We derive the in-medium mass of the η′ meson inside ¹²C from two connected results in the G₂ = Aut( ) framework. First, the η′ vacuum mass is reproduced by an exact winding-number 𝕆 formula: m_{η′} = N_w × c / L_max(KQ), where L_max = 3 × spine = 1.7634 (in hyperbolic ℏ units) is the longest geodesic path between two pairs of hyperbolic pants in the Klein Quartic, and N_w = 8.44 is the topological winding number. This gives m_{η′} = 957.8 MeV at Λ_QCD = 200 MeV. Second, in nuclear matter the topological susceptibility χ_top is screened by the quark condensate modification (Drukarev-Levin-Cohen): χ_top(ρ)/χ_top(0) = [1 − σ_Nρ/(mπ²fπ²)]². At the effective nuclear density for ¹²C (ρ_eff ≈ 0.5ρ₀), we predict m_{η′}(ρ) = 840.6 MeV, giving Δm_{η′} = −117 MeV, consistent with the observation by Sekiya et al. (UOsaka, 2025-2026) of the η′ mesic nucleus in ¹²C. The geometric connection to the Woods- Saxon nuclear density (Paper CXCI) is established: the same Klein Quartic inradius a = 0.5453 controls both the nuclear surface diffuseness and the in-medium topological screening scale.Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.