Completion of Pauli's Theorem: A Topological Derivation of the Fine-Structure Constant

This article develops one component of the Horizon Information Framework (see program repository: https://zenodo.org/communities/horizon-framework).We address the longstanding question of the fine-structure constant α. Within the framework, α is not a free parameter but arises topologically from the descent BF → Chern–Simons → QED. The boundary algebra quantization fixes α(Q₀) = 1/k with integer k, while the two-loop QED renormalization group flow from the UV anchor reproduces α⁻¹(mₑ) ≈ 137.036 without adjustable inputs. Spin-½, charge quantization, and α are thus unified as topological consequences. This result should not be viewed in isolation. It is part of a broader program where: vacuum energy normalization is principle-locked to ρΛ = (3c²/8πG)H², dark matter and dark energy emerge as dual aspects of unlocked horizon information, inflation arises from horizon trial–flux without an inflaton, particle thresholds, spin, and neutrino masses follow from horizon bit energetics and holonomy, black hole evaporation is a topological inevitability. Taken together, these results form a unified informational cosmology. The present article contributes the electromagnetic sector, showing that the most mysterious dimensionless constant of nature can be derived from horizon-topological principles.