Isolated Sudoku 3, 4 and 4H

David came up with this puzzle idea which he posted on the assassin site (among others). I've come up with a small presentation change to assist in making harder puzzles. I think that this Sudoku variant really has legs.

Each number in a box means that the adjacent four cells contain that number but do not contain its adjacent numbers. So for puzzle 3 in nonet 6 the bottom right box means that there is a 3 in r56c89 and r56c89 does not contain 2 or 4. If a box has no clues then it either has two pairs or four consecutive numbers.

By putting the isolated numbers in a box, then if the box is empty there are no isolated numbers. Whereas if there is no box no clue is given.

Isolated 3

I tried hard to find a puzzle with all the boxes and more than one solution. This one had two solutions so I used the given in r1c1 to lock it down.

Isolated 4

Isolated 4 Hard

4 and 4H are to demonstrate the value of having an empty box as a clue.