Puzzle #25: Masyu

Puzzle #25 on the 25th? Clearly it should be a 25×25. This puzzle was inspired by a 15×15 I investigated/discovered/created a long while back for a yet-to-be-finished iOS app. Except this is harder. Using a math competition analogy, if the last couple puzzles were ‘AMC’-like, and the harder puzzles here are ‘AIME’ level, this is an Olympiad puzzle. Meant to be investigated, possibly with a dose of if-then, but once the theme is understood it should be doable? That’s the hope, anyway. (The hope is also that I’m right about this being hard. :P) On an unrelated note, I put as much time into this puzzle as I did into all other September puzzles combined. After this, I hope to return to other puzzle types besides Masyu. 25.25.1