psf modeling and astrometric calibration

I had a long phone conversation with Lang today about PSF modeling and astrometric calibration. My loyal reader knows that my position is that precise catalog matching is not possible; for this reason precise calibration requires image modeling. Bovy is in fact testing this position with SDSS imaging. But there is an interesting and unresolved issue, which is that there is no necessary definition, given a PSF, of what constitutes the center of that PSF. That is, you can shift all the stars one pixel left and shift the definition of the center of the PSF one pixel right, and everything about astrometric calibration remains the same. This means many things, including (1) that decisions must be made to break the degeneracies (which are perfect, since they are logical), and (2) that atmospheric distortions to the precise astrometric mapping can be set to zero by definition if we are willing to suck them up into the PSF centroid definition, and (3) that naive tests of PSF centroiding (like what Bovy is starting) could fail because of inconsistencies about what the PSF centroid means or is. Important point: Because of atmospheric variations during an exposure, the centroid of a stellar image does not have to be the true location of the star in any sense.