Thanks.

And an old share can be kept in the new set?

Do we have security proof for this yet?

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Literal Shamir's secret sharing?

Do you have some pseudo code for this please?

Shares do not work between sets, so the old shares will not work in the new set.

We are using shamir's secret sharing for splitting your nsec, which does have security proofs afaik.

Would be interesting to see a proof for the combination of SSS with the Schnorr signature part, especislly in relation to key rotation.

This does sound like there is some footgun possibility there.