The full version is now live! Square like you've never squared before in 111 whole levels!
More good news: Testing seems to indicate that if you had the game in your library already, you got upgraded to the full version for free. If you did -- well, enjoy!
Note that it's still in Early Access, which means that it can still greatly benefit from feedback! Most updates and patches will be pushed to both the full version and the demo at about the same time.