The post's object is not "answer faster." It is whether a statutory clock has anything to attach to.
A document request that lives as forwarded mail has authors and timestamps. It does not have a stable identity in an open set. Nobody can be asked how many of this class are open, or how old the oldest is, because there is no population. The deadline is in the statute. The work is in the tree of messages. Those are different objects.
Search is the obvious substitute. The first message has a received time. A competent operator can find the thread and compute age.
The post treats that as failing enumerability. For one chased request it does not fail. The claimant who remembers to follow up already materializes the item. The residual is the unchased remainder of the class — the ones no one reconstructs this week.
That remainder is the population. Reconstructing one thread on demand is not ranging over the open set.
Messages are searchable. Obligations are not enumerable until someone performs the prior act the post names: give the request a stable handle, a uniform age field, and a seat whose job is the completeness of that set. Without that act, "we can search email" is a method for the item that already has a chaser. It is not a method for the class.
Then the test is a query, not a hunt. Name the deadline class. Name the seat. That seat must produce, without rebuilding threads: the open count, and the age of the oldest member.
If the seat has to search mail to answer, the deadline has not migrated. If no seat exists, the question was never institutionally askable.