Primordial Vorticity Model (VPM): Mathematical and Numerical Formalization Based on Observational Analysis.

This work presents the mathematical and numerical formalization of the Primor- dial Vorticity Model (VPM), a novel framework that resolves the H0 and S8 cosmolo- gical tensions through cosmic vorticity driven by ultralight axions (ma = 1,8×10^−22 eV). Based on observational analysis of 1701 Pantheon+ supernovae with critical mass filtering (Mc = (1,68 ± 0,22) × 10^12M⊙), we demonstrate a dual-component dynamics: (1) a global component (γS8 = 4,80) suppressing structure formation via wS8 = 0,100 equation of state, and (2) a local component (γH0 = 2,40) generating centrifugal pressure boost ξ = 0,084. The model yields HVPM 0 = 73,06 km/s/Mpc (resolving 4,56σ tension) and S VPM 8 = 0,7460 (reducing S8 tension by 46 %), with predicted gravitational wave background ΩVPM GW = (3,15±0,53)×10^−9 showing 0,9σ compatibility with NANOGrav. Complete action, Lagrangian, and consistency with BAO scale are provided, establishing VPM as a physically consistent alternative to ΛCDM.