pushed/provided?

... sparse-deposit. While a ...

Maybe condense the sample?

With ${type} in {snp (snapshot), rev (revision), rel (release) }:

.. code:: xml
	​
	​  <swh:deposit>
	​    <swh:reference>
	​      <swh:object id="swh:1:${type}:aaaaa............"/>
	​    </swh:reference>
	​  </swh:deposit>

or something?

revision_metadata, etc...). Contrary to the complete and sparse deposit, there will be no object creation.

will not is better than won't. As far as i remember, contraction is ok to speak orally but in writings, it's better not to use it.

the missing directories/contents paths must be...

That list will be refer`r`ed

I'm confused.
I thought we said we did not integrate empty paths in the tarball anymore...
I might be misremembering though ;)

I seem to recall otherwise. As this does add some unnecessary checks...
(cf. prior comment around line 14)

Each failing check...

swh-id?

Also, make smaller line, it's more readable ;)
You can split that sentence at the ,. And starts a new one with That's why...