You wouldn't need to sign the commits, you just need to give the latest hash to a trusted (by the authorities) third party, and that will validate the existence of all history up to that point at that time, so ideally at the end of each day, you give your SHA-1 HEAD to the authority.

This is basically what the block chain does, except that instead of having somebody designated as special and trusted, they have the signers perform proof of work.