file timestamps in linux

So how do file timestamps actually work?
Is it safe to rely on them to know the time of creation even if the files were moved from disk to disk, or between Linux and Windows? Or is it better to write the creation time somewhere else like directly in the filename or to separate file along with file's hash?

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Put it in the filename: file.20130201
modified/creation timestamps can be easily changed.

>4

Timestamps, owner, group, SetUid and other such flags are part of the metadata of a file. Different file systems (fat, ntfs, ext4, hfs, etc) use different sets of metadata flags, thus even moving a file b/w disks on the same computer can mess it up. If you want to have the creation time always available even across multiple computers, best to store it in the file itself.