Does the uncovering of the thigh invalidate the prayer, and is it permissible to follow those who permitted the uncovering of the thigh or half of it, with an explanation of the reason for considering the thigh as 'awrah (private part) in prayer but not outside of it, and how was its 'awrah determined without an authentic hadith, and why is the shoulder not considered 'awrah despite the explicit hadith concerning it?

The claim that there are no authentic hadiths proving the thigh to be awrah (private parts) is not accepted, as several hadiths have been narrated which, when taken collectively, are strong enough to be used as evidence. Among them are the hadiths of Ali, Muhammad ibn Jahsh, Ibn Abbas, and Jarhad al-Aslami, all of which indicate that the thigh is awrah. Therefore, the opinion of the majority of scholars, which favors that the awrah of a man is what is between his navel and his knee, and that it is awrah both in prayer and outside of it, is the more preponderant view. As for covering the shoulders in prayer, the majority of scholars have interpreted the prohibition as being a recommendation.