I found an interesting math result, but now I see a contradiction

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I found an interesting math result ("halting problem is essentially solvable") yesterday, but now I see a contradiction (it follows "halting problem is solvable"). Participate in finding my error.
I found an interesting math result ("halting problem is essentially solvable") yesterday, but now I see a contradiction (it follows "halting problem is solvable"). Participate in finding my error.

Here is my short yesterday article (with links to other yesterday articles):

[Unacceptable reference redacted by the Mentors]
 
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I've found an error myself:

In the linked article [Unacceptable reference redacted by the Mentors] I describe the error in bold font.

The linked article nevertheless had another valid very interesting result that replaces the paradigm that mathematics is theorem proving by another paradigm.

You have a new release of mathematics.
 
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I glanced at the article, and found that it referenced your prior article on using Peano Arithmetic to avoid Godel's incompleteness result ##-## the only 'support' in that article for your contention was 'faith'; not science. Please understand that PF is a set of forums for science; not for exploring faith-based ideas about scientific and mathematical matters. Please read the guidelines, and if you have questions or concerns about any of them, please PM one of the Mentors.
 
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