We present a simple, quantitative model that predicts the ionization behavior of a weak polyacid as strong polyelectrolyte layers are deposited. The theory treats such layered self-assemblies akin to one-dimensional, ionic solids via electrostatics but, importantly, includes local pH response of solution via buffer capacity. The model reduces to a nonlinear, iterative map having a single free parameter and agrees well with experiment. The map shows that steady-state is determined by the polyacid's initial ionization and that polyelectrolyte charges self-adjust.