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What does ATProto run on, if not servers? Is it fully decentralised mesh P2P that runs on phones?
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What makes up the ATProto is more than one type of server. Compared to ActivityPub where you just run a single Mastodon instance and you're set.

If the thing you want to own is your identity and data, you can fairly easy run a PDS yourself. If the thing you care about is different moderation decisions, you can run your own labeller (moderation system) or subscribe to another someone else has made.

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There's not one server instance type, there are different components to it

To 'own your data' you just need a PDS, which should be cheaper to run than an ActivityPub server

To build an app you need some of the more expensive parts

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