When Cooper finishes his investigation at the Roadhouse, he has Ed come there, along with Leo. Then he realized that the waiter, and possibly Briggs, were missing. This might not make any impact, though, so look at it as an interpretation, connecting these three people to the Giant's three clues.
1. Big Ed: at the hospital, Cooper and company saw Ed outside Nadine's room and decided to stick around and listen to what had happened. That is when Cooper noticed the smiling bag in the bathroom. If they hadn't seen Ed out there, they would have probably missed this clue.
2. Briggs: I think this one is the most obvious. Briggs brought Cooper the owl transmissions and Cooper somehow deduced that Briggs was missing from this fateful reunion. Of course, the Giant brought him there, possibly because he saw Cooper come to a moment of realization earlier during the warm milk scene.
3. Leo: Maybe a bit far-fetched, but we were never told explicitly what the significance with boots was. Leo bought the boots from the Phillip Gerard, who is the basis for the third clue. Cooper put two things together and deduced that Leo had to be there.
And that's it. The Giant saw that Cooper had compiled everything that was needed and gave him the ring, which represents the investigation coming full-circle. He also said the magic phrase about the gum, which triggered Cooper's memory.
Thoughts?
