Geometry and Topology of the Universe according to Topological Angular Mathematics (MAT)
Pascal Moulin MOULIN · Zenodo (CERN European Organization for Nuclear Research) · 2025
This article introduces the framework of **Topological Angular Mathematics ($\mathbf{MAT}$)**, a formalism derived from $\mathbf{PR-TAU}$ 5.0, applied to the study of the Universe's geometry ($\mathbf{G}_{\text{Universe}}$). $\mathbf{MAT}$ replaces the continuous metric approach with a discrete one where geometry is an emergent **Specific Angular Topological Configuration ($\mathbf{CATS}$)**. Cosmological curvature is encoded in the **Angular Configuration Tensor ($\mathbf{T}_{\mathbf{CATS}}$)**, whose invariant is linked to the background angular tension ($\mathbf{\Pcrit}$). We demonstrate that the **Angular Minimization Principle** of $\mathbf{MAT}$ predicts an **angularly flat spatial geometry** on large scales, consistent with current Cosmic Microwave Background (CMB) observations.