What continuity exists?
A trust exists.
An office of trustee exists within it. A holder — Trustee A — occupies the office.
The holder, when acting on behalf of the trust, signs records. The signature is produced by a cryptographic credential: a key, a token, a certificate. The credential is the instrument through which the holder speaks in the chain.
It is important to be precise here. The credential is not the holder. The holder is not the office. The office is not the trust. There are four distinct things, each at a different level of permanence, each bound to the next by an explicit, witnessed record.
The holder holds the office through a credential. The credential is, for now, key v1.