Bridge 3: Microscopic Derivation of J and the COCM–VFT Connection

Under the hypothesis of a dynamically coupled five-dimensional bulk warp factor and the quasi-circular orbital approximation, we derive an analytic expression for the COCM invariant J from the bulk geometry of C0 via the Israel junction conditions and the linear back-reaction of Rn. Within this framework, J > 0 throughout the physically admissible regime and J < 1/4 is satisfied automatically without fine-tuning. Three internal consistency conditions are shown to be mutually compatible. The orbital ellipticity is assumed as a working hypothesis. As a conditional corollary, the VFT optical control parameter ε is expressible without residual free parameters once ωᵦ is confirmed by DESI DR3 and the bulk hypothesis is accepted. Title revised: “Bridge 3: Microscopic Derivation of J and the COCM–VFT Connection” (previously “Conditional Closure of Bridge 3…”). The cautionary qualifier is now carried by the abstract and declared hypotheses, not the title. No changes to content or results. Setting correct title.