[I got some clues, and it seems that the domain core is embedded at the center of the gate, disguising itself as one of the gate's decorations.]
Ainsley didn't know the detailed appearance of the gate, but the core should be in the form of some precious stones.
But the core was placed at the center of the gate, which means it should be near the handle of the gate.
But the bad thing was, the gate was completely open, and it was hard to find the stone when the door didn't face their direction at all.
It was possible to go to one of the two sides to see the stone on the door handle, but it would definitely waste a lot of time and energy because the gate was too big, and they were now right in front of the center of the opened gate.
[Should we wait until the gate is closed or about to be closed? There should be fewer angels around then, and we can also end things right when the angels don't expect it.]