tchrist explains in that thread why neither uppercase nor lowercase is the best option:
> Mapping to lowercase doesn’t work for Unicode data, only for ASCII. You should be mapping to Unicode foldcase here, not lowercase. Otherwise yours is a Sisyphean task, since lowercase of Σίσυφος is σίσυφος, while lowercase of its uppercase, ΣΊΣΥΦΟΣ, is the correct σίσυφοσ, which is indeed the foldcase of all of those. Do you now understand why Unicode has a separate map? The casemappings are too complex for blindly mapping to anything not designed for that explicit purpose, and hence the presence of a 4th casemap in the Unicode casing tables: uppercase, titlecase, lowercase, foldcase.
of course 'σίσυφοσ' is not correct as a written word but if you were to encounter it then you should clearly consider it equivalent to 'σίσυφος'