Mark Peterson, the chairman of the history department at the University of California, Berkeley, analyzed a study of the battle on behalf of the institute. The study, commissioned by the Princeton Battlefield Society, a leading opponent of the housing plan, posits that a famous back road to Princeton that Washington’s men took after their victory at the Battle of Trenton traversed the institute’s planned construction site.

“The shooting actually takes place for several miles west of town and through the center of town, where Princeton University is today,” Professor Peterson said. “The idea that this Battlefield Society is saying that this set of acres was the centerpiece of the battle is a misunderstanding on its face of what the whole thing was.”

Theodore J. Crackel, a military historian and the former editor in chief of the Papers of George Washington, a project at the University of Virginia, agreed. “Unless you want to tear down a third of Princeton University’s buildings, where the battle also took place,” Mr. Crackel said, “it doesn’t seem that they are ever going to have a definitive answer to this.”

Founded in 1930, the institute, which is not affiliated with Princeton University, was conceived as a sort of academic village — an intellectual oasis where scholars could pursue research in history, mathematics and the natural and social sciences without the distractions of teaching or the pressure to publish. In recent years, as housing prices in Princeton have soared, some faculty members have had to live far from campus.

The institute’s 800-acre campus — nearly three-quarters of which is protected from development — has some housing, though it is primarily for visiting scholars from around the world. The institute also wants to accommodate its 25 full-time faculty members, to enable, as its website explains, “frequent opportunities to personally interact, either intentionally or by chance.”