Boolean standards and all.
You said "the link" is to be identified as a false positive. There is problem with this.
The so called "link" is observed "unique inherent characteristics", in other words fact. The unique inherent characteristics is what forms a nested set. Now the point is this;
a branching process can created a nested set AND is the only process we know about that can produce a nested set. The second point is, if a nested set is created by a
branching process then the nested set implies a hierarchy based on kinship.
Therefore whenever a branching process is connected to a nested set then unique inherent characteristics implies a common ancestor. And we can do that in the case of life - namely the well established parent-child relation.
Knowing this, we do not have to observer every single birth to know if there is a kinship or not. If we know kinship implies a nested set determined by unique inherent characteristics then we can do the reverse: we can determine kinship by the unique inherent characteristics. Therefore
if we observe two individuals sharing unique inherent characteristics them we know as a fact they are related via kinship!
The question is, how is anything of this "on paper" only?
In my opinion, the "link" is justified by factual observations and evidence, it is not just something imagined, as you claim it to be. The "link" is a real thing - it is an observed fact!
Yet you claim claim to know something that we other does not know, when you claim the nested set is a false positive, and I am trying to find out what that is, or what you mean with that, and so far you have not been very helpful to even hint what it is. So I will need to start to guess for you then.
Do you with "a false positive" mean:
a) life can come to exists by other means than parent-child relations, or
b) the observed "unique inherent characteristics" are somehow erroneous
or do you mean something else?
[Notice, only claiming a) still leads, based on the observations, to the conclusion that
all life shares a common ancestor].