XPost: comp.theory, comp.lang.c++   
   From: polcott333@gmail.com   
      
   When the halting problem requires a halt decider   
   to report on the behavior of a Turing machine   
   this is always a category error.   
      
   The corrected halting problem requires a Turing   
   machine decider to report in the behavior that   
   its finite string input specifies.   
      
   This analysis in done in the C programming language   
   so that it is 100% concrete without any key details   
   being abstracted away.   
      
   int DD()   
   {   
      int Halt_Status = HHH(DD);   
      if (Halt_Status)   
        HERE: goto HERE;   
      return Halt_Status;   
   }   
      
   (a) The key issue is that HHH(DD) does report on the   
   behavior that its input finite string specifies.   
      
   (b) Reporting on anything else is outside of the   
   scope of Turing Machine Computable functions.   
      
      
   *Detailed analysis shown below*   
      
   After many very extensive discussions with LLM   
   systems there are two principles that prove that   
   I have correctly refuted the halting problem itself.   
      
   (1) Turing Machine based Computable functions   
   only transform input finite strings into some value   
   on the basis of a semantic of syntactic property   
   that this finite string specifies.   
      
   (2) the behavior that an input DD specifies to halt   
   decider HHH is the sequence of steps of DD   
   simulated by HHH according to the semantics of   
   the C programming language.   
      
   Computable functions are the basic objects of study   
   in computability theory. Informally, a function is   
   computable if there is an algorithm that computes   
   the value of the function for every value of its argument.   
   https://en.wikipedia.org/wiki/Computable_function   
      
   DD() executed from main() calls HHH(DD) thus is   
   not one-and-the-same-thing as an argument to HHH.   
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning expressed in language"   
   reliably computable.   
      
   This required establishing a new foundation   
   for correct reasoning.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)