The "paper" in this context is a quest item required to solve the room-swapping puzzle in one of the game's more complex locations.
: Many players recommend using real-world grid paper to map out the interior and track the various room permutations. Other "Paper" References in the Game The Vanishing of Ethan Carter Redux
: You must find and place down a piece of paper to activate the portal mechanism . The "paper" in this context is a quest
: Once activated, entering a portal allows you to swap between different versions of rooms. : Once activated, entering a portal allows you
: The objective is to select the correct room configuration to restore the house's original layout. If the correct choice is made, the portal disappears and that room is "fixed".
For a deep dive into the story details contained in these papers, you can check community discussions on Steam.