OFT–VGM Constitutive Closure: From Organizational Dependency Architecture to Physically Admissible Response Laws

Abstract

This work formulates the constitutive closure required to connect the constructive hierarchy of Organizational Field Theory (OFT) to the covariant physical-response sector of VGM. The full organizational ancestry, Ξ→Ω→κ→Φμ→Ψν\Xi \rightarrow \Omega \rightarrow \kappa \rightarrow \Phi^\mu \rightarrow \Psi^\nu, is represented as a regular dependency manifold, and a VGM realization is defined as a controlled reduction of this structure rather than the independent introduction of new physical variables. The analysis establishes conditions for dependency preservation, covariance, dimensional and differential-order closure, variational commutativity, Noether–Bianchi compatibility, degree-of-freedom control, dynamical admissibility, and a regular general-relativistic correspondence limit. A dependency-preserving massive-vector witness demonstrates the conditional nonemptiness of the admissible constitutive class, while explicit distinguishability, identifiability, validation, and rejection gates separate mathematical consistency from physical admissibility. The work provides a systematic bridge from OFT organizational ancestry to testable VGM response laws without claiming an observational anomaly, evidence for new physics, or a unique final constitutive law.