Using quotes from Saki's "The Open Window," what is a claim about a character/character type?
I am assuming that by character/character type you are referring to a stereotype of defining of a stock character. By identifying a character based upon his or her description, a reader is relying on established stereotypes (or stock characterizations). Therefore, to support the claim that Frampton Nuttel exists as a stock character, one must simply look to what his sister states about him: "you will bury yourself down there and not speak to a living soul, and your nerves will be worse than ever from moping."
Readers know that Frampton is suffering from a nerve disorder which he needs rest in order to cure. Readers also know that his sister does not believe that he will be able to cure himself (since he will only "bury" himself" and speak to no one). Essentially, Frampton seems to be the type of person who does not function well with others and does even worse when alone. Frampton has no middle place where he can be healthy. The claim to his character, therefore, lies in both his sister's indirect characterization and a readers interpretation of who Frampton essentially is.