Certification number
A certification number is the unique number printed on a graded card's label, which you can look up on the grading company's site to confirm the card and its grade.
In more detail
Every slab from the main grading companies carries one. Type it into the company's site and the record should show the card's name, year, set and grade, and often a photo. That lookup is what ties a card in a case to the company's own record of it.
Check that the record matches what you are holding: the same card, the same grade and the same label text. A number that brings up another card, or no record at all, is a reason to walk away. When a photo is shown, compare it with the card in the case.
A cert number identifies one slab and the record the company holds for it, so check the number against the card in front of you each time you buy.
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