Greeting jarnos:
My definition is somewhat different:
Feel free to invent your own theoretical body of work - and publish it.
This is how science progresses over a period of time.
Let me know when you have published - so I can download and read it.
In relation to the definition of 'PET':
E.g. a TIB knot may exist before forming the eye
The key point is whether any knot tying maneuvers are
required (ie be pre-existing)
before the eye is sized and formed.
If such maneuvers are a necessity, and the eye
cannot be sized and formed without such a pre-existing condition, then the knot cannot be deserving of the title of 'PET'.
From a technical standpoint, your alleged pre-existing 'TIB' knot could be tied after the eye has been sized and formed.
A 'TIB' structure is equivalent to the 'unknot' (ie an unknotted length of rope).
some other maneuvers such as forming a loop (like in case of a bowline) may be needed before forming the eye.
With regard to a 'Bowline', it is
not a pre-existing condition that a
loop is formed
before attempting to size and form the eye.
...
In terms of the history of the invention and use of the term 'PET'; it was likely that grandmasters such as
Xarax and
Dan Lehman evolved the concept either independently of each other or in one of their great debates... not sure which.
Mobius also appeared to be motivated to add a dimensional object to qualify the definition of 'PET'.
I believe that it isn't necessary to add such a qualifier.
However, one could state that; "By default, the eye of a PET knot can be formed through a ring".
Although, the inclusion of a 'ring' to qualify the definition is not essential to understanding.
...
You appear to be struggling to understand many basic concepts...
Not sure why?
