American Sign Language:  "put down"

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One of the means of "put down" is to "to record," "make a note of something," "write something down," or "put it down on paper."

If you want to know how to sign "make a note of" see: NOTE
 

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Another meaning of "put down" is to criticize.  See: CRITICIZE
 

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If you mean "put down" as in "put something down on the table," See: PUT