That still doesn't answer the question, that IF the Ponchartrain WAS in the White River on the date of Hindman's dispatch, per Hindman report, How did It get past the entire Union fleet, that was in The White River, to get to Little Rock, by the 21st per Dunnington's report?

One of the two statement is incorrect either Hindman's or Dunnington's. The Union fleet did not leave the White River until after July 2.

The White River is a narrow River and the shipping channel is even narrower. The Ponchartrain would have had to have past withing 100 yards of any Union ship, that it encountered, to get to the mouth of the White River and then enter into the Arkansas River to get to Little Rock as stated in its commanders report of June 21st?

This is clearly impossible since the Union navy commander report that this was completely impossible, if for no other reason than the water level of the White River force them to withdraw accross the shallows in the White River for their own safety and to keep them from being trapped. And when they did this those shallows were already 3 feet shallower than was necessary from the Ponchartrain to keep from running aground.

I don't know of any other way to explain how that happened beside the fact that either Hindman or Dunnington, who I might add would have been the person who would write the ship log that you are hoping to find, was lying. Or else the Ponchartrain way the first gunboat that could Fly.