Part 121: "A company shall not use and an airman shall not serve..." & blah blah...

By the nature of operational control the CP, scheduler, dispatcher, airman shall ensure that the crew member (basically the "company" as specified in your FOM, or equivalent) is current and qualified before operating under that rule. I find it strange if a crew member must carry documents (other than cert. and medical) showing their qualifications and currency. I have never seen anything about this in 8400.10 but that doesn't mean its not there.

And as always, call your local FSDO if in doubt.