Is the proof of the following theorem correct?

[X.Y. Newberry]

For FOM:

Is the proof of the following theorem correct?

THEOREM 1: There are numbers k and s and a program A(n,m) satisfying the
following conditions.

1. If A(n,m) halts, then C_n(m) diverges.
2. For all n, C_k(n) = A(n,n) and C_s(n) = Ck(s).
3. A(k,s) halts and for all n, A(s,n) diverges.

Here C_n(*) is a program with index n in some exhaustive enumeration of all
possible programs.

The proof is here.
https://xnewberry.tripod.com/Theorem.pdf

-- 
X.Y. Newberry

*There are two ways to be fooled. One is to believe what isn't true; the
other is to refuse to believe what is true.*
― Søren Kierkegaard
<https://www.goodreads.com/author/show/6172.S_ren_Kierkegaard>
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