H(P,P) is computationally distinct from P(P)

[olcott]

// Simplified Linz Ĥ (Linz:1990:319)
// Strachey(1965) CPL translated to C
void P(u32 x)
{
if (H(x, x))
HERE: goto HERE;
}

int main()
{
Output("Input_Halts = ", H((u32)P, (u32)P));
Output("Input_Halts = ", P((u32)P));
}

The direct execution of a machine is a distinctly different computation
than the simulation of this same machine description by a simulating
halt decider that aborts its simulation of this input. This allows the
execution of P(P) to halt and the simulation of P(P) to be correctly
decided as never halting without contradiction.

https://www.researchgate.net/publication/351947980_Halting_problem_undecidability_and_infinitely_nested_simulation

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein