Selection of modulated pulled pattern-forming fronts

Let $u_\mathrm{pl}(\xi,\tau)$ be a modulated pulled pattern-forming front satisfying the stated pinched-double-root, periodic-wake, exponential-asymptotic, marginal-Floquet-stability, and no-resonance hypotheses. Selection of modulated pulled pattern-forming fronts. $u_\mathrm{pl}(\xi,\tau)$ should be a selected front.

The source reports that this claim was formally resolved by matched asymptotics, but without control of the errors. Thus a rigorous proof remains unavailable.