per Derek:
You have allowed the Eskimo Bwl into the group you defined as Bowlines.
Actually, the so-called Eskimo Bowline (and its slipped variant) are in a sub-class called 'anti-Bowlines'.
Link:
https://en.wikipedia.org/wiki/Eskimo_bowline Ashley never depicted anti-Bowlines in his book (in so far as I have not been able to find an illustration by him).
Dan Lehman actually used the term 'anti' to describe this sub-class. With 'anti' referring to everything being in an opposite
relative direction:
1. The direction the tail takes is in the opposite direction relative to the #1010 Bowline.
2, The
collar forms around the
ongoing eye leg (instead of the SPart).
There are 4 different forms of the 'anti-Bowline'.
If the Eskimo SPart is left unloaded and you only use the structure as a round sling, is it then ejected from the Bowline family simply due to loading profile / application?
Not clear on what you meant by "family"? Do you mean excluded from being identified as a sub-class of 'Bowline'?
EDIT NOTE: I exercised my literary licence and reworded your question!
The answer comes down to the following:1. The original intent of the knot tyer; and
2. The intended loading profile of the knot structure.
If I intended to form a
round sling from a length of rope, I wouldn't be conceptualising an 'eye knot'.
I would be thinking in terms of uniting the 2 ends with an
end-to-end joining knot (eg a Sheet bend).
There is a correspondence between eye knots and end-to-end joining knots (we already know and understand this).
And so, there is a correspondence between #1431 Sheet bend, and an 'anti-Bowline'.
In Grant Prattley's case, this is not how his report was written (in his Blog report on his 'Over the edge rescue' web site).
He did not clearly depict the loading profile in his photo and indeed, the knot tyers intended application.
He did not state that the configuration of the structure was intended to be used as a 'round sling' - using #1431 Sheet bend to unite the 2 ends. The configuration as depicted in his report was that the structure was used for abseil descent - so it was tied and used as an eye knot (with the 'eye' linked to an anchor point) and the SPart was loaded.
In #1053 Butterfly eye knot, it is formed 'TIB' (without access to either end) - and the intent is to load the 'eye' (ie eye loading).
If I destroy the 'eye' by cutting it - I effectively end up with 2 pieces of rope united with an end-to-end joining knot (ie #1053 derived Butterfly bend).
In drawing a relationship between an eye knot and [a] corresponding 'bend' (ie end-to-end joining knot) - one has to be clear on intended configuration and loading profile.
In the immediate case you have offered (with an 'anti-Bowline' deliberately loaded to bypass the SPart) - I see this configuration as a
round sling, and not an eye knot. Also, in such a configuration - load is split 50/50 between
each leg of the sling. In other words, the end-to-end joining knot (within a round sling configuration) is only subjected to 50% of the load (relative to a direct
linear loading when there is no round sling).
But I do accept your point re the core of a #1431 Sheet bend as having a
correspondence to the core of an 'anti-Bowline'
when both are loaded in in a specific manner.