# Every "rebuttal" simply ignores this key fact

computation that halts… “the Turing machine will halt whenever it enters a final state” (Linz:1990:234)

⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly reach its own simulated final state of ⟨Ĥ.qn⟩ and halt in any finite number of steps of correct simulation.

Therefore when embedded_H aborts the simulation of its input and transitions to its own final state of Ĥ.qn it is merely reporting this verified fact.

Can you see that the Linz Halting Problem proof contains a fatal flaw?

As people told you multiple times, if you want anyone to take your claims seriously, write a machine-checked proof (in Coq, Agda or whatever). As per analogy in https://academia.stackexchange.com/questions/18491/i-believe-i-have-solved-a-famous-open-problem-how-do-i-convince-people-in-the-f/18570#18570 , your claim is stronger than "I invented the time machine" (I would say it's along the lines "I have a working prototype of Infinity Gauntlet").

As people told you multiple times, your claims would indicate that the foundation of math is contradictory. If you have any idea what it implies, you should understand that your proof must be extremely formal (meaning, exactly as formal as the machine-checked proof requires). Since you don't understand it, it's yet another flag that you have no idea what you are trying to prove.

To summarize:

1. You lost all the trust. You already demonstrated more than enough of the cranky behavior, so I'm genuinely surprised that there are people trying to argue with you about anything. You got a lot of good feedback (in fact, the same feedback multiple times). So far you only demonstrated that your only criterion of correctness is whether the person's statement supports your "proof". The fact that you completely ignored Dan Doel's machine-checked proof speaks extremely negatively of your reaction to constructive feedback.
2. Your inability to understand the norms of the sites (that were explained to you multiple times) and your spammy behavior (such as reposting the same thing again) raise further doubts about your comprehension ability. Since you can't comprehend very simple things that people explicitly told you multiple times, how can we expect you to comprehend anything in computer science?
3. The only way to prove your correctness is to provide an argument that doesn't require the tiniest bit of trust. Namely, a machine-checked proof. Since you already spent 200 years working on this problem, you should be able to spend one more year learning Coq and converting your proof to Coq. The proof should have (see the Dan Doel proof for some ideas; you'll need to do a lot more):
• A definition of TM that exactly matches the standard definition
• A definition of the halting problem that exactly matches the standard formulation
• Only the axioms that anyone would consider absolutely trivial. Just to make it clear: "C is Turing equivalent" is not one of them.
• Your final proven statement must be "there exists a TM that solves the halting problem"

I guarantee that when you satisfy all of these conditions, then people would take you seriously. On the other hand, until you do this, you are a crank.

P.S. And, based on the discussion below, you are a confirmed crank, even worse than I ever suspected. I thought that you were avoiding writing machine-checked proofs because it's too much work (which it is, and you yourself are to blame), because you suspected that you have no chance to formalize your mess, or simply because who cares about the feedback you got? It was beyond my imagination that you would declare machine-checked proofs incorrect simply because they disagree with your idea (and, as far as I can tell, without having the slightest idea how they work).

So before doing anything else: seek medical attention. It's my genuine advice, no malice.

P.P.S.: Also, a bit about terminology (I, of course, have zero expectation that you would follow it, but at least I let you know).

• Stop saying "the fact that I proved/refuted, etc". This sounds simply laughable given that you are the only person who believes in its correctness
• Stop saying "I published a paper". We say this for results published in peer-reviewed conferences/journals. The wording we use for your case is "posted a preprint" if you plan to ever publish it, or "posted a paper" if you don't (and then certainly don't expect any recognition). Just to make it clear: when you say that you published a paper, you lie.
• Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, or in Theoretical Computer Science Chat. Comments continuing discussion may be removed. Feb 26, 2023 at 23:56
• I somewhat disagree with the last point. A preprint is a paper. (Also, a technical report is a paper, a bachelor thesis is a paper, etc.) The key word is published. A paper is published if it appears in a peer-reviewed journal/conference; it is not published if it is merely posted on the ArXiv or on a personal blog. Also, a preprint (literally meaning "before being printed") is a paper that will eventually be published in a journal/conference, but in a version before final acceptance. A paper that's not intended to be submitted to a journal/conference is not a preprint. Apr 7, 2023 at 7:08
• I can't really find the place where polcott would say they published anything, so I can't be certain about the context, but the right wording should be "posted a paper", not "posted a preprint", and definitely not "published a preprint" or "published a paper". Apr 7, 2023 at 7:14
• @EmilJeřábek, thank you! I thought that the word "publish" is acceptable when you make it clear that you are talking about preprint (I certainly met very reasonable researchers who were saying "publish a preprint on arxiv"). Is the current version correct? Regarding the context: they were talking referencing something from researchgate (probably about one of researchgate.net/profile/Pl-Olcott). I don't remember and don't really want to spend time searching for where they said it:) Apr 7, 2023 at 12:57
• You dodged the key point of the updated question ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly reach its own simulated final state of ⟨Ĥ.qn⟩ and halt in any finite number of steps of correct simulation and embedded_H merely reports on this verified fact. Apr 10, 2023 at 23:38