A Geometric and Energetic Framework for Matter-Antimatter Asymmetry, Dark Components, and Cosmic Evolution

The Standard Cosmological Model (ΛCDM) currently faces a foundational crisis, primarily manifested in the persistent 5σ Hubble Tension and the unexplained nature of the dark sector. This paper introduces a framework that redefines existence as a dynamic Rate of Transformation (μ ≡ dE/dt) on a closed S1 manifold. By deriving the geometric constraints of a circular-to-linear projection, we provide a parameter-free resolution to these anomalies.We demonstrate that the observed matter density of the universe is an irreducible residual of this projection, yielding an exact value of 1/π ≈ 0.3183, in 1σ alignment with Planck 2020 data (Ωm ≈ 0.315). Furthermore, by accounting for the scaling bias between the global circular manifold and the local interactive linear footprint (4R), we reconcile the early-universe expansion rate (H0 ≈ 67.4) with the local Freedman/JWST 2025 measurement of 73.1 km/s/Mpc. This paper offers a unified, falsifiable derivation for the evolution of dark energy as observed by DESI 2025, suggesting that the "Crisis in Cosmology" is a predictable consequence of manifold geometry.