In general relativity, the metric field describes spacetime intervals between events relative to any ideal material reference frame as if the frame were not present; in this sense, the metric encodes these intervals. In quantum mechanics, by contrast, such events are naturally accompanied by correlations with that frame. Motivated by this complementarity, we propose a geometry-information equivalence hypothesis (GIEH), according to which the metric field geometrically encodes the relational information otherwise carried by correlations with a local reference frame (LRF). In a small geodesic ball, the GIEH yields the full nonlinear Einstein equation when ideal-LRF conditions are imposed, without assuming an AdS background or an underlying CFT. The framework further allows background correlations to provide an informational origin for the cosmological constant, with their local mutual-information density equal to the Gibbons-Hawking entropy per unit thermodynamic volume.