Emergence of Spacetime Curvature and Mass-Energy from Informational Density Gradients

We present a unified field formulation wherein classical spacetime geometry and relativistic mass-energy emerge from spatial scalar field variations governing local informational density gradients I(x). Operating within a composite Hilbert space Hsys ∼= HA ⊗ HT , physical fields are modeled as continuous projections of unobserved potential modes (A ∈ HA) into realized spatial configurations (ρT ∈ HT ) mediated by a self-adjoint recognition generator Kˆ . We demonstrate that varying the informational action S[I,gμν] reproduces the Einstein field equations in the classical limit, while generating explicit quantum corrections at high informational density. Furthermore, rest mass and structural inertia are derived from first principles as the continuous Lindblad phase relaxation rate of localized gradient configurations. The framework yields testable micro-lensing metric corrections near horizon regimes.