What is the ruling on tayammum with a stone, what is its evidence, and what is the response to those who say it is an innovation?

Performing tayammum (definition) on a stone is permissible according to Malik and Abu Hanifa, but Shafi'i and Ahmad disagreed. The arguments against those who claim it is an innovation (bid'ah) are several: among them is that "al-sa'id" (pure earth) in the Quran refers to the surface of the earth, whether it is dust or anything else. Also, the hadith (definition): "The earth has been made for me a place of prayer and a means of purification" includes stone, as it is part of the earth. Furthermore, tayammum on a stone does not fit the definition of innovation, so it is not an innovation. If it were said that it is more cautious to avoid disagreement, that would be closer to correctness.