The Hydrogen Bond

We derive the hydrogen binding energy from first principles using icosahedral geometry, achieving exact agreement with CODATA 2018 to computational precision. The electron and proton are modelled as face and vertex modes of a shared standing wave, with 180° phase difference generating a harmonic expansion in powers of the fine structure constant α. All coefficients emerge from icosahedral topology using only five parameters {V, E, F, χ, D}: dimensional bouncing ((D³−1)/D² = 26/9), electron face coupling (+χ/(F+χ) = 1/11), proton vertex stabilisation (−(V−χ)/(5²+6²) = −10/61), face-vertex interaction (−χ²/[(F+χ)(V+χ)] = −1/77), electron-proton coupling (+3F/[V×D²×(V+χ)] = 5/126), and proton bridge stabilisation (−χ/(V+χ) = −1/7). The denominator 126 = D²×(V+χ) is simultaneously the 7th nuclear magic number and the number of E7 root vectors, revealing deep connections between atomic binding and nuclear stability. This represents QED-level precision from pure geometry, with no fitted parameters.