Hibernate and archive
To put a thread away for a while, hibernate it: hover its row and press the moon, or use the Thread menu or the ... menu. Pick when it should come back: in an hour, this evening, tomorrow, next Monday or a time of your own. It leaves the list, its agent stops, and it comes back marked unread when the time comes. Hibernating threads wait in the Hibernating section at the foot of the list, soonest to wake first.
Or pick Wake when… and say it in your own words: "at the weekend", "in a few weeks", "next time I talk about woodworking". Opus works out what you meant (the row says Thinking… for a few seconds) and the thread says what it settled on. A topic waits for you to bring it up: when the librarian sees you talking about it in another thread, it wakes this one and says where.
When a thread is done, archive it: press ⌘E, hover its row and press the box, or swipe the row left with two fingers on the trackpad (or drag it left with the mouse) and let go once the space behind it turns blue (a quick flick works too). However it's archived (⌘E, a button, or an agent or your phone doing it), its row slides off the same way. The Archived section at the foot of the list has them, most recently archived first, with the older ones behind Show more (the search at the top finds any of them). Unarchive, or the same swipe there, puts one back. The iPhone app and the website call the archive the Den.
Hibernating or archiving a thread that's partway through a turn stops that turn. From the row's hover buttons, Threadbear asks first.