There is a small group of new Players suffering from a shortage of Fragments. (I know, many others have too much). It is those, that have only one Moonstone set (which is the standard for new players) and own two Pilgrims Manors-sets. So they get 3 Combination Catalysts a week, but just a few Fragments. I am one of them. In spite of climbing the spire all the way to the top every, every week.
^...
Moonstone set give 1 catalyst every day, thats 7 a week. And you have two Pilgrim sets, thats also 2 catalyst /day. so you are getting 21 catalysts a week an not 3 only a week, as stated in your post.