Does Sasuke have the purest form of the Sharingan ?

[salamander uchiha]

Yeah it's something like that but I think it has less to do with purity and more to do with potency, Sasuke does have Hagoromo's Yang as it's required to unlock the Rinnegan.

But because the Sage gave Sasuke his chakra Sasuke ended up having Indra's chakra + Hagoromo chakra which is the same as Indra's chakra + (Indra's chakra + Ashura's chakra), Sasuke has twice the amount of Yin as Madara.

Yes was referring to potency not purity.
However the problem is Hogaromo gave his yin power not yang (Ashura's power) because he would still have yang nature. It could be that Hogaromo gave him the bodily ability to produce Yin chakra which powers his rinne sharingan and that potency is what keeps it stronger. That could be why Ashura's would be necessary in non Hogaromo power up cases. It's interesting somebody should Do a theory thread on it.