Based on the provided knowledge sources, it is not possible to set a TOTP authenticator credential directly using the "update identity" REST endpoint on Ory Network. The documentation for the

updateIdentity

endpoint specifies that credentials can be provided via the

credentials

field in the request body, and these credentials will be imported and added to the existing credentials of the identity. However, the credential types explicitly supported for import are OIDC, password, and SAML. There is no mention of TOTP as a credential type that can be set or imported via this endpoint. The TOTP credential is managed through user-driven flows (such as the settings flow) and not through direct admin updates to the identity object via the REST API. The TOTP credential is added to the identity when the user enables TOTP through the appropriate self-service flow, not by an admin API call to

updateIdentity

 [Ory API Reference – updateIdentity](https://raw.githubusercontent.com/ory/docs/master/docs/reference/api.json), [TOTP Documentation](https://www.ory.sh/docs/kratos/mfa/totp#identity-credentials). In summary: You cannot set a TOTP authenticator credential using the

updateIdentity

REST endpoint. TOTP must be enabled by the user through the self-service settings flow.