Does .root exist?
No. No — .root is not a TLD. The DNS 'root' is the top of the tree above all TLDs, not a TLD itself.
The full story
The root zone is the master file that lists every real TLD; '.root' would be a name inside the very thing it names, which is why it has never been delegated. Unix's root account and root directory add to the intuition that it should exist. It doesn't. For a systems or security brand, the resolvable options below carry the same connotation.
What to use instead
.io — The default startup TLD of the 2010s.dev — Best value in domains for anything developer-facing.net — The eternal runner-up
Wondering about another extension? Every real TLD is in the directory.
This answer is generated from the live IANA root zone list, not from vibes. If the DNS changes, this page changes.