The following article contains an answer for the question: Which piece of jewelry does the inventor of Rearden Metal give his wife for their anniversary? , can you please find it? 

In 2016, the United States is in a sustained economic depression. Industrial disasters, resource shortages, and gasoline prices at $37 per gallon have made railroads the primary mode of transportation, but even they are in disrepair. After a major accident on the Rio Norte line of the Taggart Transcontinental railroad, CEO James Taggart shirks responsibility. His sister Dagny Taggart, Vice-President in Charge of Operations, defies him by replacing the aging track with new rails made of Rearden Metal, which is claimed to be lighter yet stronger than steel. Dagny meets with its inventor, Hank Rearden, and they negotiate a deal they both admit serves their respective self-interests.
Politician Wesley Mouch—nominally Rearden's lobbyist in Washington, D.C.—is part of a crowd that views heads of industry as persons who must be broken or tamed. James Taggart uses political influence to ensure that Taggart Transcontinental is designated the exclusive railroad for the state of Colorado. Dagny is confronted by Ellis Wyatt, a Colorado oil man angry to be forced to do business with Taggart Transcontinental. Dagny promises him that he will get the service he needs. Dagny encounters former lover Francisco d'Anconia, who presents a façade of a playboy grown bored with the pursuit of money. He reveals that a series of copper mines he built are worthless, costing his investors (including the Taggart railroad) millions.
Rearden lives in a magnificent home with a wife and a brother who are happy to live off his effort, though they overtly disrespect it. Rearden's anniversary gift to his wife Lillian is a bracelet made from the first batch of Rearden Metal, but she considers it a garish symbol of Hank's egotism. At a dinner party, Dagny dares Lillian to exchange it for Dagny's diamond necklace, which she does.

bracelet