Diagonal Discovery

Normal sudoku rules apply.

Each cage is either full of "oil" (even digits), full of "water" (odd digits), or a mix of both. In all cases, each "row" within a cage is of just one type (oil or water). Oil floats on water, so even digits will always be in rows above odd digits in mixed cages.

Digits in cages do not repeat.

Digits do not repeat along the marked diagonal.

White dots separate consecutive digits. Black dots separate digits where one is double the other.

The grid is covered in fog; placing a correct digit MAY (or may not) clear fog somewhere in the grid, revealing more clues.