A Model for Frequency-Dependent Negentropic Gravity: Astrophysical Signatures of a Dynamic Coherence Field

(version 2: updated mathematical framwork including corrected lagrangian terms) Standard General Relativity (GR) assumes a constant vacuum energy density and does notincorporate a dynamical mechanism for vacuum-matter coupling. We propose a diffeomorphisminvariant Lagrangian framework in which the effective vacuum pressure is governed by a scalarCoherence Field Ψ. The theory introduces a covariant retarded Green’s function kernel tocouple Ψ to the matter stress-energy tensor without violating the Bianchi identities. Thisresolves conservation issues that arise in many modified gravity frameworks and yields testablepredictions: (1) a small but measurable reduction in the gravitational weight of high-coherenceBose–Einstein condensates (Project Libra), and (2) inertial-response suppression in engineeredhigh-coherence vacuum environments (Project Icarus). Cosmologically, the model replaces thestandard Big Bang singularity with a boundary condition of maximum coherence and vanishingeffective density. This formulation offers a mathematically consistent pathway for exploringvacuum-engineering phenomena within a rigorous variational structure.