Logic Masters Deutschland e.V.

Here is my homage to that amazing series currently on TV, His Dark Materials.

The Sudoku universe contains just 9 states of matter, given the numbers 1 to 9.
There are the Elements (denoted by prime numbers).
There are Compounds, made with two or three identical molecules of the Elements. The number of the Element is raised to a power to give the number of the Compound.
Finally, there are the two types of Dark Matter.

In each of the nine 3x3 boxes, there is a diagonal containing at least one molecule of Dark Matter, with the centre being either the sum or difference of the numbers at the ends of the diagonal.
Compounds never appear in the centre of a box.

In prime numbered boxes, the centre is an Element. Each of these boxes has a different Element at its centre.
One diagonal is of interest in each box, and all the diagonals (one in each box) in the prime numbered boxes are either sums or differences, not a mixture.

In boxes with the same number as Dark Matter, the centre is an Element and in this case there are two molecules of Dark Matter on one diagonal.
In addition, there are two Elements at the corners of the other diagonal.
In one of these boxes the centre is the sum of either of the diagonals, and in the other the centre is the difference for both diagonals.

The Subtle Knife has slashed a line in the fabric of the Sudoku universe, a single line yet square.

Normal sudoku rules apply. Cages do not have repeated digits.
The little killer clue (the Subtle Knife) may have repeated digits on the diagonal.

Solve the puzzle online F-Puzzles