How to check membership of an old coordinator in the initial fast quorum in non-thrifty Egalitarian Paxos

Develop a concrete mechanism that allows the new coordinator in the non-thrifty version of Egalitarian Paxos to determine whether a past coordinator was part of the initial fast-path quorum for a command under recovery, given that any process may have been in that fast quorum.

Background

In the non-thrifty version of Egalitarian Paxos, any process may be part of the fast quorum that initially pre-accepted a command. During recovery, the new coordinator may encounter replicas that tentatively pre-accepted dependencies proposed by prior coordinators. Safety rules in the original protocol require checking whether an old coordinator was in the initial fast quorum before proceeding.

However, because the non-thrifty mode does not fix a specific fast quorum in advance, the protocol provides no clear way to perform this check, rendering the recovery procedure incomplete without a method to verify such membership.