Logic Masters Deutschland e.V.

This is another one of the puzzles I've been working on featuring this variant of cycles. I believe this should be much more approachable to people that haven't tried one of my earlier puzzles using this variant, as the Kropki dots are fairly powerful on their own.

Links:

F-puzzles
CTC (with solution check)

Rules:

Normal Sudoku rules apply.
Cells separated by a white dot are consecutive. Cells separated by a black dot have a ratio of 1:2. Not all dots are necessarily given.

Let a cycle be the path created along a row in the grid by starting with the cell in column X with a digit A, then going to column A with a digit of B, then going to column B with a digit C, etc. until arriving at a column with digit X which goes back to where you started.

Let the order of a cycle be the number of unique digits in a cycle.

e.g. If in a single row, column 1 contained a 5, column 5 contained a 9, and column 9 contained a 1, this would form a cycle with an order of 3.

In addition to normal Kropki rules, orders of the cycles of cells separated by a white dot differs by one, and orders of cycles of cells separated by black dots have a ratio of 1:2

Additional notes:

Whereas by Sudoku rules, digits along the same row/column can't repeat, this is not true of cycles. So while 3 cells in a row connected by black dots would need to have digits of 1,2,4 or 2,4,8, the orders of the cycles cycles could be 1,2,4, or 1,2,1, or 4,2,4, or 3,6,3 etc.

It is similarly possible for the cycles to overlap within a chain of cells connected by dots. For instance, if a single row had a chain of 3 cells connected by black dots with cycles of 2,4,2, then there could be a single order 2 cycle which contained both outside cells with an order 4 cycle containing the cell in the middle.