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JeremyHahn comments on Why is the A-Theory of Time Attractive? - Less Wrong Discussion
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I apologize for the snipy remark, which was a product of my general frustrations with life at the moment.
I was trying to strongly stress the difference between (1) an abstract R-torsor (B-theory), and (2) R viewed as an R-torsor (your patch on A-theory).
Any R-torsor is isomorphic to R viewed as an R-torsor, but that isomorphism is not unique. My understanding is that physicists view such distinctions as useless pendantry, but mathematicians are for better or worse trained to respect them. I do not view an abstract R-torsor as having a basis that can be changed.
Indeed it wouldn't. A function space defined on an R-torsor would have a basis which you could change.