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You don't need to trust the provider of the snapshot very much. Once you have imported the snapshot, you can simply check that the hash of a recent block is the same as the hash given by some explorer that you will trust. For instance, if block 1,730,000's hash is BLmKPfoMB6E52tdvTHJsWPHTGG7jUWXiW5yW9pAopEuWgYh69zp on several public explorers and on your ...
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If you like the way tzkt displays the storage of contracts, you should probably use their API instead of trying to get the information from a node.
If you want to redo the same work, the human-readable names used for the fields very probably come from the field annotations in the type of the storage. To get this type you can do curl -s http://localhost:8732/...
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