Table T (all Turing Machines on each other as input)
<M1> <M2> <M3>... <D>... <Mk>
M1 accept reject
M2 reject accept
M3 ~halt accept
...
D reject accept accept accept
...
Mk

~Halt -->reject
reject -->reject
accept -->accept

Table TH (Turing Machine H on all Turing Machine pairs)
<M1> <M2> <M3>... <Mk>
M1 accept
M2 reject
M3 reject
...
D reject accept accept reject
...
Mk

On the diagonal: a TM is executed with its own TM description.

Because D only has a single input its behavior can be specified in a
list and need not be specified in a matrix.

Table TD (reverses H decision along the diagonal of table TH)
<M1> <M2> <M3>... <D>... <Mk>
reject accept accept accept

// C++ syntax
bool D(u32 P)
{
if ( H(P, P) )
return false;
return true;
}

When H is a simulating halt decider H(D,D) rejects its input as a
halting computation on the basis that H(D,D) specifies infinitely nested simulation to H unless H aborts its simulation of D(D).

https://www.youtube.com/watch?v=jM6osxSX9GA

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

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