All of the recent discussions are simply disagreement with an easily
verifiable fact. Any smart software engineer with a sufficient technical
background can easily confirm that H(P,P)==0 is correct:

Where H is a C function that correctly emulates its input pair of finite
strings of the x86 machine code of function P and criterion for
returning 0 is that the simulated P would never reach its "ret" instruction.

(1) Good software engineering proves that H(P,P)==0 is correct.

The only other remaining objection is whether or not a halt decider must
compute the mapping of its input finite strings to an accept or reject
state on the basis of the actual behavior actually specified by its
input OR SOME OTHER MEASURE.

A decider must compute the mapping from its inputs finite strings to an
accept of reject state. A computable function must compute the mapping
of from inputs finite strings to its corresponding output.
https://en.wikipedia.org/wiki/Computable_function

(2) Good computer science shows that a halt decider must
compute the mapping from its input finite strings to an accept or
reject state on the basis of the actual behavior actually specified by
its input. Since P(P) is not an input to H(P,P) it is excluded.

Halting problem undecidability and infinitely nested simulation (V5)

https://www.researchgate.net/publication/359984584_Halting_problem_undecidability_and_infinitely_nested_simulation_V5

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Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer