Xjyuk

Rules of MASYU, for those unfamiliar: https://www.gmpuzzles.com/blog/masyu-rules-and-info/

Hey guys! So I just discovered this really cool puzzling site called the Puzzling Stack Exchange (puzzling.stackexchange.com), and it's really cool! Users create cool new puzzles to challenge each other. I really want to contribute to this site with a bold new puzzle. But I can't come up with any new ideas!

Here's the best plan I got so far: Since I really like MASYU, I'm thinking of creating a MASYU puzzle for PSE. But just an ordinary MASYU puzzle would be boring. For a site like PSE, I need it to be really special somehow!
Specifically, I want this MASYU puzzle to be free-floating.

What's a free-floating MASYU?

A free-floating MASYU puzzle is a MASYU puzzle that has no edges.

Many MASYU puzzles require deductions using the edge of the board in the solution. I want a MASYU puzzle that, in a sense, takes place on an endless board, and is just "floating" in the middle, with no edges for its solution to grapple on to.

As an example, here's a possible attempt at creating a free-floating MASYU:

However, this isn't a valid MASYU because more than one solution can be found:

Your task is to create a free-floating MASYU puzzle with a unique solution... or prove that no such puzzle exists.

I claim that

yes, it is possible: the below Masyu puzzle has only one solution.

The proof:

Stacks of 3 (or more) vertical white dots must all be passed through horizontally.




The segments in the second and third rows must not continue horizontally, or one of the white dots they currently pass over would be violated. This also lets us determine that the white dots in the first and last column are passed vertically:




The black dots in the center can be finished, and so can the other ends of the segments in rows 3 and 6.



And finally, the remaining white dots must be passed horizontally, and the remaining segment ends in rows 2 and 7 must continue vertically, completing the loop.