On the Field Equations of Admissibility

This work introduces a Lorentz-invariant scalar–tensor framework in which a dimensionless admissibility field Ξ(x) governs dynamical persistence across physical scales. The action is constructed to reduce to General Relativity in the stationary limit while permitting calculable deviations through finite-mass scalar dynamics. The theory yields Yukawa-screened corrections in the weak field, identifies black hole horizons with admissibility zeros, and produces late-time cosmic acceleration through slow relaxation of the background field. A single variational principle generates screening, clustering, and filamentary organization, providing a unified dynamical equation whose limiting regimes reproduce known gravitational phenomenology.