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In the final scaffold scene, some people do not see the letter "A" on Dimmesdale's chest at all. So, for them, it never existed. For those that did see it, some surmise that Dimmesdale had put it there himself, others that Chillingworth's medicine had somehow caused the "A" to emerge. Others suggested it was God's mark of sin. The most likely theory is that Dimmesdale put it there in order to punish himself. Chillingworth had discovered the "A" there earlier and seemed surprised and it is doubtful that any medicine would mark a person with a specific letter.