Model Tajín v3: The S/U Equation, Cosmological Factor H0 = 67 km/s/Mpc, and Baryonic MAD Recycling — Sgr A_ as Galactic Ejector

We present the updated formulation of Model Tajín (v3), integrating the cosmological factor H0=67 km/s/Mpc anchored to Planck 2020 ( 67.4±0.5 km/s/Mpc) and JWST CCHP TRGB 69.85 and JAGB Carbon 67.96 km/s/Mpc, discarding SH0ES 73.04 due to crowding systematics. We propose the phenomenological structure-to-unit coordinate S/U(z)=(2/R)(1+z)−1 and its direct link to baryonic recycling mediated by Magnetically Arrested Disks (MAD) observed in M87_ and Sgr A_ by the Event Horizon Telescope. The model yields today S/U(0)=0.8, i.e. Ωclustered=0.2 and Ωvoid=0.8 without fine tuning. Sgr A_ 4×106M⊙ ejects S5-HVS1 at 1800 km/s via Hills mechanism 4.8 Myr ago, feeding the IGM. We establish falsifiable predictions: cold mass increment +0.8M⊙ in Gaia BH3 ( 32.7M⊙, 590 pc, ED-2 stream) testable with Gaia DR4.