To what extent is the hadith "There is no prayer for one who uncovers his shoulders" authentic, and what is the limit of 'uncovering' for the shoulders?

It was not reported from the Prophet (peace and blessings be upon him) that he forbade praying bare-shouldered. Rather, he forbade praying in a single garment with nothing on one's shoulders. The Hanbalis acted upon the apparent meaning of this prohibition, making it obligatory to cover one of the shoulders in obligatory prayers. The majority of scholars, however, held that covering the shoulders is recommended, and that the prayer is valid even if they or one of them are not covered, whether in obligatory or supererogatory prayers. What is obligatory according to the Hanbalis is to cover most of one of the shoulders.