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To improve security, we’d prefer to distribute the key with multisig, but Bark’s use of pre-signed transaction trees makes that impossible with current MuSig implementations.
This sounds very interesting. Your blog does a nice job setting the scene, but I'd be interested to read more about nested musig and how it's different from things like musig2 or frost.
If you ever write a blog about that, do give us a heads up here!