This paper presents the Quantum-Spacetime Theory (QST), a novel paradigm that unifies the description of spacetime geometry and quantum phenomena through a fundamental duality. QST is built upon three postulates: (I) a constitutive relation between the metric tensor and a scalar source field, (II) a topological constraint linking the representation dimension of a quantum state to a discrete topological number, and (III) a dynamical equation coupling their evolution. From these foundational relations, QST naturally derives the electron spin quantum number s=1/2 and the Schwarzschild metric without recourse to internal symmetry groups or prior geometric assumptions. The theory is mathematically self-consistent, fully compatible with all established gravitational and quantum mechanical experiments, and predicts a testable quantum spin offset effect (Δs ≈ 2.3×10⁻⁴) in strong gravitational fields, accessible to next-generation X-ray polarimetry missions. QST posits that these relations represent the irreducible bedrock of physical description.