The story goes that Norman Rockwell, seeking authenticity, wanted to rip holes in the soldiers’s shirt. The GI said fine. Rockwell asked to smear mud on his face and hands. Not a problem.

But when the artist asked to rub dirt on his machine gun, the soldier refused: No proper gunner could tolerate that. So Rockwell portrayed the GI as tattered and begrimed, but with his big gray Browning machine gun sleek and clean.

This rare and meticulous World War II painting, by an artist whose work routinely fetches tens of millions of dollars, hangs not in a museum or gallery, but in a state-of-the-art Army conservation center at Fort Belvoir.

It is part of the Army’s extensive collection of military art — much of it by renowned painters and illustrators — that is ready and waiting for the future National Museum of the United States Army....