The view of Chicago Integrate from Nicholas van Rijn's penthouse on the roof of the Winged Cross:
"Whenever they visited, the Falkayns never tired of that spectacle."
-Poul Anderson, Mirkheim IN Anderson, Rise Of The Terran Empire (Riverdale, NY, 2011), pp. 1-291 AT Prologue, Y minus 9., p. 11.
Consecutive readers of Poul Anderson's Technic History know that David Falkayn works for van Rijn but do not yet know of any couple called the Falkayns. However, the text continues:
"To David it was comparatively fresh; he had spent most of his life off Earth." (ibid.)
This confirms that one of these "Falkayns" is the one that we already know and also fits with what we know about him.
"But Coya, who had been coming to see her grandfather since before she could walk, likewise found it always new." (ibid.)
This informs us that van Rijn's granddaughter, Coya Conyon, introduced in the concluding story of the previous volume, is now married to David.
After this prologue, future history will accelerate:
in Mirkheim, Chapter I, the Falkayns had stopped space traveling to bring up their daughter, Juanita, and Coya is pregnant again;
in Chapter XVIII, Nicholas Falkayn is born;
in the following story, "Wingless," Nicholas Falkayn, an engineer on the planet Avalon, advises his son and the viewpoint character of the story, Nathaniel/Nat;
the last work to be collected in Rise Of The Terran Empire, which is another complete novel, The People Of The Wind, features a remote descendant, Tabitha Falkayn, who is also Hrill of Highsky Choth on Avalon, but that is the last that we see of the Falkayns.
After that, the narrative slows way back down again with twelve of the remaining nineteen works devoted to a single influential figure, Dominic Flandry. But none of that should be in our minds as we read about the Falkayns' visit to van Rijn on the Winged Cross.