Unified Geometry: Complete Archive of the Sq³ Noncommutative Grand Unified Theory, Core Theorems & Testable Predictions

Based on the noncommutative geometry of the quantum 3-sphere Sq³ and the quantum flag manifold SUq (3) /T, this work establishes a complete grand unified theoretical framework from a single geometric axiom. We rigorously prove the Representation Splitting Theorem, providing the first-principles geometric origin of the three generations of fermions in the Standard Model (SM). Via the Scale Self-Duality Axiom and the topology of the quantum flag manifold, we derive the classical benchmark value of the fine-structure constant and perform semi-quantitative estimation of higher-order corrections, achieving high consistency with experimental data. The framework naturally unifies the four fundamental interactions: gravity (Einstein-Hilbert action) and the full SM gauge group SU (3) c SU (2) L U (1) Y are directly derived from noncommutative spectral triples. We also fix the geometric benchmark exponent of fermion masses, fully derive the CKM and PMNS mixing matrices, resolve the cosmological constant fine-tuning problem, and systematically propose 9 testable predictions covering neutrino physics, cosmology, quantum gravity, and black hole physics. All results are derived without free parameters or ad hoc fittings, presenting a self-consistent, falsifiable, and experimentally verifiable scheme for fundamental physics unification. This archive preserves the complete theoretical framework, core theorem derivations, and experimental verification roadmap, laying a foundation for future academic exchanges and experimental tests.