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Yes, it's Linux.
(lemmy.ml)
From Wikipedia, the free encyclopedia
Linux is a family of open source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991 by Linus Torvalds. Linux is typically packaged in a Linux distribution (or distro for short).
Distributions include the Linux kernel and supporting system software and libraries, many of which are provided by the GNU Project. Many Linux distributions use the word "Linux" in their name, but the Free Software Foundation uses the name GNU/Linux to emphasize the importance of GNU software, causing some controversy.
Community icon by Alpár-Etele Méder, licensed under CC BY 3.0
The unstable part is just compared to other versions of Debian. Every now and then a package dependency breaks, but usually nothing serious and you can still use the system until it is fixed within hours. It is not like the system will constantly crash, it is still linux.
I have used sid for years without any major problems. Usually only on desktop though.