Owners close these properties annually to protect themselves against any possible claim of “adverse possession,” a concept with ancient roots. It holds — to put it simply — that if someone openly and notoriously uses another’s property for a long period without ever being challenged by the rightful owner, the property becomes that of the possessor. Think of a farmer using an out-of-the-way corner of a neighbor’s acreage to pasture sheep for a generation or two, without the neighbor ever objecting.

Annual closings are how modern owners assert their dominion (as opposed, say, to killing someone’s sheep, or hauling him up before the folkmoot assembly).

Lever House has been closing itself once a year since 1953, when it was the brand-new headquarters of Lever Brothers. On Sunday, temporary barricades are to be erected, bearing signs saying: “This area is closed to public use on behalf of and in the name of the owner.” Some time later, an employee who was present will sign an affidavit attesting to the closing.

These days, the hurdles to prove adverse possession are very high. It seems inconceivable that Park Avenue passers-by could ever make a claim that they are the actual owners of Lever House’s courtyard. Among other things, the owner has to have let the adverse possession go unchallenged for 10 years.

One wonders why owners even bother to go through the ritual. “I don’t want to call it a vestige of the past — because it’s still done — but it does have a quaintness to it,” said Jerold S. Kayden, director of the Urban Planning Program at Harvard, and arguably the nation’s leading authority on privately owned public space.