My gut tells me that it can't be done, because of the semi-uniqueness of the conjugation function. A given ordered vector has a unique ordered vector conjugate, meaning there can be no intermediate conjugation vectors, meaning you need all of the information in a vector to be able to accurately find its conjugate.

But that is all very hand-wavy.

Your gut has no idea what it's talking about.

You'd best watch out lest you get punched out.

By whom, your gut? Hah!

Indeed.