Existence and Consistency Conditions for a VGM Physical Response Law: Covariant Closure, Conservation, and the General-Relativistic Limit

This work investigates the existence and consistency conditions for a nontrivial physical response law within the VGM framework, formulated as an extension of the constructive architecture developed in Organizational Field Theory (OFT). The response tensor is derived from a covariant variational structure rather than introduced as an arbitrary correction, while preserving the hierarchical dependency chain from organizational structure to physical response. The analysis establishes conditional existence, symmetry, Noether–Bianchi compatibility, conservation properties, and a controlled general-relativistic limit, together with explicit admissibility and falsification criteria. A reduced vector-sector construction provides a concrete nontrivial existence witness and clarifies the distinction between geometric consistency and full dynamical viability. The paper does not claim the establishment of a new physical theory; rather, it defines the mathematical and methodological conditions that any physically admissible VGM response law must satisfy before phenomenological or observational application.