Subject: Re: Next step after the C portion of my halting theorem refutation --- Mike

On 11/1/2026 8:09 PM, Mike Terry wrote:

On 02/11/2026 00:36, Python wrote:

You have STILL advanced exactly ZERO steps.

You started with:

ÿÿÿ simulated DD never reaches its final return state
ÿÿÿ in any finite number of steps

and now conclude:

ÿÿÿ simulated DD never halts
ÿÿÿ in any finite number of steps

because "halting" means reaching a final state.

Fine.

THAT IS STILL THE SAME FUCKING PROPOSITION.

Now comes the part you keep avoiding:

How does HHH, which is supposed to be a HALT DECIDER, terminate and
return 0 to DD?

If HHH(DD) never returns, then HHH is not a terminating halt decider
on DD.

If HHH(DD) returns 0, then DD executes:

ÿÿÿ return Halt_Status;

and halts.

If HHH(DD) returns 1, DD loops.

Those are the three cases.

So your endless rewriting of:

ÿÿÿ "DD does not reach its final state while HHH keeps simulating it"

does not refute the Halting Theorem.

It merely describes the case in which HHH DOES NOT RETURN.

I'm not sure you're understanding the situation correctly...

I mean, "DD does not reach its final state while HHH keeps simulating
it" correctly describes the situation where HHH never aborts,

01 int DD()
02 {
03 int Halt_Status = HHH(DD);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }

<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
If simulating halt decider H correctly simulates its
input D until H correctly determines that its simulated D
would never stop running unless aborted then

Since we can see that the Professor Sipser approved
criteria has been met then it is reasonably plausible
(actually dead certain yet over everyone's head)
that HHH can see this too. When HHH does see this
then the the above "if" has been fully satisfied.

What HHH does after verifying that the above paragraph
conditions have been met is irrelevant. When these
conditions have been met what follows them is stipulated
to be correct.


--
Copyright 2026 Olcott

Computation(Olcott)
Paraphrase of Emil Post definition of computation
All computations are equivalent to the application of finite
string transformation rules to finite string inputs to derive
any and all outputs.

Because Post canonical systems are Turing-equivalent, anything
that cannot be derived by applying finite string transformations
to finite strings is outside the scope of Church?Turing computation.

Decider(Olcott)
Correcting the misnomer term-of-the-art: decider
Every Decider(Olcott) must apply finite string transformation
inference steps to their finite string inputs that are relevant
to the decision criteria. It must make its decision on this basis.

Halt Decider(Olcott)
Decider(Olcott) entails that Halt Decider(Olcott) H(D) must apply
finite-string inference steps according to the operational semantics
of the source-code computation language of D. The only way to determine
the halting property of a finite string input is to examine the same
beha