Where α comes from: the full derivation to 10⁻¹⁰

α is measured, 1/α = 137.035999177(21), and there is no accepted derivation of it from principles. Here it follows from the closure of light, with no number taken from measurement: light is given, and matter is born from it when Eunex > Eex, below 0.866c. The circle of light closes into a hexagon, because only the hexagon places the balance Eex = Eunex at the middle of the side, and on the sphere the closure stops at the cuboctahedron. The remainder of the side, π/3 − 1, gives N₀ = 133.125240 steps, and α is the share of one step, 1/N. Four matter circles give 1/α = 137.011774, the hexagon gap 137.036131, its absorption at the vertices, along the spiral and continuous, 137.035999099, and the wave that speeds up from vertex to vertex 137.0359991494: a difference of −2.0×10⁻¹⁰, 1.3 times the measurement uncertainty. The gap and its absorption follow from the motion of the wave at the vertices. The last step gives about two thirds of the term of order α³; the rest is not derived.