Begin with the person.
The PKI operation first checks for a live person at capture, within the evaluated presentation-attack detection scope.
A private key for this operation.
Your live biometric generates the PKI key-pair in memory. Its public key is stored; its private key is generated for face sign or face decapsulate and is never retrieved from storage.
Sign or decapsulate with your live biometric.
Face sign creates a signature; face decapsulate recovers the encapsulated shared secret. Both use a transient private key. Stored public keys enable signature verification or encapsulation with compatible standard libraries.
Public keys stay. Private keys do not.
The PKI private key is discarded after face sign or face decapsulate. Public keys, signatures and decapsulated shared secrets go directly to relying party endpoints, without the IdP seeing them.