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stamp something (up)on someone or something
to affix an informative label onto someone or something, as with a rubber stamp. (Upon is formal and less commonly used than on.) The attendant stamped a date upon each person who entered the dance hall. The person at the door stamped something on my hand when I came in.
stamp on someone or something
to strike down hard on someone or something with the bottom of the foot. The attacker stamped on his victim after he had knocked him down. Walter stamped on a spider.