4Ag + 2H2S + O2 = 2Ag2S + 2H2O (silver coin, hydrogen sulfide from paper, atmospheric oxygen = silver sulfide + water vapor)
AKA "toning" if you like it, "corrosion" if you don't (note that like aluminum oxide or copper carbonate/verdigris it's a protective patination, not a destructive loss of metal like iron corrosion)
In other words, it's the natural product of the silver surface of the coin reacting with the proof set case in which it is stored. Some collectors enjoy the look, others don't. Given a long enough exposure in the right environment it can color the whole coin on both sides, sometimes with beautiful iridescence, sometimes with ugly dark black tarnish, or golds, greens, blues, and everything in between.
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