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As long as both rocks are relatively flat on the connected faces, in most cases no. A piece of paper is, what, 8 inches wide on its second shortest axis? For two "relatively" flat pieces of rock, your going to have multiple places where a small segment juts out. Those are the segments that will support all the weight of the rock, and a heavier rock will have more/thicker supporting segments. Both of those factors combined, especially on rocks as heavy as these, would lead me to expect not being able to stick a fairly large piece of paper between them. Something much thinner, like a sticky note, would be significanly easier to fit through those gaps. But a standard piece of notebook paper would not be able to fit through the gaps on my window hinges, and they are by no means sealed.