Re-visiting my reply to you at R1- please do not pre-judge the future of debate but see what happens by giving your view! (Thanks for the copy of your paper - I can think of a few mathematicians I could ask to analyse it).
Quoting you: "I am talking about reality. It is an abstract concept".
R1 is an abstract concept. But 'reality' is not necessarily so. To assume that it is, is to "beg the question".
To start equivocating "reality" as the world knows it (what exists) and R1 would be "the fallacy of equivocation".
"That definition though vague is complete because it is defined to be correct" -correct for R1 in abstract hypothesizing perhaps; but not necessarily correct for 'reality' as one must not 'beg the question'.
"I have made absolutely no constraints whatsoever on what reality is"- this is not correct for R1 or for 'reality'.
You have placed the constraint: "I have not the slightest idea what reality is". Vagueness is a constraint.
Further, it is a logically invalid constraint. "I have not the slightest idea" relies on you having the very definite idea that: "I have not the slightest idea". That is, you appear to have a very good idea about your not having the slightest idea!
That very good idea is a piece of reality. You always have some reality Dick, and always have some R1.
"I have made absolutely no constraints whatsoever on what that mental image of reality is!" -not true, you've constrained R1 and reality by the constraint "vague".
If I take the witness stand in a court case and say "I have no idea which of those people broke the window"; the prosecution case is constrained by my very vagueness. Vagueness imposes a limit. The limit: this witness can not be used. This exclusion law is a real constraint. They are constrained from using me as a witness.
You are begging the question, by placing an exclusion law on reality, and excluding reality as a 'witness'.
"My mental model of reality might not be reality"- you can not have a mental model without having some reality. R1 is another issue. With reality, you have at least some reality: the reality of having a model. You always have some reality.
"I have made absolutely no constraints whatsoever as to what it is, how it works or why it works" regarding the connection between R1 and the mental image of R1-
not correct, as you have made the very serious constraint of "vagueness", and imposed an 'exclusion law'.
Fig. 1 appears to be "begging the question": assumption made: "vagueness" ; constraint: vagueness, and 'exclusion law'.
"alternate view of our senses in R1" - not necessarily correct; vagueness is a constraint.
"transformation"- assumption: transformation assumes the exclusion of any 'non-transformed direct experience (and I've shown you must have with reality some direct non-transformed experience). R1 might be different.
To say "no way of distinguishing all possible representations of reality, from reality"- clever idea but:
all possible representations of reality include some direct reality (the reality of 'being a representation'). R1 might be different.
How to discriminate between the direct non-transformed reality and the model? Honesty: Existence is directly detectable.
I see no proof that the fundamental transform exists as you define it. I have shown that for reality, there is a non-transformed portion always.
A 'correct concept' of reality sounds like a contradiction in terms; to be fully correct it must include the direct-portion that is non-transformable thus not-fully-communicable by your constrained form of communication. It might be communicated by direct non-transform mode though.
I see no justification for equivocating R1 with reality; a set of numbers with reality.
"There exists no way you can prove I am wrong": I just did didn't I? Can you prove I'm wrong?