Information-Gauge Corrections to the Relative-Entropy Derivation of Semiclassical Einstein Equations

This preprint develops a minimal information-gauge effective-field-theory extension of the relative-entropy derivation of the semiclassical Einstein equations. The modular energy flux associated with horizon relative entropy is interpreted as an information current sourcing a coarse-grained vector response field. The resulting information-gauge stress tensor produces an additional Raychaudhuri focusing contribution, defining an operational null-test residual (ΔIG=δ A-4G Sᵣₑₗ), which vanishes in conventional semiclassical gravity but can be nonzero in the information-gauge extension. The manuscript derives the leading Gaussian-pulse scaling, introduces a dimensionless sensitivity parameter, and discusses possible analog-horizon and quantum-simulator tests.