For the sake of HN archival history...
The executive summary of my paper is that provably there are fatal inconsistencies in Cantor's Diagonal Argument (CDA).
They take a few forms:
(1) Application of basic classical analysis tools reveals that the contradiction sought by CDA does not hold if those tools are used.
E.g.
Assume we have the table of all unique infinite length binary strings {0,1}* (where * represents the supremum of the natural numbers, e.g. the first ordinal infinity in set theoretic language).
Assume that those strings represent the fractional part of binary represetations of real numbers in the continuum interval [0,1].
Assume they start big endian, so for some string s, the value v(k) of some bit at the k-th position of s is v(k) = s(k)/2^k, for k = 1,2,3....
Let f: \N x \N -> {0,1}, be a function that accesses bits in the binary strings viewed as a matrix M(i,j).
Create the binary number z as z(k) = 1 - f(k,k).
Now deploy basic analysis.
Note that k -> \infty implies v(k) -> 0.
So no matter what the value of z(k) is, k -> \infty implies |z - f(k)| -> 0, for some suitable k.
Let f be the limit of f(k) as k -> \infty.
Then in the limit k -> \infty the number z = f, and (for all practical purposes) the diagonal z coincides with a binary number in the table f within a countable limit.
This is independent of any ordering of the table rows of M(i,j).
So the contradiction of CDA does not hold convincingly when these basic tools of analysis are used.
(2) Corollary: Platonists would need to prove that infinite digit existence somehow invalidates basic analysis in order to cling to CDA. Moreover, they would have to prove that "higher" infinite digit existence does not invalidate useful concepts of numbers and limits at all.
As far as I know, no one has done that yet.
(3) Using the same basic tools of analysis, key arguments about powersets having cardinalities that are "higher" infinities do not go through, and moreover aspects of "higher" cardinal arithmetic, as presently defined, can be shown to be self-inconsistent.
Therefore:
A) When the tools of basic classical analysis are so useful, why would any pragmatic user of mathematics throw them out at some key point within CDA (and CDA only) to endorse a notion of "uncountability" that creates manifold inconsistencies further on?
B) Why should any pragmatic mathematician allow the extra unconvincing machinery of higher infinities into maths?
In the absence of decent answers to those questions I am compelled towards the recommendation is that mathematicians should throw CDA out.
Edit: formatting.