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 The mint is running on a server, but it's not accessible via IP.
You communicate with the mint using its npubs via nostr relays.

afaiui.
🫂 
 You can't communicate with a server without having its address. 
You might be able to discover the address via another route that isn't traditional DNS (pigeon comes to mind. Or Nostr), but you ultimately need the IP to connect to it. 
 Of course you can communicate with a server without having it's address!

In the same way that I'm communicating with you without knowing your address: using a #nostr relay to deposit and get the notes. 
 Sure, if two parties rely on a third party to act as a sort of proxy to hold messages for them, then both parties can just connect to the proxy.
That is a form of "communication", but it's indirect. I was talking about making direct connections, because that seemed to be the spirit of the OP 
 Exactly, that's what a #nostr relay is for.

And the spirit of the OP (cc.  nostr:nprofile1qqs9pk20ctv9srrg9vr354p03v0rrgsqkpggh2u45va77zz4mu5p6ccpremhxue69uhkummnw3ez6ur4vgh8wetvd3hhyer9wghxuet59uq32amnwvaz7tmjv4kxz7fwv3sk6atn9e5k7tcppemhxue69uhkummn9ekx7mp069f2j4) is about communicating using a relay knowing just the npub, without needing a direct connection.

🫂 
 I missed a detail in your comment:

> The mint is running on a server, but it's not accessible via IP.
> You communicate with the mint using its npubs **via nostr relays**.

You're saying messages intended for the mint are stored on proxies, and the mint will ask the proxies for said messages. The messages don't ever go directly from users to the mint. 

Okay yea that makes sense.