Normal Sudoku rules apply. In addition, a king's move constraint is in effect, i.e., no digit can be diagonally adjacent to a cell with the same digit value.
For each cell with a number in the corner, this indicates the sum of all cells that are a knight's move away, that is, all cells that are two cells away in one and one cell in another perpendicular direction. From R5C5, the cells R3C4, R3C6, R4C3, R4C7, R6C3, R6C7, R7C4 und R7C6 would need to be added together.
If there's a tilde in the corner of the cell, then that cell's value is the average of all cells that are a knight's move away.
Inspired by Sumanta Mukherjee's puzzle featured here: Cracking the Cryptic
You can also try out the puzzle via Penpa.
Solution code: The cell values in the middle box (Box 5), reading from left to right, row by row (9 digits)
on 1. June 2020, 23:46 by Brad_R
Started fast, then slowed way down. Thinking about the tildes helped me.