Logic Masters Deutschland e.V.

This is a funky one, but hopefully an interesting journey. I was interested in how torus topology would affect Yin Yang logic, and this is where I wound up. A big thanks to Bootenks, whose enthusiasm when testing this puzzle is what convinced me to start publishing my stuff on here!

Edit: I've added a moat for taking notes. Big thanks to ThePedallingPianist for the help!

Rules:
Place the digits 1-9 once each in each row, column, and box.

Galaxies: Draw two spiral galaxies in the grid, one shaded, and one unshaded. The purple circles indicate the centers of the galaxies. Each galaxy is a set of orthogonally connected cells with rotational symmetry.

Twins: Both galaxies have the same shape (i.e. it is possible to overlay one galaxy on the other through a combination of rotation, translation, and reflection). Every cell in the grid is part of exactly one galaxy, except for one cell, which belongs to neither. No 2x2 region of the grid belongs entirely to one galaxy.

Curved Space: The border of the grid 'wraps', so a galaxy may pass from the top row to the bottom, or the first column to the last and be considered orthogonally connected.

Cages: Digits may only repeat in cages if they belong to different galaxies. A number in the top left cell of a cage indicates the sum of all the shaded cells in that cage. A number the bottom right cell of a cage indicates the sum of all unshaded cells in that cage.

Cells separated by black dots have a 1:2 ratio.
Cells separated by white dots have consecutive digits.

Play here on SudokuPad