Here (and unfortunately only here) is where I assume we more or less understand each other:

I imagine there's a distribution of arm lengths and as a result a very, nearly exact distribution of cubits. — Cheshire

I don't quite get the 'very nearly exact' but never mind that. The puzzle (for an enthusiast of the heap puzzle who recognises here a classic case) is: exactly where (along a reasonably long line of arms positioned in ascending or descending order of length) does the distribution of cubits end, and the distribution of non-cubits begin?

Every other part of your latest post you would have to help me further with, I'm afraid. Including the imputation of bad faith. — bongo fury

I think you have the core of the matter highlighted. I may have misunderstood the intent, so I don't think bad faith is really in play.

I don't quite get the 'very nearly exact' but never mind that. The puzzle (for an enthusiast of the heap puzzle who recognizes here a classic case) is — bongo fury

"very nearly exact" sounded funny, but I see injecting subjective satire is probably not the best strategy for navigating this puzzle.

exactly where (along a reasonably long line of arms positioned in ascending or descending order of length) does the distribution of cubits end, and the distribution of non-cubits begin? — bongo fury

According to non-Bayesian statistics if the value is continuous there isn't one. There are some very unlikely cubits and the limit of observed cubits, but by definition both extend to infinity. Or said another way, the 1 micron cubit is very unlikely, but not excluded by the definition on an impractical yet technically accurate level.

According to non-Bayesian statistics if the value is continuous — Cheshire

But unnecessary presuppositions aside...

there isn't one. — Cheshire

So, finally,

Unbounded precisely, i.e. not graph 4; or unbounded ever i.e. graph 2? Or unbounded how? — bongo fury

So graph 2, i.e. ditch P1, because after all, "everything's relative", or "on a spectrum".

obviously it's a puzzle if we accept also the premise that calling a single grain a heap is absurd. If calling it a heap is tolerable then, as I keep saying, no puzzle.

[1] Tell me, do you think that a single grain of wheat is a heap?
[2] Well, certainly, it's the very smallest size of heap.

Game over. — bongo fury

Which is cool, if you find [2] an acceptable description of usage, and would say that black is minimally white, bald is minimally hairy, off is minimally on etc.

the limit of observed cubits — Cheshire

... is a questionable notion, but key to my

antonym-based constructive solution — bongo fury

Which of course is of no interest if there is no problem.

Which of course is of no interest if there is no problem. — bongo fury

A problem remains if the question/puzzle is subject to context. If the heap amount has any future purpose or supposed representation of value. You can't sell 1 grain heaps and expect to keep a good business rating. So, the conclusion is true in a vacuum, in reality we rely on what is reasonable. Pretending irrational things are true for the sake of pretending objectivity isn't doing philosophy any credit. Or maybe it is; I never owned the gate keys. Fun though, well played sir.