The Geometric Derivation of Fermion Spin-1/2

We present a deterministic, geometric derivation of fermion spin-1/2 (ħ/2) without reliance on abstract matrices or complex probability spaces. By applying the strict topological constraints of 3D spherical closure (Euler's formula V - E + F = 2) to the invariant de Broglie relation (λp = h), we demonstrate that the emergence of half-integer spin is an unavoidable mechanical requirement. When the physical wave path is forced across a 4π angular defi cit to close the topology, the momentum must inherently halve (p/2) to conserve Planck's constant h, naturally generating ħ/2.