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⏖′ = Nw × c / Lₘax (KQ), where Lₘax = 3 × spine = 1. 7634 (in hyperbolic ℏ units) is the longest geodesic path between two pairs of hyperbolic pants in the Klein Quartic, and Nw = 8. 44 is the topological winding number. This gives m⏖′ = 957. 8 MeV at ΛQCD = 200 MeV. Second, in nuclear matter the topological susceptibility χₜop is screened by the quark condensate modification (Drukarev-Levin-Cohen): χₜop (ρ) /χₜop (0) = 1 − σNρ/ (mπ²fπ²) ². At the effective nuclear density for ¹²C (ρₑff ≈ 0. 5ρ₀), we predict m⏖′ (ρ) = 840. 6 MeV, giving Δm⏖′ = −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.
Bharathi Jagadeesan (Fri,) studied this question.