The celestial central charge \(c_{2D}\) equals \(\kappa _0\) times the Weyl anomaly \(c_{4D}^{\mathrm{Weyl}}\).

Formalized: The identity is asserted as axiom link6_from_physics with four supporting physics axioms: Weinberg soft graviton theorem, Cachazo-Strominger celestial OPE, Capper-Duff one-loop Weyl anomaly, Adler-Bardeen non-renormalization. The algebraic corollary link6_corollary (\(c_{2D} = 0 \iff c_{4D}^{\mathrm{Weyl}} = 0\)) is proved clean.