Local Constitutive Equivalence Between COCM and the VFT Optical Sector

This technical note establishes a local constitutive equivalence between the infrared deformation sector of COCM and the optical deformation sector of VFT. Taking as its starting point the open constitutive question identified in Dziabura (2026) — the microscopic origin of the VFT optical control parameter β_opt — we show that there exists a unique radius r* at which the COCM gradient invariant J maps constitutively to β_opt, at fixed orbital phase and in the subcritical domain J < 1/4. The equivalence fails globally due to inequivalent radial profiles and symmetry-breaking classes. As a corollary, once J is fixed microscopically by Bridge 3, the identification of β_opt requires no free parameters.