The Fine-Structure Constant as a Spectral Invariant of the Unique Simplicial 2-Sphere

We derive the inverse fine-structure constant α⁻¹ = 137.035 999 086 to 12 significant digits from the bandwidth constraint B = 1 on the 2-sphere S², with zero free parameters and zero experimental inputs. The bandwidth constraint forces the octahedral simplicial complex K_oct as the unique simplicial triangulation (Schütte–van der Waerden 1951). Three independent routes yield α⁻¹: a spectral trace formula gives the integer part 137 from pure topology, the Capacity Balance Equation T + c₁ε − c₂ε² + c₃ε³ = 1 gives the full value to 12.8 parts per trillion of CODATA 2018, and a harmonic number identity independently confirms the integer as numerator(H₅). The Apéry Blockade proves the capacity series terminates exactly at three terms. The Alpha Integrality Theorem proves K_oct is unique among Platonic simplicial complexes for this formula. This prediction is pre-registered (OSF: https://osf.io/65fkg) before CODATA 2026. A standalone verification script (66 checks, all pass) is included.