Board Thread:Naruto Discussions/@comment-32624156-20170721153715/@comment-25122992-20170728170847

Nope, Hagoromo clearly meant not just a sheer authority, for a simple reason there was no authority he could've granted to Naruto/Sasuke, but he bestowed them with actual power. Combine it with the fact that Hagoromo admitted trying to fix the mistake by giving his power to both of son's reincarnation, and it leads to the logical conclusion that Asura also received some power of his as his successor.