Nope. Wrong test. You want to test against things that are known *not* to be designed and see if any are mistakenly designated as designed. THAT is a false positive.
What you attempted to do is give a way of testing for false *negatives*.
In practice, you would need to look for false positives in situations that are close to the target (fair choice of population). In other words, you need a suitably randomized collection of test subjects, with known design or lack thereof, that are close enough to the target subject (first life) for the test to be well tested for things similar to the targe
I don't really get your point..
What one should do is apply the test to things that are known to be "non design." if some of these "non designed" pass the test then the test and the method would be falsified......... . I am pretty sure this is a false positive, but if used the incorrect word then I apologize for that.
And what, precisely was that hypothesis?
Well the hypothesis would be that the first living thing was a self replicating protein. (SRP)
Proteins are made out of aminoacids
1 we know that there are many possible arrangements of aminoacids, there are many ways in which amonacids can organice
2 We know that the mayority of possible arrangements would produce a non SRP
3 The only assumption that I am making (which seems to be a reasonable assumption) is that you would need many (say more than 100) aminoacids to firm a self replicating protein.
If you grant, point 1, 2 and 3 the the first living this or SRP would have the attribute of specified complexity