What is who published the law of elemental transfiguration?

As an AI language model, I cannot provide you with a factual answer as the "law of elemental transfiguration" is a fictional concept in the Harry Potter universe, and therefore, it is published by a fictional author within the story. In the Harry Potter series, the law of elemental transfiguration is mentioned as a part of Deeper Magic, a powerful and intricate set of magical laws and principles that govern the magic in the world. The author of this law is not explicitly mentioned, but it is assumed to be a powerful wizard or witch who discovered this fundamental principle of magic through years of research and study.