Can an abort decider be defined that cannot be fooled by any pathological input?

Can an abort decider be defined that cannot be fooled by any pathological input?
01 int D(ptr x)  // ptr is pointer to int function
02 {
03   int Halt_Status = H(x, x);
04   if (Halt_Status)
05     HERE: goto HERE;
06   return Halt_Status;
07 }
08
09 void main()
10 {
11   H(D,D);
12 }
Of all of the elements of the set of H(D,D) where H simulates its
input there are matched pairs of otherwise identical elements that
only differ by whether they abort their simulation or not.
The half of these that don't abort are incorrect because all deciders
must halt. This makes the other half correct about the abort/no abort
decision.
I don't think an abort decider can be fooled by a pathological input.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer