What are git subtree push assertions?

I asked this Q on http://stackoverflow.com/questions/26068474/what-are-git-subtree-push-assertions

but from previous experiences with git-subtree, people on stackoverflow (general public) don't really have complete answers so I resort to you!

* What exactly are these assertions doing, and why does it have to
start from the beginning of the assertion count every time I subtree
push?
* Is there a way to limit the number of assertions? Something like git
subtree pull --squash perhaps. I don't want to wait this much or that
it'll break at some point when there's just too many.

Please refer to link above for full question details. Thanks in advance for any info you can give.

Jorge O.