The lawsuit began like so many others: A man named Roberto Mata sued the airline Avianca, saying he was injured when a metal serving cart struck his knee during a flight to Kennedy International Airport in New York.

When Avianca asked a Manhattan federal judge to toss out the case, Mr. Mata’s lawyers vehemently objected, submitting a 10-page brief that cited more than half a dozen relevant court decisions. There was Martinez v. Delta Air Lines, Zicherman v. Korean Air Lines and, of course, Varghese v. China Southern Airlines, with its learned discussion of federal law and “the tolling effect of the automatic stay on a statute of limitations.”

There was just one hitch: No one — not the airline’s lawyers, not even the judge himself — could find the decisions or the quotations cited and summarized in the brief.