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 Kₒct 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 Kₒct 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.