What I stated was that the little horn person commits the
transgression of desolation.
It is an act, not a thing to be placed in the temple. There is a distinction between the transgression of desolation and the abomination of desolation.
The term
transgression of desolation is Daniel 8:12-13.
12 And an host was given
him against the daily
sacrifice by
reason of transgression, and it cast down the truth to the ground; and it practised, and prospered.
13 Then I heard one saint speaking, and another saint said unto that certain
saint which spake, How long
shall be the vision
concerning the daily
sacrifice, and
the transgression of desolation, to give both the sanctuary and the host to be trodden under foot?
The little horn person at the time he commits the transgression will have been in the role of being the King of Israel (illegitimate as the Antichrist) for about around 3 years.
The transgression act reveals him as the man of sin. The transgression act is him going into the temple, sitting, claiming to be God.
I show the transgression of desolation on my chart. Also on my chart I show him being killed and brought back to life as the beast. After becoming the beast,
the abomination of desolation image (a statue) of him is made and placed in the temple. Which is also on my chart down at the bottom.
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Now as to your point that in Daniel 11:31, the king of the north is responsible for the abomination of desolation - and why isn't that the little horn person?
That act was when Antiochus placed a statue of Zeus in the temple.
Thus the king of the north
in that verse is not the end times little horn person, but Antiochus.
Daniel 11 doesn't get into the end times until Daniel 11:36. In Daniel 11:36, that King is the end times person after he has become the beast.
Of the various kings in the remainder of the verses, he will be the king of the west (implied). Neither the king of the north, nor the king of the south, nor the king(s) of the east (implied)