This is the architectural paper of the Pentagon Physics programme — the paper that shows how the axiom σ = 1/(1+σ) generates equations of motion, not just static parameters. The Lagrangian forced by self-reference is derived (T − V where T is the escape fraction and V is the capture fraction of the axiom). The equations of motion applied to the 600-cell spectrum produce the Spiral Engine — the unified description of how coherence propagates, freezes, and creates the observable world. The paper derives the deuteron magnetic moment to 0.39%, the neutron-proton mass difference to 0.52%, nuclear magic numbers from character table dimension products, and calcium isotope charge radii.