Who is Arishima-san? Why does the narrator ultimately decide the Woman in the Purple Skirt cannot be Arishima-san?

Arishima-san attended junior high with the narrator. She was a tough girl with bleached hair who always carried a knife. After dropping out of school, it was rumored that Arishima-san had joined a gang. The narrator decides that Arishima-san must be in prison by now so she cannot be the Woman in the Purple Skirt.