Is the thief's recantation of his confession to theft admissible without any doubt, and what is the ruling if he is lying to cover himself?

The admission of the one who confessed to theft is accepted, and the prescribed punishment (hadd) is waived, because the hudud are based on leniency and averting punishment, unlike the rights of human beings. As for the financial rights of Allah Almighty, such as zakat and expiation, retraction is not accepted. For a definitive amputation due to theft, either two witnesses are required, or a confession that the confessor adheres to until the punishment is carried out. If the confessor retracts, it is accepted from him. In the case of theft, retraction is valid for the right of amputation but not for the right of property. This is because amputation is a right of Allah Almighty, so retraction from it is valid, whereas property is a right of the servant, so retraction from it is not valid.