PAPER_1172: Independent Re-Derivation of the 26-D Curvature Coefficient $\\rho_{R_{26}} = (13/2)\\,v_{UA}^{2}\\,\\rho_{\\mathrm{SCm}}$ via Two Routes

PAPER_1170 §3 obtained the 26-D curvature contribution to the vacuum-energy ledger as $\rho_{R_{26}} = \tfrac{13}{2}\,v_{UA}^{2}\,\rho_{\mathrm{SCm}}$ through Kaluza-Klein reduction of the 26-D Einstein-Hilbert term. This paper verifies the prefactor $13/2$ by an **independent route** using the Gauss-Bonnet trace identity on $\mathcal{M}^{26} = \mathcal{M}^{4}_{\mathrm{BSFG}}\times T^{22}$, arriving at the same rational with no free parameters. The double derivation closes a potential ambiguity in the ledger. ---
