9
Maximum rebirths
The official update notes set the current rebirth cap at 9.
The latest official notes make two Science changes: it no longer resets on rebirth, and Science purchases are no longer required before you rebirth.
The official update notes set the current rebirth cap at 9.

The official description frames progression around building, gaining powers, and defending territory.
Develop your base and territory as the foundation of your run.
The official game description confirms more than 30 powers and weapons to use.
Battle other players while protecting the territory you have built.
Exact rebirth costs and requirements beyond the Science change are not published in the official notes and are not guessed here.