From The Duchess and The Jeweller, explain the statement about things being "rotten at the core" in the context of the narrative.
In The Duchess and The Jeweller, Oliver Bacon, has not always been "the richest jeweller in England." Oliver, in fact, had very humble beginnings and remembers his life "in a filthy little alley." He has been able to amass his own wealth and mixes in high circles, with "duchesses, countesses, viscountesses and Honourable Ladies" sending him invitations to dine and spend time with them. Despite his apparent success, Oliver's life still lacks substance and Oliver strives to find a depth to his existence in all the wrong places.
Oliver attributes qualities to precious stones and relishes his ownership of them, giving him a power not unlike “Gunpowder enough to blow Mayfair — sky high, high, high!” He gets satisfaction from being able to make the duchess "wait his pleasure....till he was ready to see her" and he wishes to be able to mix in the same circles as the prime minister and the duchess's daughters, especially Diana.
When he is offered an opportunity to spend the weekend in the presence of Diana, he can think of nothing better but he knows, if he does, he must effectively pay the duchess for what he thinks may be worthless pearls. He has been invited for the whole weekend but must authenticate the pearls. He agrees and, upon looking at them again after the duchess has left, he confirms what he suspected.
The duchess, for all her finery, all her luxury and opulence, is shallow and manipulative. He knows that what he strives for, the upper echelons of society, are worthless as are the pearls that the duchess claims to be authentic. They look beautiful but are "rotten at the core." The things he desires, the gems, the company of beautiful ladies, everything is not what it seems.