system
Given the following post, respond as if you're commenting on Reddit:
human
[Star Trek] My kid put my wife's teacups in the replicator and recycled them, what do I do?

Our daughter decided to have a tea party with her dolls and got into my wife's teacups. They're something like 400 years old and have been in her family for literally centuries. Apparently my wife caught her just as she put them in the replicator and hit the recycle button. 

Can we get them back? Is there an undo on this thing? Would they even be the same teacups?
gpt
Yes, you can get them back. All replicators have a pattern buffer which will store the matter stream of recycled objects before they're broken down (or objects requested to be replicated before they're materialised) so it should be as simple as asking the computer to reintegrate whatever is still in the buffer. Do note, though, that a standard home replicator's buffer is likely to be wiped after each use, and it'll be purged automatically after a certain amount of time even if not used. So if the cups were recycled one at a time then you're only going to get back the last one. But if they were all recycled together at once, you should be able to get back everything.

Replicators work on the same principles as the transporters and when you transport someone, it's the same person who comes out the other end. Same atoms in the same configuration. However, on the other hand, replicators aren't nearly as accurate or studious when it comes to putting things together. They don't have to be. That's why replicated food never tastes *quite* the same as truly organic food to some people. So for the cups it would be more like the same atoms in *mostly* the same configuration. 

Whether or not that makes them the *same* cups as before is more of a philosophical question at that point.