How can the story of Vishnu getting Sudarshana Chakra later be reconciled with Aniruddha holding the Chakra at the time of creation?

Question

Many scriptures describe how Lord Vishnu got the Sudarshan Chakra - some say that he got it from Shiva; while, other say he got it from Viswakarma.

Now, coming to the description of creation of the universe, when Vishnu manifested in the Anirudhha form; he had held in his four hands, the mace, lotus, shell and the chakra.

So, what is the authentic version of how he got the chakra? How can these stories be reconciled?