What derivation path does Core-Lightning use to end up at the Node Public Key (and private key), given a mnemonic seed?

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The node public key is not derived using BIP32. It's derived from the hsm_secret using an HKDF. The hsmtool utility can help you derive keys from your hsm_secret.

I described in this issue how every key managed by Core-Lightning is derived. It was a while ago but i don't think it's changed since.

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