write down

verb

1. Used other than figuratively or idiomatically: see write, down.

   “I can't write down in the basement; it's cold there and my fingers cramp and get stiff.”

2. To produce or set (something) down in writing; to record something.
3. To write (something) in a simple or condescending style.

   “Good heavens, I can't write down to the level of the vulgar public!”

4. To make a downward adjustment in the value of an asset.
5. To condemn in writing; to document the faults, offenses, or wrongdoing of.

   “By 1859, D. Morier Evans was exhibiting [George] Hudson as the principal character in his rogues' gallery entitled "Facts, Failures and Frauds"; and at the hands of modern economic historians he has been written down as a common swindler.”

   “See also: cite”