A simulating halt decider correctly predicts whether or not its
correctly simulated input can possibly reach its own final state and
halt. It does this by correctly recognizing several non-halting behavior
patterns in a finite number of steps of correct simulation. Inputs that
do terminate are simply simulated until they complete.

When a simulating halt decider correctly simulates N steps of its input
it derives the exact same N steps that a pure UTM would derive because
it is itself a UTM with extra features.

My reviewers cannot show that any of the extra features added to the UTM
change the behavior of the simulated input for the first N steps of
simulation:
-- Watching the behavior doesn't change it.
-- Matching non-halting behavior patterns doesn't change it
-- Even aborting the simulation after N steps doesn't change the first
N steps.

Because of all this we can know that the first N steps of input D
simulated by simulating halt decider H are the actual behavior that D
presents to H for these same N steps.

computation that halts… “the Turing machine will halt whenever it enters
a final state” (Linz:1990:234)

When we see (after N steps) that D correctly simulated by H cannot
possibly reach its simulated final state in any finite number of steps
of correct simulation then we have conclusive proof that D presents non-
halting behavior to H.

*Simulating (partial) Halt Deciders Defeat the Halting Problem Proofs*
https://www.researchgate.net/publication/369971402_Simulating_partial_Halt_Deciders_Defeat_the_Halting_Problem_Proofs

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer