The Bethe-Weizsäcker semi-empirical mass formula has five fitted coefficients and has served nuclear physics for 90 years. It works, but it cannot explain why the binding energy curve peaks at iron, or why its shape has the form it has. Pentagon Physics replaces all five coefficients with a single parameter-free equation derived from the 600-cell spectral weight. The dynamic correction introduces a self-consistent binding fraction b satisfying b² + b = Σλ⁺/A, with unique stable solution at b = σ = 1/φ (iron-56). The formula achieves 0.11% RMS agreement across all nuclei with zero free parameters — matching the precision of models with many more degrees of freedom.