WASHINGTON — For the past several months, journalists, legal experts and close followers of the special counsel’s investigation have been trying to uncover one particular secret about the inquiry: Is the special counsel, Robert S. Mueller III, in a closed-door legal battle? If so, with whom?

In October, Politico reported that Mr. Mueller appeared to be in a secret fight with a witness who was refusing to testify before a grand jury investigating Russia’s efforts to interfere in the 2016 election. A CNN journalist reported seeing two of Mr. Mueller’s top prosecutors enter a courtroom in September to argue against lawyers for an unnamed client before a judge who deals with grand jury matters.

A confidential hearing in the dispute was held on Friday at the federal courthouse in Washington. One floor of the building was closed to protect the identities of the lawyers involved. But that failed to deter roughly a dozen reporters who were spotted rummaging around the courthouse trying to figure out who was involved.

Here is what we know, and do not know, about the battle:

What exactly is this fight about?

From the clues that have emerged, it appears that the dispute is about whether a witness can be forced to answer investigators’ questions. When witnesses refuse to cooperate, prosecutors often go to court to get a judge to send them to jail in order to pressure them to talk. Prosecutors are supposed to exhaust all other investigative avenues before doing this.