Paper XXVIII: Rotation Curves, Bullet Cluster, and Dark Matter Without Particles

The sump mechanism (Papers XXVXXVI) generates dierential absorp- tion of sump pressure by concentrated baryonic matter, producing at galaxy rotation curves, the Bullet Cluster lensing-gas oset, and the cluster conundrum resolution all without any new particle. The T2* coherence radius r_T2* = p GMBH/a0 is a zero-free-parameter prediction conrmed against the 175-galaxy SPARC sample (Spear- man r = 0.37, p = 0.048, N = 34 with published M_BH). Rotation curve diversity is resolved by the T2*/T2 ratio. The Bullet Cluster lensing-gas oset is explained by the temperature-dependent coupling f(T) ∝m_p c2/k_B T ≪1 for hot ICM. The cluster conundrum is resolved by three contributions: sump apparent mass M_sump = a0r2/G, BCG T2* jerk, and f(T) suppression of hot gas. Three lensing predictions follow: strong lensing excess ∝M_BH{1/2}, weak lensing granularity ∝ p Σ⋆(r), bar-axis Einstein ring enhancement. 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.