The assembly number point is a simplification of the process for obtaining the source code for a given assembly. You can use git show -s --pretty=format:%h to get a sha1 number that uniquely identifies the version so that any developer can check it in their repository.
However, sha1 is not an incremental number, and in most cases it cannot be used even with other VCSs. If you want to get it, it is better to introduce a continuous integration system (for example, Jenkins), which will increase the number in stages and create tags for these numbers. In this case, it will grow more moderately, because CI usually does not create every commit.
In addition, the aforementioned git describe does a great job of creating good version names.
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