Is Harry Potter The Heir To Tom Marvalo Riddle and Slytherin?

Since the Harry Potter films and books started we all are aware that Harry Potter is a distant cousin to his arch enemy Tom Marvalo Riddle (Voldermort) and is also distantly related to Salazar Slytherin one of the founders of Hogwarts and the founder of Slytherin house we now from the chamber of secrets that Voldermort is Salazar Slytherins heir but with Voldermort now dead and having one living relative in Harry Potter witch will make Harry Voldermorts heir and i presume in turn the new heir of Salazar Slytherin via Voldermort it just seems funny because when Harry started school the sorting had was going to place him in Slytherin but Harry opted for Gryffindor maybe he was ment to be in Slytherin as the decendent of Salazar Slytherin and the true heir of Voldermort please leave plenty of comments cuss if Harry is the heir of Voldermort then he by right owns 1/4th of Hogwarts Castle comment and tell me if you think Harry should of been placed in Slytherin or stayed in Gryffindor