The Geometric Foundation of the 5+5 Self-Dual Universe: Decomposing the 10D Continuum and Resolving Macro-Geometric Anomalies

We present a background-independent, parameter-free 10D geometric framework that resolvesfundamental cosmological and particle physics tensions without empirical fine-tuning. Rather thantreating time as an independent coordinate axis, temporal dynamics emerge as a derived physicalrelation of force acting across spatial distance (T = Ωm · F/D). The 10D physical manifold is struc-tured as a symmetric product of a 5D spatial torus (T5) and a 5D flux-threaded force sphere (S5)under O(5, 5) T -duality. By sweeping the coupling across physical transition boundaries from thesub-Planckian quantum foam floor (10−38 m) through the Planck boundary (lP ≈ 10−35 m) to thenucleon interaction scale (10−15 m), we show that the geometry locks onto a unique attractor fixed5point at R = 1.02143 lP . At this self-dual turnaround threshold, the internal volume of the T spatialtorus yields a first-principles derivation of the fine-structure constant (αEM−1 ≈ 137.036). Furthermore, we introduce the macro-geometric projection mechanism: localized sources in compactified 1/R torus space project into macroscopic R sphere space as circular or arc-like cross-sections, providing a natural geometric origin for “impossible” large-scale structures such as the Big Ring (∼ 1.3B ly) and Giant Arc (∼ 3.3B ly) without violating causality.