On Nostr, for a public key that I subscribe to, how can I verify that my relays aren’t filtering out messages from that key? Is there a merkle hash on your latest note that I can use to verify that your previous notes were all received?

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No but that sounds a good idea Simpler than the solution I've kept suggesting, which is p2p data verification over Tor (although the extra complexity with mine also helps with other stuff) As far as I know, no nostr app has really solved data verification for all the posts from an npub or all the replies on a post
Giving it a second thought, how do yow know what the last note is? This can't be assured in Nostr.
You ask their relays for their content, not your relays. Relays don't have to keep everything from everyone and can't have what they don't know about. If your followers don't post to your relays, then your relays won't have it. That's why nostr uses the outbox model, so you know where to find your followers posts.
P2P data verification would work better for that, at least when the original poster is online
True, but that is a separate issue and there are various mechanisms that can be used to verify that a single recent note was received.