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Given a relay chain block, is there some way to construct a proving system for any connected parachain's state at that relay block?

I imaging there could be some information persisted on the relay that a(n archive) parachain node could be instructed to generate something like a vector commitment that anyone could verify out of band.

Meaning you could that a relay block + that commitment to verify a specific part of state for a parachain at that time.

Specifically a Substrate Devs chat member asked a question related to verifying state across parachains (on the same relay) is why I am asking here.

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When using Cumulus for building your runtime, the head data of your parachain stored in the relay chain state corresponds to the header of your parachain. The header of the parachain contains the storage root. With the storage root you can proof a certain storage value being present in the state of the parachain.

So, yes you can build a proof system that based on a relay chain block can proof some storage value in the parachain state.

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