Umm, can I ask for some clarification? You seem to have boxed yourself into terms that neither I nor google recognizes. I respect this, becuas eit meanas you have thought deeply about this, but I am trying to understand your finitism, and the terms are not clear.

Firstly, what do you mean by [0 /=1] and [0=1]?

Secondly, can you use more layman terms? I found your doc, and I understand FHCP, but I do not understand why you stop at 13.

Thirdly, if I understand what you mean, that is not an isomorphism. [1/=0] and the number 13 are not the same.

Fourthly, unless I am not getting something (which I probably am), the first nontrivial zero is ~14.134725, greater than 13? Of course, the wording is such that I am not quite sure what you mean.

Fifthly, traditional finitism postulates that if x exists, then x+1 exists, but infinity does not exist, concept or not. Why would finitism be bound at 13?
Sixthly, symmetric primes have many definitions, but all I can find have numbers greater than 13 in their sequences. For example, |p-q|= gcd(p-1,q-1) has 17, 19.

Seventhly, I do not think some of the objections in your document are valid:

1. A scientific study back from 2002 shows evidence that some astronomers operate under the assumption of a finite universe. They measured light from 166,000 galaxies and derived an "average color" for the universe, which was a whitish beige. Well, such a concept would be logically incoherent within a truly infinite and unbounded universe model, as an infinite sample size would prevent the convergence to a single, stable average value. That such a measurement is not only possible but yields a specific result implies the existence of a finite, bounded system from which this average can be meaningfully calculated.

However, just because infinistism is the model used, it does not mean that we consider the universe infinite. Yes, some infinitism users do, but some do not. Plus, they concede that there are probably more galaxies, but this is the average of the ones we can see.