For some reason... people like to list Ubuntu instead of "Linux" when stating they support Linux. The 12.10 is probably just to ensure you have a relatively recent disto.
I tend to think when people specifically claim to support "Ubuntu" (instead of "Linux") it means they actively tested it with Ubuntu and have determined that it is compatible with Ubuntu. I guess it's easier to just assume everyone uses Ubuntu rather than put in the time/effort to confidently assert that it works with any distro you throw at it.
Probably a fair assessment. However, it should "just work" on any Linux disto provided any dependencies are installed on the distro and/or packaged into the toolkit.
If there are system-side dependencies... I'd like it more if they just listed those... then I can determine if my Fedora system, for example, will work or not... and I know what I need so that it will work instead of just guessing.
Looking at the toolkit... well.. it's Java... so it will "just work" provided java is installed on your machine (a given if you are writing or running a java program). There is some native C in there, likely for hooking into the OS and making windows, etc.... that could be system specific... but probably still does not require any external dependencies. So... this toolkit... probably "just works".
> Ubuntu 12.10 or any compatible (x86_64)
Is it gtk compatible or what? Why just 12.10? Some specific gtk version? I don't get it.