Not really :) Please follow the links. "Paxos Made Simple" describes the write once variant, but it's possible to choose a new value for the next ballot cycles to make it rewritable.

Proof of the algorithm: http://rystsov.info/2015/09/16/how-paxos-works.html

Moreover, I built a system on top of it and extensively tested it with fault injections: https://github.com/gryadka/js.

It seems that GoshawkDB[1] uses the similar idea, Treode[2] used it too.

[1] https://goshawkdb.io/

[2] http://treode.github.io/design/