Hello Derek,
You likely (and probably) entirely missed the underlying purpose of my post.
This topic thread contains no apparent knot species for which the mathematical content is directed.
That is, it appears to be framed as pure math.
There is a wide readership - and not all who visit the IGKT forum have a solid grasp of math.
The grass roots of this forum is knots and knot tying, rather than pure math.
So some readers may be left wondering how the pure math applies to a knot - since no specific practical examples are tendered. And because no specific practical examples of knots were tendered, it is left to the imagination of readers to link the math to some imagined knot structure.
You might also have missed that I have asked the forum moderators to consider adding a new child folder titled, “Mathematical concepts and explorations”.
…
As for the principal thrust and underlying purpose of your post - which is to point out shortcomings in understanding of the ‘normal force’ - I can comment as follows:
In a nutshell, the ‘normal force’ is the force that surfaces exert to prevent solid objects from passing through each other and it is a contact force that acts perpendicular to the surface that an object contacts.
I did not specifically include the word ‘crushing’ the surface in that definition (although in this instance, crushing is likened to strangulation rather like a python snake wrapping around and crushing its prey). Also, consider that the host typically undergoes plastic deformation when being crushed (rather than elastic deformation) - sort of like boots sinking into the mud.
Now, you may wish to debate this as a serious omission and point out severe gaps and weaknesses in my understanding of knots - I am happy for you to publicly point out such deficiencies 
In terms of crushing its ‘host’, a slide and grip progression hitch may contain ‘n’ number of turns (which wrap around the host).
Force per unit area is well enough understood - in that the crushing of the host may not necessarily occur in a localized point position - but may be distributed over a distance. Depending on the exact geometry of ‘a’ slide and grip hitch, force may be distributed or it may be localized on its host.
Again, the fundamental issue is that I do think the discussion of pure math without a specific reference to a knot structure is moving away from the grass roots of this forum. On the other hand, if images of knot structures (eg such as slide and grip hitches, tensionless hitch and #206 Munter/Crossing hitch) with mathematical examples might have more practical appeal.
Now - if you wish to declare that I am a lone voice, or lonely in pointing out these matters, again, I am happy for you to do so
Apart from that, hope 2021 is shaping up well for you!
EDIT NOTE:
While I was contemplating my suggested deficient understanding of knots and the normal force (and possible lone voice), an image of a #206 Crossing hitch suddenly popped into my consciousness.
Images of the capstan effect and coefficients of friction danced around in my mind…and I yearned for a mathematical proof for how brake power manifests from the geometry of the Munter hitch (when used as an improvised climbing belay).
I’ve also added an immobilized simple (#1010) Bowline originally devised by Xarax.
This was in relation to a potential capstan effect created by the collar against the SPart.
I don’t believe a mathematical analysis of the role friction played - and a capstan effect - was ever definitely undertaken. I do recall a fair bit of shouting and the odd insult or two for good measure…but might be worth another look.
