@jonah-soundhound-com
37 CFR 1.78 requires that "[t]he reference also must identify the relationship of the applications, namely, whether the later-filed application is a continuation, divisional, or continuation-in-part of the prior-filed nonprovisional application, international application, or international design application." Not the same weight as 35 USC 120, of course, but still something I think should be complied with.
I suspect that you may be correct that it might not actually impact the priority claim's validity if one did not, but I would not want to test it--at the very least, there could be an argument that a patentee committed inequitable conduct by, for example, labeling a CIP priority claim as a normal "continuation" priority claim. This might cause an Examiner to mistakenly assume that the subject matter in the application is identical to that in the parent, and thus incorrectly apply the parent's priority date to all claim elements when some of those claim elements were not in the priority application and not entitled to that earlier date....
