From Microscopic Structural Interdependence to Causal Dispersive Geometry

This manuscript develops a causal effective completion of General Relativity in which spacetime curvature cannot respond instantaneously to microscopic structural change. The central result is a necessity theorem showing that finite microscopic structural persistence enforces a universal low frequency dispersive correction to gravitational coupling.

The construction begins with a scalar structural observable called the Quantum Structural Triad, built from quantum Fisher information, entropy, and mutual information. Under assumptions of locality, genuine cross cut coupling, and windowed weak stationarity with mixing, this observable possesses a finite Green Kubo correlation time. Standard principles of linear response then imply, through Kramers Kronig analyticity, that any causal geometric response must inherit a universal near static phase lag. The effective gravitational coupling therefore becomes frequency dependent, with its leading low frequency behavior determined entirely by the microscopic structural relaxation time.

The work establishes the Green Kubo to Kramers Kronig necessity chain underlying frequency dependent gravitational response, provides a covariant Closed Time Path construction ensuring conservation, and derives associated kinematic scales. The Einstein limit is recovered in the slow varying regime, while causal attenuation appears at higher frequencies.

This manuscript places dispersive gravity on a structural linear response foundation without introducing new propagating degrees of freedom.