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

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→ΨνΞ → Ω → κ → Φ^μ → Ψ^ν, 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.