When we replace the code of HHH with the code of
Claude AI then this HHH refutes the halting problem
proofs.

These systems figure out the recursive simulation
non-halting behavior pattern on their own and are
able directly see for themselves that this pattern
is matched.

They can see this because they can see that recursive
simulation is essentially mutual recursion. Then they
perform the execution trace on this simplified basis
to match this pattern. Once the pattern is matched they
confirm that HHH(DD)==0 is correct on that basis.

What I love about LLM systems is that they do not
begin with strong bias against me. It is this strong
bias that causes people to look for errors at a much
higher priority than understanding what I am saying.

<Input to LLM systems>
Simulating Termination Analyzer HHH correctly simulates its input until:
(a) Detects a non-terminating behavior pattern:
abort simulation and return 0.
(b) Simulated input reaches its simulated "return" statement:
return 1.

typedef int (*ptr)();
int HHH(ptr P);

int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}

What value should HHH(DD) correctly return?
<Input to LLM systems>

https://claude.ai/share/da9e56ba-f4e9-45ee-9f2c-dc5ffe10f00c

https://chatgpt.com/share/68939ee5-e2f8-8011-837d-438fe8e98b9c

https://grok.com/share/c2hhcmQtMg%3D%3D_810120bb-5ab5-4bf8-af21-eedd0f09e141


Gemini had to be forced into do not guess mode https://g.co/gemini/share/4f44c883b348

ChatGPT 5.0 had to be forced into do not guess mode https://chatgpt.com/share/68abcbd5-cee4-8011-80d7-93e8385d90d8
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer


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