The painting in the living room is the four-panel piece with the pink flowers on it. Thing is, by the time you collect any of these artifacts, you no longer have access to that painting. Assuming the soda can is the first one, you get it in a reality of Regular House where you can no longer get back upstairs (I think). The rest of them are in ruined house, brutalist, and airport, where there is no painting there at all. I couldn't figure out anything to do with the walls where the painting should be either (in Ruined House, the wall is ripped open and you just walk through from room to room). By the time you have all the artifacts I found, the only places you could possibly get the clue are airport and ruined house 2, unless there's a secret way to return somewhere else. (Do you have to use noclip? Oh god.)