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4) An abridged chain. I wish I could find the link for this or remember what it was called, but there's a lot of research towards making a compressed chain that's still verifiable and would be small enough to have on your phone. I believe their thesis stated they should be able to get it down to 2mb if my memory serves correct.

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I think you're thinking of Wimblemimble and ZK-snarks. They use cryptographic techniques where the signatures need to "add up" to what they should in order to be valid -- demonstrating that no new tokens have been added in the course of the new block.

Quite cool approaches. The problem is that you can't attach data to transactions, so only useful for a subset of applications, those unlikely to create much bloat in the first place.

No neither of those are it, I'm familiar with those. I believe this would still be the same old Bitcoin, but there will clients that use these proofs to run a lightweight full node without relying on external sources or resorting to a lite wallet model.

Sounds interesting -- if you remember the details pls post.

https://codaprotocol.com/

Coda uses ZK-snarks -- not suitable for affixing data to transactions.

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