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I really can't imagine getting paper to sink any more easily than wood?

Try toilet paper. Let it into the water vertically as to not catch air pockets.

It floats, unless it is burdened with matter. Even when fully wet.

because the fibers are denser than wood and hydrophilic - so the pockets between the fibers fill with water that displaces the air.

Air pockets become water pockets = neutral.

Fibers denser than water = sink.

Because the air is squished out I suppose