void Px(ptr x)
{ int Halt_Status = Hx(x, x);
if (Halt_Status)
HERE: goto HERE;
return;
}

int main()
{ Output("Input_Halts = ", Hx(Px, Px));
}

*THIS HAS BEEN AGREED TO* // *understanding the above code proves this*
There are zero elements of infinite set of Hx/Px pairs such that the
correct *partial or complete* simulation of Px by Hx reaches the final
state of Px.

*THIS LOGICALLY FOLLOWS (as a subset) FROM ABOVE*
(A) Every element of the infinite set of Hx/Px pairs that does a correct
and complete simulation of its input never reaches the final state of
this input.

*THIS IS THE DEFINITION OF A UTM THUS KNOWN TO BE TRUE*
(B) A correct and complete simulation of this input derives the actual
behavior of this input.

*THIS LOGICALLY FOLLOWS FROM (A) AND (B) PREMISES*
(C) The actual behavior of this input never reaches the final state of
this input.

When the criteria for a simulating halt decider (SHD) is to correctly
predict that its complete and correct simulation of its input would
never reach the final state of this simulated input then:

void Infinite_Loop()
{ HERE: goto HERE;
}

*H0(Infinite_Loop)==0 // is correct*

void Infinite_Recursion(int N)
{ Infinite_Recursion(N);
}

*H(Infinite_Recursion, 0x777)==0 // is correct*

*Hx(Px,Px)==0 // is correct*

*Halting problem proofs refuted on the basis of software engineering* ?
https://www.researchgate.net/publication/361701808_Halting_problem_proofs_refuted_on_the_basis_of_software_engineering

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer