Universal selection of pulled fronts

We establish selection of critical pulled fronts in invasion processes as predicted by the marginal stability conjecture. Our result shows convergence to a front with logarithmic shift for open sets steep initial data, including one-sided compactly supported conditions. rely on robust, conceptual assumptions, namely existence and spectral traveling at linear spreading speed demonstrate that assumptions hold classes spatially extended systems. Previous results relied comparison principles or probabilistic tools implied nonopen conditions data structure equation. Technically, we describe process through interaction Gaussian leading edge wake. Key ingredients are sharp decay estimates control errors nonlinear matching corrections from data.