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That's a lot of good info about witnesses - thanks.
What you did not include, however, is a description of what the actual
function of witnesses is.
Basically witnesses are publicly known, reputable users who prevent doublespending, because they
witnessed the reality for those users who came after them. So their function is to witness the reality. They let us know which branch in the DAG is the real one when there are two conflicting branches. The presentation I linked does a very good job of explaining it all.
For convenience:
https://docs.google.com/presentation/d/1dpbE1l4Aj8Te2_i9wjVsW48igZMhdyjKJVcWY-45qd8/edit#slide=id.p3