A patient states, with complete and unshakeable conviction, that he is the reincarnation of an ancient king, offering no coherent account of how he arrived at this belief and showing no interest in any evidence that might challenge it, despite this being entirely out of keeping with his cultural background. What is this?

This is a delusion: a false, unshakeable belief, out of keeping with the person's social and cultural background, held with fixed conviction that is impervious to counter-evidence, and not arrived at through an ordinary, understandable process of reasoning. It is not an overvalued idea, which is more comprehensible in its origins and somewhat less rigidly fixed than the belief described here. It is not delusional perception specifically, which is one particular mechanism by which a delusion can arise from a normally perceived stimulus, not described in this vignette. And it is not a confabulated memory, which concerns invented recollections of the past, not a general belief about identity.