What a certification number actually tells you
It is not a serial number and it is not a receipt. It is the one part of a graded card you can check without trusting the seller.
A graded card arrives sealed in a slab with a number printed on the label. That number is the certification number, and it is the single most useful thing on the card, because it is the only claim on the whole object that you can verify without asking the person selling it to you.
Type it into the grader’s own lookup and you get back what they recorded when they graded it: the card, the set, the year, the grade, and the date it was graded. If what comes back does not match what the listing says, the listing is wrong — and you found that out in about fifteen seconds, for free, from a party with no interest in the sale.
It is also why the number, not the title, is the identity of the product. Titles repeat. Five cards can share one. A certification number belongs to exactly one slab, and if that slab is ever cracked open the number no longer describes anything.
Two practical consequences. First: never buy a graded card whose certification number the seller will not show you before payment. Second: check it yourself rather than trusting a screenshot, because a screenshot is a picture of a number and the lookup is the number.
On this store every card page carries its certification number in the breadcrumb, in the specification table, and as a link straight to the grader’s own verification page. We would rather you checked.