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Tom,
I see your arguments presented in a horribly confusing manner and also most likely wrong.
In your "Buridan's Principle and the point at infinity" you wrote: t goes to infinity. You introduced "(x,y) variables are either fixed or fluctuating values of a continuous range. In other words, the car (x) at time t and the tree (y) at time t..." This is not understandably explained to me.
You referred to Wheeler: "The binary relation (bit) is that which constructs, not that which is derived from a construction necessitating the axiom of choice (Zorn's lemma); it's the most fundamental relation, as Wheeler allows, in nature as well as in mathematics."
I consider this idea wrong, no matter whether or not you accepts AC. I see Euclid's abstraction to the notion unity the basis of mathematics and any repetition of this operation already belonging to the level of abstraction in my Fig. 1. Accordingly there is obviously no exact equality in reality, and trichotomy is something artificial that decouples mathematics from logics.
What about Planck's constant h, I don't see it necessarily related to the uncertainty principle which is also valid for time and frequency. Plank's constant is just a factor of proportionality that relates position to momentum.
Eckard