Picasso's prints are documented in standard catalogues that record each image's edition size, printer, publisher, paper and state. Matching a print against its catalogue entry — dimensions, paper, edition, state — is the substance of the argument.
The ceramics made at the Madoura pottery in Vallauris carry edition stamps on the base: marks identifying Madoura, the edition status, and on many pieces an edition number. Those stamps are impressed into the clay before firing, so they are part of the object rather than applied to it.
A stamp that has been applied after firing — sitting on the glaze rather than under it, or cut into a fired surface — is a serious problem, because the genuine process cannot produce that.
For paintings and drawings, there is no lookup. The route is a recognised specialist opinion and a provenance chain, and the cost of getting that wrong is high enough to justify the expense of getting it right.