I am trying to understand a little bit more about how keypairs are derived from the initial mnemonic seed phrase.
What I think happens is that from the seed phrase, you can derive a 'root keypair' (i don't know if this is the right term, but i've seen it used elsewhere). With the Solana CLI for example, this is what you get if you don't specify a derivation path, or explicitly pass m/44'/501' as the path.
As far as i'm aware it isn't possible to take this root keypair and get the seed phrase back (this is by design as part of the BIP39 standard).
You can also pass other paths to get other keypairs eg by passing m/44'/501/0/1', m/44'/501/1/1', and this is what something like the Phantom wallet app will give you as your account, rather than the root.
What i'm not sure on is whether you can derive these additional keypairs from the root key, or only from the seed phrase.. I know that if someone gets hold of one of the non-root derived account private keys, they can't infer anything about any of the other private keys, or the root key, because the paths are 'hardened'. Also, if someone gets hold of your seed phrase they can clearly derive your root keypair, and all other derived keypairs, but if someone gets hold of the root keypair (but not the seedphrase) can they derive other accounts from that?
Thanks for any help!