The non-existence of a super-Janko group

Locally projective graphs in Mathieu–Conway–Monster series appear in thin–thick pairs. A possible thick extension of a thin locally projective graph associated with the fourth Janko group has been questioned for a while. Such an extension could lead, if not to a new sporadic simple group, to something equally exciting. This paper resolves this issue ultimately in the non-existence form confirming that the list of 26 sporadic simple groups, although mysterious, is now stable. The result in fact concludes the classification project of locally projective graphs, which has been running for some twenty years.