Most sources I can find state that under current spelling rules, adjectives formed from proper names should either keep the capital letter and use an apostrophe, or else have lowercase but no apostrophe. So Gauß’sche and gaußsche are both correct, but not Gaußsche. For instance, this stackexchange answer describes and illustrates the rule carefully.
However, some other sources disagree with this rule, recommending the Gaußsche form as correct and/or saying that Gauß’sche is incorrect. It seems at least that many native speakers hold this belief. Some people suggest that this may be because at some period, Gaußsche was indeed the accepted form, but that it changed to Gauß’sche in the 1996 or 2006 orthographic reforms. But having skimmed/searched those reforms and several summaries of them, I’ve not found where this rule is discussed. More generally, none of the online sources I found gave authoritative sources for their claims.
Overall, there is clearly some confusion and disagreement about this rule, even among well-educated native speakers, so I would like to find an authoritative source presenting this rule, and ideally also noting if it has been different in the past, and I have so far been unable to find such a source. An ideal source would be a reference within the spelling reforms themselves, or another up-to-date document from the Rat für deutsche Rechtschreibung itself. If that can’t be found, then e.g. something from a well-established dictionary or similar publication would be good; or, generally, whatever best source can be found.
