanglement density of the cosmological horizon (exactly ΛCDM in the single-sector limit); and a falsifiable, structure-correlated modification of late-time growth, with a single coupling bounded simultaneously by DESI DR2's dark-energy evolution and by redshift-space-distortion measurements, its sign diagnostic of the S8 tension. This is a companion to Paper II, which computes the perturbed-horizon response in detail.