Warning: Contains SPOILERS For Joker
One of the biggest mysteries at the heart of the story of Joker is whether or not Thomas Wayne truly is Arthur Fleck's father. While the movie presents this idea as a delusion that Arthur adopts from his equally unbalanced mother, there is some evidence to suggest that Penny Fleck was telling the truth about a love affair with the famous billionaire and that he fathered her son.
One of the key challenges in interpreting the plot of Joker lies in the problem of the Unreliable Narrator. Due to our protagonist Arthur's mental instability and inability to perceive events around him accurately, it is unclear just how much of Joker takes place inside Arthur's head and what events truly happen. This places the audience inside of Arthur's head as they too are left unable to tell fantasy from reality and are left confused in the wake of a world that has seemingly gone mad.
One of the subplots that pushes Arthur over the edge involves his mother's repeatedly sending letters to billionaire and mayoral candidate Thomas Wayne, on the grounds that he might help them financially because he is a good man. Out of curiosity, Arthur reads one of the letters instead of sending it and learns that his mother is begging Thomas Wayne for help while making reference to "our son." This leads Penny Fleck to confess that she used to work for Thomas Wayne and that their relationship turned romantic, but societal expectations forced him to abandon her because a high-class captain of industry like Thomas Wayne could never marry a lowly secretary.
This leads Arthur to confront Thomas Wayne directly in the restroom at a gala event. Wayne violently asserts that he is not Arthur's father as soon as Arthur introduces himself, and point-blank tells Arthur that he was adopted and that Penny Fleck had been committed because of her delusional belief there was something between her and Wayne. This leads Arthur to Arkham State Hospital, where he steals his mother's medical records and seemingly confirms Wayne's story. The files show that Penny Fleck had been committed to the insane asylum several times due to a delusion that she was Thomas Wayne's secret lover. The files also contain an adoption record for an unnamed baby boy.
Granting that neither Penny nor Arthur are reliable sources of information, there is still evidence that Penny's story in Joker is true. The most convincing piece of physical evidence is a photo of his mother that Arthur handles before going to appear on the Murray Franklin show. The photo is signed with the initials T.W. - Thomas Wayne. However, the most damning bit of proof is that Wayne specifically presented the idea of Arthur being adopted to him during their confrontation, raising the question of how exactly he knew that Arthur was adopted.
Allowing that it is possible that Wayne would have kept tabs on Penny and might know that she had adopted a son, it seems unlikely that he would specifically state this rather than simply saying that he wasn't Arthur's father, unless he had a reason for the more firmly worded denial. It seems probable then that Wayne could have made arrangements to have Penny Fleck falsely committed after discovering she was pregnant and faked adoption papers in a bid to throw off any request for a blood test years later. This seems particularly likely when one considers how impossible (even in a hellhole like Gotham City) it would have been for Penny Fleck to have adopted a baby as an unmarried woman with a history of mental illness or to have kept Arthur if the reports of his being abused were true. Of course, Arthur could just be imagining the details of the medical report to be worse than they really were, but such is the ambiguity that makes Joker such a divisive film.
