Does "a brief" here mean "a document stating the facts and points of law of a client's case"?

But it seems that Harkonen is not Steven Goodman's client. His supporter though.

Context:

The United States’ highest court will soon decide whether to hear Harkonen’s final appeal. His supporters, who include statisticians, clinical researchers and legal scholars, say that his conviction relied on a poor grasp of statistics, and sets a precedent that could criminalize speculation in grant applications and papers.
“You don’t want to have on the books a conviction for a practice that many scientists do, and in fact think is critical to medical research,” says Steven Goodman, an epidemiologist at Stanford University in California who has filed a brief in support of Harkonen.

MOre:
http://www.nature.com/news/uncertainty-on-trial-1.13868