A Universal Geometric Invariant Linking the Fine-Structure Constant to Lepton and Nucleon Magnetic Moments

The fine-structure constant, α, has remained one of the most persistent mysteries in modern physics: a dimensionless constant that governs electromagnetic interaction strength yet lacks a definitive theoretical origin. In this work, we introduce the QTP–α framework, a geometric–dynamic model in which α emerges from a universal invariant quantity QTP = πmpllpl, together with a particle-specific confinement factor satisfying QTP = γimiri. When applied to the electron, the relation yields α = π/γe without renormalization, relying solely on the experimentally determined confinement radius and mass. A second outcome is a universal γ-series for the anomalous magnetic moment of elementary fermions and nucleons, ai = [(afactor)^–1]*∑_(n=1)^∞[(1/γi*n)〗^n. This series reproduces measured values with high accuracy, naturally distinguishing elementary fermions (afactor = 2) from composite nucleons (𝑎factor ≈ ±1) via their structural normalization. These results suggest that mass, charge, and spin are organized by a deeper structural invariant connecting Planck-scale geometry to atomic observables.