Does the prohibition of cauterization include cauterization over a barrier? And do those who cauterize not enter Paradise without reckoning, along with the seventy thousand, knowing that cauterization is used to treat stomach ulcers resulting from anxiety?

Cauterization is the burning of the skin with an iron or similar object for treatment. If cauterization from above a barrier leads to the burning of the skin, then it falls under the ruling of forbidden cauterization. However, its ruling is permissibility, not prohibition. It has been mentioned in the descriptions of those who enter Paradise without reckoning that they do not undergo cauterization.