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if it's chain state, does that mean it has to be redone with each new block ?

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This is just a demo that verifies block header chains, but I think the goal is to do what would normally require IBD in a STARK proof.

If you're talking about serving these STARK proofs, I'd imagine it would require recreating them with each new block unless there's a way to incrementally build them.

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unless there's a way to incrementally build them

I got the impression that these guys seem to think there is a way?

ZeroSync & Blockstream Satellite: ZKPs to Scale Bitcoin Node Running - Blockstream Talk #22:

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This is awesome. Cant wait to run core on an old android phone due to this achievement 😀

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Yes, we are winning!

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